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Partner selection and group formation in cooperative benchmarking
JOURNAL OF ELSEVIER Journal of Accounting and Economics 19 (1995) 345 364
Accounti.ng &Economi&
Partner selection and group formation in cooperative benchmarking D a n E l n a t h a n a, O l i v e r K i m *'b aSchool of Accounting, University of Southern California, Los Angeles, CA 90089-1421, USA bAnder.son Graduate School of Management, University of California at Los Angeles, Los An aeles, CA 90024-1481, USA (Received May 1993; final version received May 1994)
Abstract This paper investigates partner selection and group formation in cooperative benchmarking, a practice of information sharing among firms to improve their operations. Firms gather preliminary information about potential partners only when the choice problem is difficult, and more information is gathered when there is more uncertainty. Based on an analysis of benchmarking benefits and costs, there is a unique equilibrium group structure characterized by a segregation of firms by their stock of technological information. It is argued that today's changing business environment tends to increase group size and the number of firms participating in cooperative benchmarking.
Key words. Cooperative benchmarking; Partner selection; Information gathering JEL class!fication: D83; 033
1. Introduction Increased competition in the modern business environment has led many firms to actively seek information about other firms' operations, in efforts to improve their own competitiveness. One unique method used for such * Corresponding author. We gratefully acknowledge the comments and suggestions of Gerald Feltham, Stephen Hansen, Mark Young, and the participants of workshops at Hebrew University of Jerusalem, University of Southern California, and the 1993 KPMG Peat Marwick/John M. Olin Conference on Organizations, Incentives and Innovation at the University of Rochester. We also thank Ray Ball and Glen MacDonald (the editors) and Ray Deneckere (the referee) for many helpful suggestions. 0165-4101/95/$09.50 (C~, 1995 Elsevier Science B.V. All rights reserved SSD1016541019400387 K
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information gathering is a practice called benchmarking. Benchmarking is a search for the best practices which is intended to improve the performance of the company. In particular, there is a growing interest in cooperative benchmarking, where several firms voluntarily share information about selected areas of their operations in order to identify and learn from the best practices. There are many books and articles on benchmarking in the business press and practitioners' journals, and executive education programs on benchmarking attract hundreds of participants.1 Despite such interest at the practitioner level, the general academic profession has been silent about the practice, and in particular about its unique aspect of information sharing among firms. In a closely related study Kirby (1988) analyzes theoretically how information sharing can occur in a noncooperative equilibrium among direct competitors in an oligopoly settingfl The oligopoly models of Kirby and others assume that each firm knows its own technological opportunity set and the information about others' operations is valuable only because the firms are direct competitors (and thus share a common industry demand function). However, cooperative benchmarking as it is practiced today is not limited to firms in the same industry. 3 Camp (1989) describes benchmarking as a process in which an organization targets key areas for improvement, identifies and studies best practices in these areas by other organizations, and implements processes and systems to enhance its own productivity and quality. It is clear from this typical definition that the main purpose of benchmarking for a firm is to learn about its own technological opportunities by learning about others' similar operations. This paper offers a theoretical investigation of a critical phase of cooperative benchmarking, that is, how individual firms select their partners and form benchmarking groups. Partner selection is important because the extent of learning can be very different with different groups of partner firms, and because once the firm's operations have been changed as a result of a benchmarking effort, the change often accompanies substantial sunk costs. In a survey of 45 leading benchmarking organizations, 87 percent deemed the selection of benchmarking targets (i.e., partners) to be of 'great' or 'very great' importance among factors contributing to the success of benchmarking, and none deemed it to be of'little' or 'very little' importance (IBC, 1992). We consider firms that are
~See, for example, Business Week (October 25, 1991), Rivest (1991), and Tonkin (1991). 2There is an extensive literature on information sharing in oligopoly settings. See Kirby (1988), Gal-Or (1985), Shapiro (1986), and Vires (1984).
3For example, firms in many instances engage in what is sometimes called 'best-in-class benchmarking' across industries. See Leibfried and McNair (1992).
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rational profit-maximizing agents. 4 A critical assumption made here is that firms only have local knowledge about their technological feasibility. In other words, a firm knows from experience the effect of a small variation of its input combination or of technology on its profit, but does not know what will happen if very different input combinations or technologies are used from the one adopted now or in the past. This assumption reflects the fact that today's technological innovations are sufficiently frequent and diverse to prevent individual firms from grasping their contents or oftentimes even their existence. When there is substantial uncertainty about benchmarking benefits and costs, an individual firm may gather some preliminary information to be able to select benchmarking partners with reasonable confidence. For example, it is essential for the firm to identify its benchmarking needs (relative weaknesses) and its appeal as a potential partner to other firms (relative strengths) in order to succeed in partner selection. We first provide a separate analysis of this exploratory information gathering decision because we believe that a sizable portion of today's benchmarking activities may be exploratory. 5 Here, we examine how much information is gathered by individual firms about potential partners before deciding whether and with whom to benchmark. We show that a firm gathers costly information only when the choice problem is sufficiently difficult, i.e., when there are more than one available options that are sufficiently close to one another in their attractiveness without additional information. 6 More information is gathered when there is more uncertainty. We then examine how cooperative benchmarking activities generate benefits and costs to individual member firms. The major benefit of benchmarking for a firm is the expected increase in the profit due to improvements and innovations of its operations based on the information obtained through benchmarking. This can be in the form of increased productivity, reduced production costs, or both. We use a simple model to derive a function which describes the benefits of a firm from benchmarking with a group of partner firms. Information sharing among partners allows each firm to learn a certain amount of technological information contained in the others' operations. The same information may be obtained from different partners. We assume that firms know before benchmarking only the amount of information possessed by potential partner
4Some firms motivate benchmarking as a tool for achieving strategic goals such as improved quality or increased market share. The analysis of this paper can be made consistent with the behavior of firms pursuing such specific goals by appropriate interpretations of 'the benchmarking benefits'. 5There is a growing interest in database benchmarking in which member firms contribute to and share a database. Database benchmarking serves, among others, two purposes: sharing technical information and identifying needs and opportunities that could lead to further benchmarking. The second purpose is that of exploratory information gathering. 6This also happens when there is too little information to separate out different options.
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firms but not how their technologies overlap. The benefit of benchmarking is then understood as proportional to the amount of newly obtained information. The cost of cooperative benchmarking for each firm is assumed to be increasing and convex in the group size due to increasing complexity and coordination problems. Abstracting away from exploratory information gathering, we analyze how cooperative benchmarking groups are formed among a set of firms that possess different amounts of technological information contained in their operations. We show that there is a unique equilibrium group structure characterized by grouping among firms with similar amounts of technological information. The first group consists of a certain number of the best firms chosen by the best firm, and all members of the first group are shown to prefer that group to any other possible group. The second group is formed among a certain number of the best firms among the remaining firms, and so on, until all firms are exhausted. A comparative static analysis shows that group size and the number of firms participating in cooperative benchmarking tend to increase as learning becomes more efficient, as technology becomes more complementary, and as the marginal cost of benchmarking is reduced. We argue that today's changing business environment is likely to encourage cooperative benchmarking and increase group size because increased competition and technological progress in information processing increase benchmarking benefits relative to costs. Also, the rapid pace of technological progress makes different firms' technologies more likely to be different, thereby increasing the chance that firms can complement their technological knowledge by learning how other firms operate. In turn, the increases in cooperative benchmarking activities induced by today's environment contribute to innovations, accelerate technological progress, and increase competition. The rest of the paper proceeds as follows. We first analyze in Section 2 how much preliminary information is gathered by individual firms about their potential partners when there is uncertainty about the benefit and the cost of benchmarking. In Section 3 we model how information sharing among a group of firms can be translated into benefits and costs of cooperative benchmarking for each sharing firm. In Section 4 we examine how groups are formed in equilibrium~ In Section 5 we perform a comparative static analysis and discuss group size and the number of firms participating in cooperative benchmarking in relation to the types of operations being benchmarked and today's changing business environment. Section 6 contains a brief conclusion.
2. Exploring benchmarking opportunities A firm contemplating cooperative benchmarking typically faces uncertainty from several sources. It may not know for sure what the benefits and the costs
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will be. In this case it is often useful to engage in some exploration, i.e., some preliminary information gathering about potential partner firms, the information sharing processes, or how obtained information can be translated into profits. This aspect of cooperative benchmarking is noteworthy because an important part of services provided by existing benchmarking organizations appears to be educating firms about general benchmarking benefits and processes and providing some preliminary information about its member firms a m o n g which a firm can potentially choose its benchmarking partners. In this section we examine a situation when such uncertainty is present. In particular, we analyze how individual firms make decisions of whether to join a cooperative benchmarking group or which group to join, and how much preliminary information is gathered for the purpose of making these decisions. We begin with a very simple situation in which there is a firm which contemplates benchmarking and a group of firms that are willing to benchmark with the firm. The firm is considering two options, whether or not to engage in cooperative benchmarking with the group. Let 0 be the (decision-making) firm's net benefit from benchmarking with the group. We assume that random variable 1.7 takes the value of either UI > 0 or U2 < 0 (U1 > U2) with probability ½ each. 7 In order to decide whether to join the group, the firm can obtain information 37about/.7 from various sources, such as public databases including ranks in industry and publicly known performance measures or from the potential partner firms themselves. Random variable 37is such that if U = U1, then y = Yl with probability a _> ½ and y = Y2 with probability 1 - a, and if U = U2, then y = Y2 with probability a and y = Yl with probability 1 - a. In this case the conditional probability of U1 given y = Yl is a, and given y = Y2 it is 1 - a. Symmetrically, the conditional probability U2 given y = y2 is a, and given y = y~ it is 1 - a. If the decision is made without observing 37, the firm joins the group if and only if 0 - ½(U~ + U2) > 0. 1 In this model variable a measures how accurate the information 37is. If a - 2, 37is not informative at all. As a increases, observing 37enables the benchmarking firm to assess the true value of 0 with more confidence. In the extreme where a = 1, 37 perfectly reveals the true value of 0. Let H(a) be the cost of observing 37 (exploration cost). It is a function of its accuracy a, and we assume that the
7if both U, and U2 were positive (or negative), then the obvious choice would be to join (not to join) without further information gathering. The actual benefit can be zero or negative. For example, suppose a firm completes benchmarking in the area of billing and draws a plan to improve its billing operations based on the obtained information. If top m a n a g e m e n t rejects the plan at that point, the benefit is zero and the net benefit is negative. In another scenario the benefit itself is negative if the firm adopts the plan and if the change in operation results in a decrease in profit. However, it is important to note that the decision to benchmark is made based on the expected benefit before its realization.
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function H is twice differentiable, strictly increasing, and strictly convex. Also, H(½) = 0 and H'(a) approaches zero as a approaches ½, and it approaches infinity as a approaches 1. In other words, it is very cheap to get some information about the true value of 1.7 but it is prohibitively expensive to get perfect information. The decision-making firm's problem is to choose the level of information accuracy a, and to decide whether to join the group. Once a is chosen and 37is observed, the second decision is easy to make. If yl is observed, the firm joins the group if and only ifaU~ + (1 - a)U2 > O. If y2 is observed, it does so if and only if(1 - a)U1 + aU2 > O. The choice of a must be made before the value of 37is observed. Therefore, the ex ante value of 37is the increase in the expected profit due to observing 9. There are two cases. Suppose first that U1 > - U2 so that 1.7 > 0. In this case the choice without information is to join the group because the expected profit of doing so is nonnegative. When information signal 37 with parameter a is observed, the ex post benefit of observing 37depends on the realization of 37. If y~ is observed, aU1 + (1 - a)U2 is positive regardless of a and the firm joins the group. Thus there is no ex post benefit of observing 37. If Y2 is observed, however, (1 - a)U1 + aU2 can be negative for a sufficiently close to 1. When the expected profit is negative, the decision made after observing the information signal is not to join the group. When this happens, the ex post benefit of observing )7 is - [(1 - a) U~ + aU2] because it is the expected loss saved due to obtaining the information. Since the probability of observing either yl or Y2 is ½ each, the ex ante net benefit of observing 37, denoted by Vr, for any given accuracy a is Vy = max(0, - ½1-(1 - a)U1 + aU2]) - H(a).
(:)
Information is obtained if there is a such that the above net benefit is positive. Suppose now that U1 < - U2 so that [7 < 0. In this case the choice without information is not to join the group because the expected net benefit of doing so is negative. When information signal 37with parameter a is observed, the ex post benefit of observing 37 again depends on the realization of 37. If Y2 is observed, (1 - a)U1 + aU2 is negative regardless of a and the firm does not join the group. Thus there is no ex post benefit of observing 37. If Yl is observed, however, aU1 + (1 - a ) U 2 can be positive for sufficiently large value of a. When it is positive, the decision made after observing the information signal is to join the benchmarking group. When this happens, the ex post benefit of observing 37 is aU1 + (1 - a) U2 because it is the expected gain due to the information. The probability of observing either Yl or Y2 is ½ each, and the ex ante net benefit of observing 37 for any given a in this case is Vr = max(0,½[aU1 + (1 - a)U2]) -- H(a).
(2)
Again, information is obtained if there is a such that the net benefit is positive.
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The ex ante net benefit in the above two cases when the accuracy a is freely chosen can be now written in one expression as Vr = maxa[max(0, 5[a(U1 - U2) - max(lUll,
IU21)]) - n(a)]
= max,(0, 5[a(U1 - U2) - max (IU1 I, I U21)] - H(a)), where the last guaranteed by cost function 5[a(U~ - U2) -
(3)
equality obtains due to the fact that the net benefit of zero is choosing a = 5, since H(5) = 0. Under the assumptions on the made earlier, there exists a unique a that maximizes max(I U~I, [U21)] - H(a). This unique a is characterized by
5(U1 - U2) - H'(a) = 0,
(4)
and a > 5 given the assumptions on the curvature of the cost function. Therefore, the benchmarking firm's choice is to spend H(a) and observe 37 with accuracy a such that (4) is satisfied if such an a generates a positive net benefit expressed as (3). If the expected net benefit is negative for such an a, the firm chooses a = 5, i.e., it does not gather any preliminary information. Expressions (3) and (4) suggest that the choice of a, i.e., the intensity of preliminary information gathering, depends on three factors, the uncertainty and the ease of the choice problem and the magnitude of the marginal information gathering cost. The uncertainty of the choice problem captures the degree of uncertainty of the benchmarking net benefit and is measured by U1 - /-12, the difference in the expected profits between the two possible realizations of the random benchmarking benefit. The ease of the problem is measured by max(I U~ I, I U21) which reflects how far the expected net benefit of benchmarking is from zero, which is the net benefit of the second option (no benchmarking). If it is far from zero, the correct choice is easily to benchmark (if positive) or not to (if negative). For a fixed level of uncertainty, i.e., for fixed U1 - U2, the measure of ease, max(I U1 [, I U21), reaches its minimum when U~ -- - U 2 in which case the choice problem is most difficult. It reaches its maximum as either U~ or U2 becomes zero, in which case the problem becomes easiest. The results on these three factors are stated in the following proposition. The proof follows from (3) and (4).
Proposition 1. The level of preliminary information gathering is positive only for a sufficiently difficult choice problem, and is higher for a more uncertain choice problem and for lower marginal information gathering costs. That is, the optimal a is positive only for sufficiently small max(lUll, I U21), and is increasing in U1 - U2 and in any shifts of the function H that reduce H'('). Proposition 1 is intuitive. It says that preliminary information is gathered only when the choice without additional information is sufficiently difficult, i.e., the expected profits generated by the two available options are sufficiently close
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to each other. Also, more preliminary information is gathered when its benefit is greater or its marginal cost is lower. The benefit of information gathering is greater when there is more uncertainty. In a typical situation a firm decides whether to benchmark, and if yes, with which group among multiple groups that are willing to accept the firm as a partner. We do not formally model this more general situation here. However, we conjecture the following by applying the intuition obtained above. The first part of Proposition 1 suggests that the firm in this case would compare the expected net benefits of available options and consider only the option with the greatest expected net benefit and ones that are sufficiently close to it. If there is a large gap between the best and the next best in the expected net benefit (i.e., if the choice problem is easy), the one with the greatest expected benefit is chosen without information gathering. When there are a number of options that are close to each other (i.e., if the choice problem is sufficiently difficult), some preliminary information is gathered. Also, the second part of Proposition 1 suggests that more information will be gathered about the potential partner groups (firms) if there is more uncertainty or if the marginal cost of information gathering is lower. One implication of Proposition 1 and the related discussions concerns the role of observed institutional arrangements such as a benchmarking clearinghouse or a government agency which facilitates benchmarking. 8 Such arrangements reduce the exploration costs (H) and induce firms to obtain better preliminary information about potential benchmarking partners, which in turn results in better matching and greater benefits of benchmarking. Also, as more information is provided about potential targets at low costs, more firms are induced to take part in cooperative benchmarking.
3. Benefits and costs of cooperative benchmarking Cooperative benchmarking activities affect a firm in many different ways. For convenience, we distinguish between the benefit and the cost of benchmarking. The cost of benchmarking is defined as the direct cost of benchmarking, such as the cost of preparing and processing information supplied to and obtained from partner firms. The benefit of benchmarking is defined as any change in profit due to benchmarking activities which is not included in cost as defined above. There are several sources of cooperative benchmarking benefits. First, a firm's profit can increase due to improvements and innovations of its operations based on the information obtained through benchmarking. This can be in the form of increased productivity, reduced production costs, or both. Second, a firm's profit can change if information sharing through benchmarking affects the firm's Sin Canada this service is offeredby Industry, Scienceand TechnologyCanada.
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competitive advantage within its industry. Third, there can be other political, social, or control-related effects of cooperative benchmarking. For example, emerging as a leader in cooperative benchmarking activities may help a firm improve its status among its business associates and investors, which may affect its profit. Or the informal networking by company representatives may adversely affect profit, for example, if they learn from one another new ways to defraud their companies. In this paper we mainly discuss the first type of benefit, namely, the benefit from improved operations, which is understood by most practitioners as the major benefit of benchmarking. We will only briefly mention the industryrelated effect of benchmarking when we discuss group formation in Section 4. We abstract in this paper from other effects of benchmarking mentioned above as the third type. In the rest of this section we discuss how the benefit and the cost of cooperative benchmarking would behave once the benchmarking partners of a given firm have been determined. Given a benchmarking group, G = { 1, 2 . . . . . N}, the net benchmarking benefit of firm i, i ~ G, denoted by Ui~, is written as U i , = B~.( + S~a) - Ci~,
where Bia and Cia are the benefit and the cost, respectively, of firm i from benchmarking in group G. The term Sia denotes the industry-related or some special type of benefit of firm i that we only informally discuss in Section 4 and is assumed to be zero unless mentioned otherwise. In order to gain an insight into how the benefit arises, consider a group of risk-neutral firms, 1, 2. . . . . N, sharing information about their operations in a pre-specified area such as warehousing or billing. We define wl as the amount of technological information contained in firm i's operations that can be learned through cooperative benchmarking. The quantity wg > 0 is measured in terms of how much benefit it will yield in dollars if completely learned by another firm which does not possess it. It is useful to visualize a round cake with circumference w whose face is decorated as a clock so that the original location of any slice can be determined. Each firm takes a slice and the cake is magically restored each time. Thus, several firms can have the same part of the cake at the same time, just as there can be overlaps among different firms' technologies. Firm i's technology is represented by the round edge of its slice, denoted by E~, and the size of the slice (the length Ei) is wi. Cooperative benchmarking here is thought of as sharing slices of the cake among partners. It is important to note that the same slice can be given to multiple partners at the same time just as the same piece of information can be given to many firms. Also, receiving the same part of the cake many times to
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a firm is equivalent to receiving it o n c e . 9 The information structure in this model is the following. Each firm knows wi's of all potential partners but not the locations of other firms' slices except its own. In other words, each firm knows how much technological information is possessed by any other firm, but it does not know how much of the information that can be obtained from the partner will be new to the firm. It only knows that each firm's technology is contained in a common universal set of all potentially existing technologies (the whole cake) whose size is w. Mathematically, we assume that each firm thinks that the location of any firm's slice (El) is uniformly and mutually independently distributed around the whole cake whose circumference is w. 1° The amount of new information obtained by firm i as a result of cooperative benchmarking with group G is then thought of as the amount of information possessed after benchmarking, i.e., the expected length of the union of all Eis, minus w, the amount of technological information possessed before benchmarking. The benefit of benchmarking for firm i is now defined as
where the parameter e, 0 < e ~< 1, measures how well the newly learned technological information is digested by firm i and contributes to higher profits.11 Given the above formulation, the benefit of benchmarking can be calculated as in the following lemma. The proof is provided in an appendix. Lemma 1. The benefit of firm 1 from cooperative benchmarking with group G = { 1, 2 . . . . . N} can be written as BI~ = ~(fllW2 -Jt- fllfl2W3 -~- fll[J2fl3W4 "q- "" -~ fllfl2 "" flN - 1WN), where fli - 1 - (wffw). Moreover, the benefit is invariant to the order in which the benchmarking partners of firm 1, i.e., firms 2, 3 . . . . . N, appear in the expression. Lemma 1 suggests that as more firms are added to the group, the benefit of benchmarking increases but successive additions contribute less and less to each 9Observing that the same technology is used by m a n y firms may be of value, for example, in making strategic decisions or assessing its viability. We ignore these possibilities here. °Formally, we allow each firm to have any finite number of slices from any parts of the cake with the total length of the slices w, and the proofs of the results below are based on this more general assumption. An alternative discrete version of this model is one in which benchmarking firms draw wl balls from a jar containing w numbered balls with replacements and share them. 11in a more general setting ct can also be different for different partners and for different portions of technological information. For example, certain technology m a y be more imitable a m o n g firms with comparable sizes or sufficient process similarities.
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benchmarking firm's profit. This is because 0 < fll < 1 which reflects the fact that the chance of overlap increases as there are more firms in the benchmarking group. We now turn to the cost of cooperative benchmarking. It is often the case that when a benchmarking group is formed, a coordinator is selected) 2 The coordinator is in charge of specifying the exact set of information to be provided by each member, collecting the information, processing the information if necessary, distributing the information in an efficient manner, and communicating with members for questions and verifications. Often, there are site visits to selected member companies. The cost of benchmarking is all the individual direct costs of benchmarking such as the cost of preparing and processing information supplied to and obtained from one another a m o n g the group members. If there are c o m m o n costs such as the cost of hiring a coordinator, we assume that such costs are equally divided a m o n g the members. An increase in the number of firms in a benchmarking group has at least two effects on the cost of benchmarking for each individual member firm. The first is a scale effect which reduces the cost of benchmarking for each firm due to the economies of scale in planning, data processing, and so on. The second effect is a complexity effect which causes costs to rapidly increase (so that the cost per firm increases) as the number of firms increases. This is due partly to the fact that the information about the participating firms' operations must be provided with reasonable accuracy. As the number of firms increases, this task becomes increasingly difficult because the coordinator must guarantee some minimum degree of accuracy and comparability of the information about all member firms. For example, m a n y kinds of differences, some of them qualitative differences, inevitably make the inter-firm processing of numbers (such as adding and averaging) less and less meaningful. There are also communication difficulties with a large number of firms. For example, if each firm has one question about each other member, with N firms the coordinator must handle N ( N 1) questions, which increases geometrically as N increases. For these reasons, it is reasonable to think of the cost function (as a function of the number of firms) to be increasing and concave first (due to the scale effect) and then convex (when the complexity effect eventually dominates the scale effect). Given the above considerations, we assume in our model that the cost of benchmarking for each firm is a strictly increasing, convex function, denoted by f ( ' ) , of the group size (the number of firms in the group) w i t h f ( l ) = 0. Let cn be the cost (for each existing member firm) of adding the nth partner. Then, c° = f ( n + 1) - f ( n ) and our assumptions on the cost function imply that c, is increasing in n, i.e., ca < c2 < c3 < ... <_ CL for any integer L. Given this cost structure and the expression for the benefit ill L e m m a 1, we are now ready to investigate how benchmarking groups are formed a m o n g a given set of firms. 2The coordinator is usually a person who has some experience in benchmarking and may be from one of the partner companies, or on some occasions a third party, e.g., a consultant.
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4. Equilibrium group formation In this section we analyze how cooperative benchmarking groups are formed in equilibrium a m o n g firms that possess different amounts of technological information. In order to analyze group formation, we need to consider the incentives of each firm to benchmark with any possible group of firms. For simplicity, we abstract away from preliminary information gathering. Consider L firms that are contemplating cooperative benchmarking. The amount of technological information contained in firm i's operations to be benchmarked is w~ as defined earlier. The net benefit of firm i from benchmarking in a group G = 1, 2 . . . . . N is U~ = Bi~ - C~G, and the expression for the benefit is from Lemma 1 Bt~ = ~(fl,Wz + fllflzW3 + flxflzfl3w4 + "'" + fllfl2 "'" f l u - l w u ) ,
(7)
where fli -- 1 - (wi/w) . The benefit of any other member firm i ~ 1 can be similarly written by substituting i for 1 and 1 for i in the subscripts in (7). Also, from Section 3 we summarize the structure of the benchmarking cost by 0 < C1 ~ C2 ~ C3 ~
... ~ CN_I,
(8)
where Ck is the marginal cost (for any firm) of adding any kth partner [(k + 1) th firm] to the group. We define a group structure, denoted by S, to be a partition of firms l, 2,... , L (i.e., a set of nonempty groups whose union is the set of all firms and whose pairwise intersections are all empty). A group structure, S, is an equilibrium group structure if there does not exist a set of firms which can form a new group and increase the net benefit of at least one while not reducing the net benefit of any a m o n g themselves. No side payments are allowed. We begin by making the following observations. Observation 1. Replacing a f i r m in a group by a better (with a greater wi) f i r m increases the benefits o f all other firms in the group.
This observation follows by rewriting (7) so that a firm to be replaced appears last in the equation and by noting that the benefit increases each time a firm is replaced by another with a greater wi. For convenience, we now reindex the firms so that wl > w2 > > WL- 1 > WL without loss of generality (by L e m m a 1).~3 Consider the benchmarking group, denoted by G t, that includes firm 1 (the best firm) and is most preferred by firm 1. By Observation 1 Gt is the best "
'
"
13We assume strict inequalities to avoid unnecessary complications in proving the results below in some pathological cases.
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N~ firms, 0 < N~ < L. Since the (successively decreasing) terms in (7) can be viewed as the marginal benefits of adding firms successively, Na is determined so that ~fl132 "'" fiN,- IWN, -- CN,- 1 > 0 > ~tfllfl2 "'" flN,WN, +1 -- CN,.
(9)
In other words, the marginal net benefit of adding a firm is nonnegative for the N~th firm and negative for the (N1 + 1)th firm. We also note the following: Observation 2. The marginal net benefit of addin9 a firm to a 9roup is the same for all members.
This observation follows easily from Lemma 1 that the marginal benefit is the same for all existing members and the assumption that the marginal cost is simply a function of the group size. Observations 1 and 2 imply that the group of size at least NI most preferred by any member of G~ is in fact G~. This is true because by Observation 2 any member of G1 prefers G1 to a group of the best N firms with N > N~, which, by Observation 1, is in turn preferred to any other group of size N. We make the following observation about the subgroups of G~: Observation 3. All members of any proper subset G' of G1 prefer addin9 any member of G 1 left out of G'.
This is true because the marginal net benefit of adding firm j, j ~ GI\G', to group G' of size N ' < N1 for any firm i'~ G' is ( 1 - I r ~ , f l r ) w j - cs,, which is greater than fl~fl2 "'" f i N 1 - l W N , - CN~-1, the nonnegative marginal net benefit of adding the last firm NI to complete G~. This is due to the facts that fl's are less than one, wj >_ WN,, and CN, < CNI. From Observation 3 it follows that the group of size at most NI most preferred by any member of G1 is also G1. We are now ready to state the following lemma: Lemma 2. The most preferred benchmarkin9 group by any member of G1 is G1.
The strong unanimity result of Lemma 2 implies that any group structure that does not include G1 is not an equilibrium because the members of G~ can form a new group G1 and increase their profits. Once G~ is formed, its members do not have any incentives to change partners. Now among the L - N1 remaining firms G 2 is formed among the next best firms, and then G3, G4, etc. We state this result as the following proposition. Proposition 2. There exists a unique equilibrium structure. In the equilibrium the first group consists of the best N1 >_ l f r m s , the second group consists of the next
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best N2 >_ 1 firms, and so on. The size of each 9roup can be found by considerin9 successively the preference o f the best firm amon9 the remainin9 firms, x4 This equilibrium is characterized by a segregation by wi's, the a m o u n t of technological information possessed by firms that can be learned t h r o u g h benchmarking. Firms are m o r e willing to share information with superior firms because it provides more opportunities to learn. The above analysis shows that as a result in equilibrium firms form groups a m o n g those which possess c o m p a r a b l e a m o u n t s of technological information. 15 We now check the sensitivity of Proposition 2 to some of the simplifying assumptions made above. It can be shown that Proposition 2 still obtains even when w and wi's are not k n o w n (i.e., are r a n d o m variables) to the firms. F o r any (homogeneous) beliefs of firms regarding the a m o u n t s of technologies possessed by other firms (wi's), all the proofs above hold by replacing wi's by their expectations. W h e n w is uncertain, L e m m a 1 and Observations 1 to 3 are true conditional on any value of w, therefore Proposition 2 is true for any h o m o g e n e ous beliefs of w. However, Proposition 2 is sensitive to the introduction of other factors that also affect firms' b e n c h m a r k i n g opportunities and preferences, such as any k n o w n differences in the overlaps in technologies (the locations of the slices), benefits, and costs across firms. O n c e such a factor is introduced in the model, the tendency to segregate by wi's remains but is mixed with the effect of the additional factor. We provide below an informal discussion about how the presence of such factors would affect g r o u p formation. In expression (7) for the b e n c h m a r k i n g benefit suppose that there are firms i and j such that Si~ :~ 0 and Sj~ ~ 0. Consider first a case in which S~ < 0 and S~ < 0. In this case there is a tendency for the firms to avoid each other. This arises, for example, when firms in a highly competitive industry prefer to b e n c h m a r k with firms in other industries to prevent their rivals from obtaining their proprietary information, as well as to avoid the possibility of being subject to anti-trust litigations, x6
~4This is consistent with some anecdotal evidence. For example, Bowers (1993) reports that at Digital Equipment Corporation overwhelming demand by companies to benchmark with them forced him to turn down more and more requests. Also, in Elnathan, Lin, and Conway (1992), Xerox, clearly the best company, was the one that determined the size of the group (six firms) by specifically inviting these firms to join in a particular project. It is not clear, however, if the strong unanimity implied by the present model was present in these examples. 15Note that it is difficult to predict the relative group sizes across different groups in this model because they depend partly on the number of firms possessing comparable w~'sfor each group, and because the effect of a decrease in wi's(say, from the first group to the second group) on the marginal utility in Eq.(10) is ambiguous. 16Also, they may have incentives to provide inadequate or even false information if they are in the same benchmarking group. This may be another reason why inter-industry benchmarking is often observed.
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We also consider a case in which S u > 0 and S~i > 0. In this case there is a tendency for the firms to benchmark together. For example, it is reasonable to expect that groups are formed among firms that guarantee high degrees of learning. This implies that the process or area under study may have to be reasonably similar, or of comparable size, for the benchmarking partners. Another instance of the presence of special mutual benefits is a case where a group of firms prefer to engage in several benchmarking projects over time or over different functional areas, because a long-term relationship can increase the net benchmarking benefit for each member due to the preexisting knowledge about other members and mutual trust that has developed. 17 The relative importance and the interaction among the effects of various special benefits (costs) and the general tendency to segregate observed in Proposition 2 may be complex and deserve further study. For example, when the kind of operation being benchmarked is unique in an industry with a high degree of competition, a trade-off exists between providing learning opportunities (by benchmarking with similar firms) and preserving proprietary information (by benchmarking with firms in different industries).18 Also, if a firm's size proxies for its desirability as a benchmarking partner, we would expect to observe, ceteris paribus, that firms organize into benchmarking groups of similar sizes. That may be due to certain operational attributes, or simply due to the ability of larger firms to devote more resources to benchmarking, relative to smaller companies. In a recent Wall Street Journal story (1993) it has been observed that small firms' executives created a network of what can be described as informal benchmarking. One reason cited was that they felt that best learning about improvement of their operations came from discussions with other small firms. On the surface of the story, it seems that the (preferred) segregation occurred due to high degrees of learning among small firms. Our present discussion, however, suggests that it may have occurred partly because small firms preferred but were not able (were not accepted) to benchmark with large firms.
5. Determinants of group size and firm participation In this section we examine how the equilibrium is affected by changes in the parameters of our model. In particular, we analyze how the average group size and the number of firms participating in cooperative benchmarking are affected by various factors of the benefits and costs of benchmarking. We also relate cooperative benchmarking and innovation by discussing how today's
~TSee Spendolini (1992) for a discussion of the development and advantages of benchmarking networks. lSSee Leibfried and McNair (1992) for a discussion of competitive and industry benchmarking.
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innovative environment affects benchmarking benefits and costs and equilibrium group formation. Consider N + 1 firms from any i (the ith best) to i + N and call them for notational simplicity firms 1, 2 . . . . . N , N + 1. Suppose that firms 1, 2 . . . . . N have formed a group and are considering whether to add firm N + 1 to the group. The existing members will agree to the addition if and only if the marginal net benefit of adding firm N + 1 is nonnegative, i.e., (10) is nonnegative. Given the properties of the equilibrium characterized by Proposition 2, any change that increases (decreases) expression (10) tends to increase (decrease) both the average group size and the number of firms participating in cooperative benchmarking. We consider below the effects of changes in the levels of cN, ct, w, and in the distribution of w{s.
Proposition 3. Group size and the number of firms participatin9 in cooperative benchmarkin9 tend to increase as learnin9 becomes more efficient, as technology becomes more complementary, or as the marginal cost of benchmarking is reduced. That is, OMUN+ I/O~ > O, OMUN+ I/Ow > O, and ~UN+ I/~CN < O. For Proposition 3 it is easy to see that (10) is decreasing in CNand is increasing in ~ and w. A reduction in the cost of benchmarking tends to increase group size and facilitates benchmarking in general. The same occurs when firms can more efficiently transform the new information obtained through benchmarking, into improvements of their own operations (an increase in ~). Recall that w is the amount of total technological information that potentially exists. A greater w (given wi's fixed) can then be interpreted as greater complementarity or a greater dimension of the technology of the operation being benchmarked, because it implies less overlap among firms' technologies. Complementarity is important in understanding why the best performer would benchmark with inferior partners, because it allows two (or more) firms to successfully learn from each other. To see this, suppose wl = w, i.e., the best firm possesses all potentially available technologies. Then, the firm never engages in benchmarking activities. If w is thought to be much greater than any single wi, then each firm has more incentives to benchmark. This happens, for example, when the operation being benchmarked has sufficiently many dimensions to allow mutual learning. When a group of firms engage in a study of a broadly defined function (e.g., facilities management, customer satisfaction), the number of subareas to be included almost guarantees the existence of complementarity. It also arises across multiple benchmarking projects or across multiple benchmarking rounds
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over time. That is, firms that engage together in several benchmarking projects (in different areas) can learn from one another even when in each area there is little complementarity. 19 Or firms that engage in several rounds of benchmarking (over time) in the same functional area can expect to reverse their positions in the future from the imitated to the imitator and vice versa, even when in each round only one of them benefits. This can happen in an area or an industry in which technological innovations are frequent or demand is unstable. A change in the distribution of wi's among firms also affects the equilibrium. In expression (10) increases in wl, w2 . . . . . wN for a fixed wN+ 1, or a decrease in wN+ 1 alone, reduces (10). In practitioners' jargon, this increases the benchmarking (performance) gap (Camp, 1989) between the existing members and the candidate firm. A greater benchmarking gap reduces the chance that firm N + 1 is accepted as a new partner because the addition provides fewer opportunities to learn for the existing members. Therefore, a greater benchmarking gap increases the chance of segregation. The implications of Proposition 3 can be tested empirically. For example, differences in benchmarking group size across different functional areas may be observed and linked to the characteristics of the functions being benchmarked. As a general observation the International Benchmarking Clearinghouse' survey (IBC, 1992) indicates that on average a benchmarking firm would study between three and four partners. Elnathan, Lin, and Conway (1992) indicate a lower level of participants' satisfaction from a benchmarking project with 25 participants, relative to one with six participants. Our final discussion of this section concerns the relationships among today's business environment, innovation, and cooperative benchmarking. Improvements of the operations of a firm can be attained by adopting a better process or a product either gradually (e.g., continuous improvements) or by a rather drastic change (e.g., reengineering). The information about or the right for a new process or a product can be either internally developed (e.g., R&D), purchased (e.g., a patent), exchanged (e.g., a joint venture), or shared (cooperative benchmarking). If innovation is broadly defined as doing things in new and improved ways, most improvements are innovations at the firm level. Information obtained through cooperative benchmarking is typically not new globally, and the global novelty of, say, an adopted process is not a primary concern to a firm as long as the process improves the firm's operations. Benchmarking, however, facilitates improvements through the diffusion of existing (global) innovations. Benchmarking also complements innovation by providing the 'nuts and bolts" which are crucial in the transformation of innovative breakthroughs into operating production activities. Finally, learning different ideas
~OForexample, Xerox has conducted many benchmarkingstudies across multiple functionalareas, some of them with the same partners.
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from other firms' operations can spark a new idea that is different from any existing ideas. 2° Within the context of our model, today's changing business environment can be thought of as affecting the benefits and costs of cooperative benchmarking in several ways. We conjecture that the changes in today's business environment tend to increase the benefit and decrease the cost of benchmarking expressed in (7) and (8). First, the complementarity of firms' technologies, measured by the magnitude of w, seems to increase because the rapid pace of technological progress makes different firms' technologies more likely to be different. Second, innovations in information processing reduce benchmarking costs. Third, increased competition forces firms to more actively seek improvements by quickly and efficiently absorbing information obtained through benchmarking (an increase in ~t). By Proposition 3 these changes lead to larger groups and increased participation in cooperative benchmarking. This, in turn, contributes to innovation, accelerates technological progress, and increases competition. 6. Conclusion In this paper we have provided a theoretical analysis of different phases of the cooperative benchmarking activities. We have tried to align our discussions with observed practices, and several empirical implications are derived from the analysis. Proposition 1 establishes that in the presence of uncertainty the level of preliminary information gathering about potential partner firms would depend on the amount of uncertainty involving the benefit and the cost of benchmarking, how easy the choice problem is without any additional information, and the marginal cost of information gathering. In the analysis leading to Proposition 2 we have modeled how benefits and costs arise from cooperative benchmarking and found a unique equilibrium group structure characterized by a segregation by the amount of technological information a firm can offer to its partners. Based on the comparative static results of Proposition 3, we have also discussed group size and the number of firms participating in cooperative benchmarking for different types of operations, and for today's changing business environment. For the future study of benchmarking it would be very useful to understand current benchmarking practices and organizations. Such studies would produce a clearer picture of what factors determine firms' benchmarking benefits and costs and in turn affect their benchmarking decisions. Some of the issues ignored in this study, such as those of truthful revealing of information, its verification, and optimal information sharing mechanisms, may also prove important in explaining current practices and organizations. 2°See, for example, discussion of benchmarking in Hammer and Champy (1993) and Grant Thornton (1993).
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Appendix: Proof of Lemma 1 For the first part of Lemma 1 it suffices to show that E[thelengthofjUEj]=w~
+flaw2+fitfl2w3+
'" + f i ~ f i 2 " " f l N
lW~,
where fl, _ = 1 - ( w i / w ). Set E~ is a subset with length wi of a circle whose circumference is w. The locations of E(s are uniformly distributed over the circle and are mutually independent. Consider the union UM of Ej,, j' = M . . . . . N, and set EM ~, where 1 < M < N. Suppose that UM has expected length xM. Since U u and EM 1 are independently located, the probability that any arbitrary point on the circle is an element of the union of the two sets, UM 1, is XMWM W
1 +__
W
W
1 W
,)
+ W
l t 1 --- W
,
which can be simplified as wM ~/w + tim l(XM/W). Integrating over the entire circle (or multiplying by w), the expected length of UM l is wM-~ +/3M lxM. Applying this result repeatedly, the expected length of the union of all E~'s can be written as Wl + ill(w2 +/~2(w3 + "" + W~,)'"), which is the equation that we want to prove. The second part of the lemma follows from arbitrarily in the above proof. This can also expression for BI6 in L e m m a 1. Suppose i 4:1 by each other in the expression. Deleting the N j terms, which are common, the original expression can be written, respectively, as
the fact that w/'s are indexed be verified directly from the and j :~ 1, j > i, are replaced first i - 2 terms and the last expression and the modified
and
~/~l "1~,
,I-wj +
l~jw,~, + l~jl~,. , w , + ,
+
--- +
l*jl~,+, " / ~
,w,].
The difference in the terms in the parentheses between the two expressions is {Wi
Wi) 4- ([Ji
fJj) {Wi. 1 4- / ~ i - l W i • 2 +
+/~,., "'"/~,j ,(fl~wi- l~iwO.
"'" + /Ji
1 "'" fl)
2Wi
1}
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which can be simplified as ( w i -- w))
I
1
-
wi + 1
W
~,+,&
Wi+ 2 ~i + 1 - W
Wj 1 ~i + l ' ' " /~j- 2 - W
2&-,]
by using the definitions of /~'s. N o w note that the first two terms in the parenthesis sum to/~i+ 1, the first three terms sum to/~i+ 1/~i+2, a n d so on. The inside of the parenthesis t h e n b e c o m e s fl~+ 1 ' " flj 2 f l j - 1 -- fli+ 1 "'" /~j 2/~j- 1, which is zero. Therefore, a n y pairwise switching a m o n g the partners does not change the benefit. Since a n y order of the partners can be generated by repeated pairwise switching m a n e u v e r s , the benefit of b e n c h m a r k i n g in L e m m a 1 is i n v a r i a n t to the order in which the partners a p p e a r in the expression.
References Bowers, F., 1993, The future of benchmarking, Continuous Journey, 38 42. Camp, R.C., 1989, Benchmarking: The search for industry best practices that lead to superior performance (Quality Press, Milwaukee, WI). Elnathan, D., T.W. Lin, and C.M. Conway, 1992, Cooperative benchmarking: A competitive management approach, Manuscript (University of Southern California, Los Angeles,CA). Gal-Or, E., 1985, Information sharing in oligopoly, Econometrica 53, 329 344. Grant Thornton, 1993, Manufacturers 'reengineer"their businesses to make sense, Manufacturing Issues 4. Hammer, M. and J. Champy, 1993, Reengineering the corporation: A manifesto for business revolution (Harper Business, New York, NY). IBC, 1992, Surveying industry's benchmarking practices: Executive summary (International Benchmarking Clearinghouse, Houston, TX). Kirby, A.J., 1988, Trade associations as information exchange mechanisms, Rand Journal of Economics 19, 138 146. Leibfried, K.H.J. and C.J. McNair, 1992, Benchmarking: A tool for continuous improvement (Harper-Collins, New York, NY). Rivest, G., 1991, Make your business more competitive, CMA Magazine, 16 19. Shapiro, C., 1986, Exchange of cost information in oligopoly, Review of Economic Studies 53, 433 446. Spendolini, M.J., 1992, The benchmarking book (American Management Association, New York, NY). Tonkin, L., 1991, The power of benchmarking at Seitz Corporation, Target, 6 16. Vives, X., 1984, Duopoly information equilibrium: Cournot and Bertrand, Journal of Economic Theory 34, 71 94. Wall Street Journal, 1993, Small-company CEOs share experience and advice, February 11.
Accounti.ng &Economi&
Partner selection and group formation in cooperative benchmarking D a n E l n a t h a n a, O l i v e r K i m *'b aSchool of Accounting, University of Southern California, Los Angeles, CA 90089-1421, USA bAnder.son Graduate School of Management, University of California at Los Angeles, Los An aeles, CA 90024-1481, USA (Received May 1993; final version received May 1994)
Abstract This paper investigates partner selection and group formation in cooperative benchmarking, a practice of information sharing among firms to improve their operations. Firms gather preliminary information about potential partners only when the choice problem is difficult, and more information is gathered when there is more uncertainty. Based on an analysis of benchmarking benefits and costs, there is a unique equilibrium group structure characterized by a segregation of firms by their stock of technological information. It is argued that today's changing business environment tends to increase group size and the number of firms participating in cooperative benchmarking.
Key words. Cooperative benchmarking; Partner selection; Information gathering JEL class!fication: D83; 033
1. Introduction Increased competition in the modern business environment has led many firms to actively seek information about other firms' operations, in efforts to improve their own competitiveness. One unique method used for such * Corresponding author. We gratefully acknowledge the comments and suggestions of Gerald Feltham, Stephen Hansen, Mark Young, and the participants of workshops at Hebrew University of Jerusalem, University of Southern California, and the 1993 KPMG Peat Marwick/John M. Olin Conference on Organizations, Incentives and Innovation at the University of Rochester. We also thank Ray Ball and Glen MacDonald (the editors) and Ray Deneckere (the referee) for many helpful suggestions. 0165-4101/95/$09.50 (C~, 1995 Elsevier Science B.V. All rights reserved SSD1016541019400387 K
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information gathering is a practice called benchmarking. Benchmarking is a search for the best practices which is intended to improve the performance of the company. In particular, there is a growing interest in cooperative benchmarking, where several firms voluntarily share information about selected areas of their operations in order to identify and learn from the best practices. There are many books and articles on benchmarking in the business press and practitioners' journals, and executive education programs on benchmarking attract hundreds of participants.1 Despite such interest at the practitioner level, the general academic profession has been silent about the practice, and in particular about its unique aspect of information sharing among firms. In a closely related study Kirby (1988) analyzes theoretically how information sharing can occur in a noncooperative equilibrium among direct competitors in an oligopoly settingfl The oligopoly models of Kirby and others assume that each firm knows its own technological opportunity set and the information about others' operations is valuable only because the firms are direct competitors (and thus share a common industry demand function). However, cooperative benchmarking as it is practiced today is not limited to firms in the same industry. 3 Camp (1989) describes benchmarking as a process in which an organization targets key areas for improvement, identifies and studies best practices in these areas by other organizations, and implements processes and systems to enhance its own productivity and quality. It is clear from this typical definition that the main purpose of benchmarking for a firm is to learn about its own technological opportunities by learning about others' similar operations. This paper offers a theoretical investigation of a critical phase of cooperative benchmarking, that is, how individual firms select their partners and form benchmarking groups. Partner selection is important because the extent of learning can be very different with different groups of partner firms, and because once the firm's operations have been changed as a result of a benchmarking effort, the change often accompanies substantial sunk costs. In a survey of 45 leading benchmarking organizations, 87 percent deemed the selection of benchmarking targets (i.e., partners) to be of 'great' or 'very great' importance among factors contributing to the success of benchmarking, and none deemed it to be of'little' or 'very little' importance (IBC, 1992). We consider firms that are
~See, for example, Business Week (October 25, 1991), Rivest (1991), and Tonkin (1991). 2There is an extensive literature on information sharing in oligopoly settings. See Kirby (1988), Gal-Or (1985), Shapiro (1986), and Vires (1984).
3For example, firms in many instances engage in what is sometimes called 'best-in-class benchmarking' across industries. See Leibfried and McNair (1992).
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rational profit-maximizing agents. 4 A critical assumption made here is that firms only have local knowledge about their technological feasibility. In other words, a firm knows from experience the effect of a small variation of its input combination or of technology on its profit, but does not know what will happen if very different input combinations or technologies are used from the one adopted now or in the past. This assumption reflects the fact that today's technological innovations are sufficiently frequent and diverse to prevent individual firms from grasping their contents or oftentimes even their existence. When there is substantial uncertainty about benchmarking benefits and costs, an individual firm may gather some preliminary information to be able to select benchmarking partners with reasonable confidence. For example, it is essential for the firm to identify its benchmarking needs (relative weaknesses) and its appeal as a potential partner to other firms (relative strengths) in order to succeed in partner selection. We first provide a separate analysis of this exploratory information gathering decision because we believe that a sizable portion of today's benchmarking activities may be exploratory. 5 Here, we examine how much information is gathered by individual firms about potential partners before deciding whether and with whom to benchmark. We show that a firm gathers costly information only when the choice problem is sufficiently difficult, i.e., when there are more than one available options that are sufficiently close to one another in their attractiveness without additional information. 6 More information is gathered when there is more uncertainty. We then examine how cooperative benchmarking activities generate benefits and costs to individual member firms. The major benefit of benchmarking for a firm is the expected increase in the profit due to improvements and innovations of its operations based on the information obtained through benchmarking. This can be in the form of increased productivity, reduced production costs, or both. We use a simple model to derive a function which describes the benefits of a firm from benchmarking with a group of partner firms. Information sharing among partners allows each firm to learn a certain amount of technological information contained in the others' operations. The same information may be obtained from different partners. We assume that firms know before benchmarking only the amount of information possessed by potential partner
4Some firms motivate benchmarking as a tool for achieving strategic goals such as improved quality or increased market share. The analysis of this paper can be made consistent with the behavior of firms pursuing such specific goals by appropriate interpretations of 'the benchmarking benefits'. 5There is a growing interest in database benchmarking in which member firms contribute to and share a database. Database benchmarking serves, among others, two purposes: sharing technical information and identifying needs and opportunities that could lead to further benchmarking. The second purpose is that of exploratory information gathering. 6This also happens when there is too little information to separate out different options.
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firms but not how their technologies overlap. The benefit of benchmarking is then understood as proportional to the amount of newly obtained information. The cost of cooperative benchmarking for each firm is assumed to be increasing and convex in the group size due to increasing complexity and coordination problems. Abstracting away from exploratory information gathering, we analyze how cooperative benchmarking groups are formed among a set of firms that possess different amounts of technological information contained in their operations. We show that there is a unique equilibrium group structure characterized by grouping among firms with similar amounts of technological information. The first group consists of a certain number of the best firms chosen by the best firm, and all members of the first group are shown to prefer that group to any other possible group. The second group is formed among a certain number of the best firms among the remaining firms, and so on, until all firms are exhausted. A comparative static analysis shows that group size and the number of firms participating in cooperative benchmarking tend to increase as learning becomes more efficient, as technology becomes more complementary, and as the marginal cost of benchmarking is reduced. We argue that today's changing business environment is likely to encourage cooperative benchmarking and increase group size because increased competition and technological progress in information processing increase benchmarking benefits relative to costs. Also, the rapid pace of technological progress makes different firms' technologies more likely to be different, thereby increasing the chance that firms can complement their technological knowledge by learning how other firms operate. In turn, the increases in cooperative benchmarking activities induced by today's environment contribute to innovations, accelerate technological progress, and increase competition. The rest of the paper proceeds as follows. We first analyze in Section 2 how much preliminary information is gathered by individual firms about their potential partners when there is uncertainty about the benefit and the cost of benchmarking. In Section 3 we model how information sharing among a group of firms can be translated into benefits and costs of cooperative benchmarking for each sharing firm. In Section 4 we examine how groups are formed in equilibrium~ In Section 5 we perform a comparative static analysis and discuss group size and the number of firms participating in cooperative benchmarking in relation to the types of operations being benchmarked and today's changing business environment. Section 6 contains a brief conclusion.
2. Exploring benchmarking opportunities A firm contemplating cooperative benchmarking typically faces uncertainty from several sources. It may not know for sure what the benefits and the costs
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will be. In this case it is often useful to engage in some exploration, i.e., some preliminary information gathering about potential partner firms, the information sharing processes, or how obtained information can be translated into profits. This aspect of cooperative benchmarking is noteworthy because an important part of services provided by existing benchmarking organizations appears to be educating firms about general benchmarking benefits and processes and providing some preliminary information about its member firms a m o n g which a firm can potentially choose its benchmarking partners. In this section we examine a situation when such uncertainty is present. In particular, we analyze how individual firms make decisions of whether to join a cooperative benchmarking group or which group to join, and how much preliminary information is gathered for the purpose of making these decisions. We begin with a very simple situation in which there is a firm which contemplates benchmarking and a group of firms that are willing to benchmark with the firm. The firm is considering two options, whether or not to engage in cooperative benchmarking with the group. Let 0 be the (decision-making) firm's net benefit from benchmarking with the group. We assume that random variable 1.7 takes the value of either UI > 0 or U2 < 0 (U1 > U2) with probability ½ each. 7 In order to decide whether to join the group, the firm can obtain information 37about/.7 from various sources, such as public databases including ranks in industry and publicly known performance measures or from the potential partner firms themselves. Random variable 37is such that if U = U1, then y = Yl with probability a _> ½ and y = Y2 with probability 1 - a, and if U = U2, then y = Y2 with probability a and y = Yl with probability 1 - a. In this case the conditional probability of U1 given y = Yl is a, and given y = Y2 it is 1 - a. Symmetrically, the conditional probability U2 given y = y2 is a, and given y = y~ it is 1 - a. If the decision is made without observing 37, the firm joins the group if and only if 0 - ½(U~ + U2) > 0. 1 In this model variable a measures how accurate the information 37is. If a - 2, 37is not informative at all. As a increases, observing 37enables the benchmarking firm to assess the true value of 0 with more confidence. In the extreme where a = 1, 37 perfectly reveals the true value of 0. Let H(a) be the cost of observing 37 (exploration cost). It is a function of its accuracy a, and we assume that the
7if both U, and U2 were positive (or negative), then the obvious choice would be to join (not to join) without further information gathering. The actual benefit can be zero or negative. For example, suppose a firm completes benchmarking in the area of billing and draws a plan to improve its billing operations based on the obtained information. If top m a n a g e m e n t rejects the plan at that point, the benefit is zero and the net benefit is negative. In another scenario the benefit itself is negative if the firm adopts the plan and if the change in operation results in a decrease in profit. However, it is important to note that the decision to benchmark is made based on the expected benefit before its realization.
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function H is twice differentiable, strictly increasing, and strictly convex. Also, H(½) = 0 and H'(a) approaches zero as a approaches ½, and it approaches infinity as a approaches 1. In other words, it is very cheap to get some information about the true value of 1.7 but it is prohibitively expensive to get perfect information. The decision-making firm's problem is to choose the level of information accuracy a, and to decide whether to join the group. Once a is chosen and 37is observed, the second decision is easy to make. If yl is observed, the firm joins the group if and only ifaU~ + (1 - a)U2 > O. If y2 is observed, it does so if and only if(1 - a)U1 + aU2 > O. The choice of a must be made before the value of 37is observed. Therefore, the ex ante value of 37is the increase in the expected profit due to observing 9. There are two cases. Suppose first that U1 > - U2 so that 1.7 > 0. In this case the choice without information is to join the group because the expected profit of doing so is nonnegative. When information signal 37 with parameter a is observed, the ex post benefit of observing 37depends on the realization of 37. If y~ is observed, aU1 + (1 - a)U2 is positive regardless of a and the firm joins the group. Thus there is no ex post benefit of observing 37. If Y2 is observed, however, (1 - a)U1 + aU2 can be negative for a sufficiently close to 1. When the expected profit is negative, the decision made after observing the information signal is not to join the group. When this happens, the ex post benefit of observing )7 is - [(1 - a) U~ + aU2] because it is the expected loss saved due to obtaining the information. Since the probability of observing either yl or Y2 is ½ each, the ex ante net benefit of observing 37, denoted by Vr, for any given accuracy a is Vy = max(0, - ½1-(1 - a)U1 + aU2]) - H(a).
(:)
Information is obtained if there is a such that the above net benefit is positive. Suppose now that U1 < - U2 so that [7 < 0. In this case the choice without information is not to join the group because the expected net benefit of doing so is negative. When information signal 37with parameter a is observed, the ex post benefit of observing 37 again depends on the realization of 37. If Y2 is observed, (1 - a)U1 + aU2 is negative regardless of a and the firm does not join the group. Thus there is no ex post benefit of observing 37. If Yl is observed, however, aU1 + (1 - a ) U 2 can be positive for sufficiently large value of a. When it is positive, the decision made after observing the information signal is to join the benchmarking group. When this happens, the ex post benefit of observing 37 is aU1 + (1 - a) U2 because it is the expected gain due to the information. The probability of observing either Yl or Y2 is ½ each, and the ex ante net benefit of observing 37 for any given a in this case is Vr = max(0,½[aU1 + (1 - a)U2]) -- H(a).
(2)
Again, information is obtained if there is a such that the net benefit is positive.
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The ex ante net benefit in the above two cases when the accuracy a is freely chosen can be now written in one expression as Vr = maxa[max(0, 5[a(U1 - U2) - max(lUll,
IU21)]) - n(a)]
= max,(0, 5[a(U1 - U2) - max (IU1 I, I U21)] - H(a)), where the last guaranteed by cost function 5[a(U~ - U2) -
(3)
equality obtains due to the fact that the net benefit of zero is choosing a = 5, since H(5) = 0. Under the assumptions on the made earlier, there exists a unique a that maximizes max(I U~I, [U21)] - H(a). This unique a is characterized by
5(U1 - U2) - H'(a) = 0,
(4)
and a > 5 given the assumptions on the curvature of the cost function. Therefore, the benchmarking firm's choice is to spend H(a) and observe 37 with accuracy a such that (4) is satisfied if such an a generates a positive net benefit expressed as (3). If the expected net benefit is negative for such an a, the firm chooses a = 5, i.e., it does not gather any preliminary information. Expressions (3) and (4) suggest that the choice of a, i.e., the intensity of preliminary information gathering, depends on three factors, the uncertainty and the ease of the choice problem and the magnitude of the marginal information gathering cost. The uncertainty of the choice problem captures the degree of uncertainty of the benchmarking net benefit and is measured by U1 - /-12, the difference in the expected profits between the two possible realizations of the random benchmarking benefit. The ease of the problem is measured by max(I U~ I, I U21) which reflects how far the expected net benefit of benchmarking is from zero, which is the net benefit of the second option (no benchmarking). If it is far from zero, the correct choice is easily to benchmark (if positive) or not to (if negative). For a fixed level of uncertainty, i.e., for fixed U1 - U2, the measure of ease, max(I U1 [, I U21), reaches its minimum when U~ -- - U 2 in which case the choice problem is most difficult. It reaches its maximum as either U~ or U2 becomes zero, in which case the problem becomes easiest. The results on these three factors are stated in the following proposition. The proof follows from (3) and (4).
Proposition 1. The level of preliminary information gathering is positive only for a sufficiently difficult choice problem, and is higher for a more uncertain choice problem and for lower marginal information gathering costs. That is, the optimal a is positive only for sufficiently small max(lUll, I U21), and is increasing in U1 - U2 and in any shifts of the function H that reduce H'('). Proposition 1 is intuitive. It says that preliminary information is gathered only when the choice without additional information is sufficiently difficult, i.e., the expected profits generated by the two available options are sufficiently close
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to each other. Also, more preliminary information is gathered when its benefit is greater or its marginal cost is lower. The benefit of information gathering is greater when there is more uncertainty. In a typical situation a firm decides whether to benchmark, and if yes, with which group among multiple groups that are willing to accept the firm as a partner. We do not formally model this more general situation here. However, we conjecture the following by applying the intuition obtained above. The first part of Proposition 1 suggests that the firm in this case would compare the expected net benefits of available options and consider only the option with the greatest expected net benefit and ones that are sufficiently close to it. If there is a large gap between the best and the next best in the expected net benefit (i.e., if the choice problem is easy), the one with the greatest expected benefit is chosen without information gathering. When there are a number of options that are close to each other (i.e., if the choice problem is sufficiently difficult), some preliminary information is gathered. Also, the second part of Proposition 1 suggests that more information will be gathered about the potential partner groups (firms) if there is more uncertainty or if the marginal cost of information gathering is lower. One implication of Proposition 1 and the related discussions concerns the role of observed institutional arrangements such as a benchmarking clearinghouse or a government agency which facilitates benchmarking. 8 Such arrangements reduce the exploration costs (H) and induce firms to obtain better preliminary information about potential benchmarking partners, which in turn results in better matching and greater benefits of benchmarking. Also, as more information is provided about potential targets at low costs, more firms are induced to take part in cooperative benchmarking.
3. Benefits and costs of cooperative benchmarking Cooperative benchmarking activities affect a firm in many different ways. For convenience, we distinguish between the benefit and the cost of benchmarking. The cost of benchmarking is defined as the direct cost of benchmarking, such as the cost of preparing and processing information supplied to and obtained from partner firms. The benefit of benchmarking is defined as any change in profit due to benchmarking activities which is not included in cost as defined above. There are several sources of cooperative benchmarking benefits. First, a firm's profit can increase due to improvements and innovations of its operations based on the information obtained through benchmarking. This can be in the form of increased productivity, reduced production costs, or both. Second, a firm's profit can change if information sharing through benchmarking affects the firm's Sin Canada this service is offeredby Industry, Scienceand TechnologyCanada.
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competitive advantage within its industry. Third, there can be other political, social, or control-related effects of cooperative benchmarking. For example, emerging as a leader in cooperative benchmarking activities may help a firm improve its status among its business associates and investors, which may affect its profit. Or the informal networking by company representatives may adversely affect profit, for example, if they learn from one another new ways to defraud their companies. In this paper we mainly discuss the first type of benefit, namely, the benefit from improved operations, which is understood by most practitioners as the major benefit of benchmarking. We will only briefly mention the industryrelated effect of benchmarking when we discuss group formation in Section 4. We abstract in this paper from other effects of benchmarking mentioned above as the third type. In the rest of this section we discuss how the benefit and the cost of cooperative benchmarking would behave once the benchmarking partners of a given firm have been determined. Given a benchmarking group, G = { 1, 2 . . . . . N}, the net benchmarking benefit of firm i, i ~ G, denoted by Ui~, is written as U i , = B~.( + S~a) - Ci~,
where Bia and Cia are the benefit and the cost, respectively, of firm i from benchmarking in group G. The term Sia denotes the industry-related or some special type of benefit of firm i that we only informally discuss in Section 4 and is assumed to be zero unless mentioned otherwise. In order to gain an insight into how the benefit arises, consider a group of risk-neutral firms, 1, 2. . . . . N, sharing information about their operations in a pre-specified area such as warehousing or billing. We define wl as the amount of technological information contained in firm i's operations that can be learned through cooperative benchmarking. The quantity wg > 0 is measured in terms of how much benefit it will yield in dollars if completely learned by another firm which does not possess it. It is useful to visualize a round cake with circumference w whose face is decorated as a clock so that the original location of any slice can be determined. Each firm takes a slice and the cake is magically restored each time. Thus, several firms can have the same part of the cake at the same time, just as there can be overlaps among different firms' technologies. Firm i's technology is represented by the round edge of its slice, denoted by E~, and the size of the slice (the length Ei) is wi. Cooperative benchmarking here is thought of as sharing slices of the cake among partners. It is important to note that the same slice can be given to multiple partners at the same time just as the same piece of information can be given to many firms. Also, receiving the same part of the cake many times to
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a firm is equivalent to receiving it o n c e . 9 The information structure in this model is the following. Each firm knows wi's of all potential partners but not the locations of other firms' slices except its own. In other words, each firm knows how much technological information is possessed by any other firm, but it does not know how much of the information that can be obtained from the partner will be new to the firm. It only knows that each firm's technology is contained in a common universal set of all potentially existing technologies (the whole cake) whose size is w. Mathematically, we assume that each firm thinks that the location of any firm's slice (El) is uniformly and mutually independently distributed around the whole cake whose circumference is w. 1° The amount of new information obtained by firm i as a result of cooperative benchmarking with group G is then thought of as the amount of information possessed after benchmarking, i.e., the expected length of the union of all Eis, minus w, the amount of technological information possessed before benchmarking. The benefit of benchmarking for firm i is now defined as
where the parameter e, 0 < e ~< 1, measures how well the newly learned technological information is digested by firm i and contributes to higher profits.11 Given the above formulation, the benefit of benchmarking can be calculated as in the following lemma. The proof is provided in an appendix. Lemma 1. The benefit of firm 1 from cooperative benchmarking with group G = { 1, 2 . . . . . N} can be written as BI~ = ~(fllW2 -Jt- fllfl2W3 -~- fll[J2fl3W4 "q- "" -~ fllfl2 "" flN - 1WN), where fli - 1 - (wffw). Moreover, the benefit is invariant to the order in which the benchmarking partners of firm 1, i.e., firms 2, 3 . . . . . N, appear in the expression. Lemma 1 suggests that as more firms are added to the group, the benefit of benchmarking increases but successive additions contribute less and less to each 9Observing that the same technology is used by m a n y firms may be of value, for example, in making strategic decisions or assessing its viability. We ignore these possibilities here. °Formally, we allow each firm to have any finite number of slices from any parts of the cake with the total length of the slices w, and the proofs of the results below are based on this more general assumption. An alternative discrete version of this model is one in which benchmarking firms draw wl balls from a jar containing w numbered balls with replacements and share them. 11in a more general setting ct can also be different for different partners and for different portions of technological information. For example, certain technology m a y be more imitable a m o n g firms with comparable sizes or sufficient process similarities.
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benchmarking firm's profit. This is because 0 < fll < 1 which reflects the fact that the chance of overlap increases as there are more firms in the benchmarking group. We now turn to the cost of cooperative benchmarking. It is often the case that when a benchmarking group is formed, a coordinator is selected) 2 The coordinator is in charge of specifying the exact set of information to be provided by each member, collecting the information, processing the information if necessary, distributing the information in an efficient manner, and communicating with members for questions and verifications. Often, there are site visits to selected member companies. The cost of benchmarking is all the individual direct costs of benchmarking such as the cost of preparing and processing information supplied to and obtained from one another a m o n g the group members. If there are c o m m o n costs such as the cost of hiring a coordinator, we assume that such costs are equally divided a m o n g the members. An increase in the number of firms in a benchmarking group has at least two effects on the cost of benchmarking for each individual member firm. The first is a scale effect which reduces the cost of benchmarking for each firm due to the economies of scale in planning, data processing, and so on. The second effect is a complexity effect which causes costs to rapidly increase (so that the cost per firm increases) as the number of firms increases. This is due partly to the fact that the information about the participating firms' operations must be provided with reasonable accuracy. As the number of firms increases, this task becomes increasingly difficult because the coordinator must guarantee some minimum degree of accuracy and comparability of the information about all member firms. For example, m a n y kinds of differences, some of them qualitative differences, inevitably make the inter-firm processing of numbers (such as adding and averaging) less and less meaningful. There are also communication difficulties with a large number of firms. For example, if each firm has one question about each other member, with N firms the coordinator must handle N ( N 1) questions, which increases geometrically as N increases. For these reasons, it is reasonable to think of the cost function (as a function of the number of firms) to be increasing and concave first (due to the scale effect) and then convex (when the complexity effect eventually dominates the scale effect). Given the above considerations, we assume in our model that the cost of benchmarking for each firm is a strictly increasing, convex function, denoted by f ( ' ) , of the group size (the number of firms in the group) w i t h f ( l ) = 0. Let cn be the cost (for each existing member firm) of adding the nth partner. Then, c° = f ( n + 1) - f ( n ) and our assumptions on the cost function imply that c, is increasing in n, i.e., ca < c2 < c3 < ... <_ CL for any integer L. Given this cost structure and the expression for the benefit ill L e m m a 1, we are now ready to investigate how benchmarking groups are formed a m o n g a given set of firms. 2The coordinator is usually a person who has some experience in benchmarking and may be from one of the partner companies, or on some occasions a third party, e.g., a consultant.
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4. Equilibrium group formation In this section we analyze how cooperative benchmarking groups are formed in equilibrium a m o n g firms that possess different amounts of technological information. In order to analyze group formation, we need to consider the incentives of each firm to benchmark with any possible group of firms. For simplicity, we abstract away from preliminary information gathering. Consider L firms that are contemplating cooperative benchmarking. The amount of technological information contained in firm i's operations to be benchmarked is w~ as defined earlier. The net benefit of firm i from benchmarking in a group G = 1, 2 . . . . . N is U~ = Bi~ - C~G, and the expression for the benefit is from Lemma 1 Bt~ = ~(fl,Wz + fllflzW3 + flxflzfl3w4 + "'" + fllfl2 "'" f l u - l w u ) ,
(7)
where fli -- 1 - (wi/w) . The benefit of any other member firm i ~ 1 can be similarly written by substituting i for 1 and 1 for i in the subscripts in (7). Also, from Section 3 we summarize the structure of the benchmarking cost by 0 < C1 ~ C2 ~ C3 ~
... ~ CN_I,
(8)
where Ck is the marginal cost (for any firm) of adding any kth partner [(k + 1) th firm] to the group. We define a group structure, denoted by S, to be a partition of firms l, 2,... , L (i.e., a set of nonempty groups whose union is the set of all firms and whose pairwise intersections are all empty). A group structure, S, is an equilibrium group structure if there does not exist a set of firms which can form a new group and increase the net benefit of at least one while not reducing the net benefit of any a m o n g themselves. No side payments are allowed. We begin by making the following observations. Observation 1. Replacing a f i r m in a group by a better (with a greater wi) f i r m increases the benefits o f all other firms in the group.
This observation follows by rewriting (7) so that a firm to be replaced appears last in the equation and by noting that the benefit increases each time a firm is replaced by another with a greater wi. For convenience, we now reindex the firms so that wl > w2 > > WL- 1 > WL without loss of generality (by L e m m a 1).~3 Consider the benchmarking group, denoted by G t, that includes firm 1 (the best firm) and is most preferred by firm 1. By Observation 1 Gt is the best "
'
"
13We assume strict inequalities to avoid unnecessary complications in proving the results below in some pathological cases.
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N~ firms, 0 < N~ < L. Since the (successively decreasing) terms in (7) can be viewed as the marginal benefits of adding firms successively, Na is determined so that ~fl132 "'" fiN,- IWN, -- CN,- 1 > 0 > ~tfllfl2 "'" flN,WN, +1 -- CN,.
(9)
In other words, the marginal net benefit of adding a firm is nonnegative for the N~th firm and negative for the (N1 + 1)th firm. We also note the following: Observation 2. The marginal net benefit of addin9 a firm to a 9roup is the same for all members.
This observation follows easily from Lemma 1 that the marginal benefit is the same for all existing members and the assumption that the marginal cost is simply a function of the group size. Observations 1 and 2 imply that the group of size at least NI most preferred by any member of G~ is in fact G~. This is true because by Observation 2 any member of G1 prefers G1 to a group of the best N firms with N > N~, which, by Observation 1, is in turn preferred to any other group of size N. We make the following observation about the subgroups of G~: Observation 3. All members of any proper subset G' of G1 prefer addin9 any member of G 1 left out of G'.
This is true because the marginal net benefit of adding firm j, j ~ GI\G', to group G' of size N ' < N1 for any firm i'~ G' is ( 1 - I r ~ , f l r ) w j - cs,, which is greater than fl~fl2 "'" f i N 1 - l W N , - CN~-1, the nonnegative marginal net benefit of adding the last firm NI to complete G~. This is due to the facts that fl's are less than one, wj >_ WN,, and CN, < CNI. From Observation 3 it follows that the group of size at most NI most preferred by any member of G1 is also G1. We are now ready to state the following lemma: Lemma 2. The most preferred benchmarkin9 group by any member of G1 is G1.
The strong unanimity result of Lemma 2 implies that any group structure that does not include G1 is not an equilibrium because the members of G~ can form a new group G1 and increase their profits. Once G~ is formed, its members do not have any incentives to change partners. Now among the L - N1 remaining firms G 2 is formed among the next best firms, and then G3, G4, etc. We state this result as the following proposition. Proposition 2. There exists a unique equilibrium structure. In the equilibrium the first group consists of the best N1 >_ l f r m s , the second group consists of the next
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best N2 >_ 1 firms, and so on. The size of each 9roup can be found by considerin9 successively the preference o f the best firm amon9 the remainin9 firms, x4 This equilibrium is characterized by a segregation by wi's, the a m o u n t of technological information possessed by firms that can be learned t h r o u g h benchmarking. Firms are m o r e willing to share information with superior firms because it provides more opportunities to learn. The above analysis shows that as a result in equilibrium firms form groups a m o n g those which possess c o m p a r a b l e a m o u n t s of technological information. 15 We now check the sensitivity of Proposition 2 to some of the simplifying assumptions made above. It can be shown that Proposition 2 still obtains even when w and wi's are not k n o w n (i.e., are r a n d o m variables) to the firms. F o r any (homogeneous) beliefs of firms regarding the a m o u n t s of technologies possessed by other firms (wi's), all the proofs above hold by replacing wi's by their expectations. W h e n w is uncertain, L e m m a 1 and Observations 1 to 3 are true conditional on any value of w, therefore Proposition 2 is true for any h o m o g e n e ous beliefs of w. However, Proposition 2 is sensitive to the introduction of other factors that also affect firms' b e n c h m a r k i n g opportunities and preferences, such as any k n o w n differences in the overlaps in technologies (the locations of the slices), benefits, and costs across firms. O n c e such a factor is introduced in the model, the tendency to segregate by wi's remains but is mixed with the effect of the additional factor. We provide below an informal discussion about how the presence of such factors would affect g r o u p formation. In expression (7) for the b e n c h m a r k i n g benefit suppose that there are firms i and j such that Si~ :~ 0 and Sj~ ~ 0. Consider first a case in which S~ < 0 and S~ < 0. In this case there is a tendency for the firms to avoid each other. This arises, for example, when firms in a highly competitive industry prefer to b e n c h m a r k with firms in other industries to prevent their rivals from obtaining their proprietary information, as well as to avoid the possibility of being subject to anti-trust litigations, x6
~4This is consistent with some anecdotal evidence. For example, Bowers (1993) reports that at Digital Equipment Corporation overwhelming demand by companies to benchmark with them forced him to turn down more and more requests. Also, in Elnathan, Lin, and Conway (1992), Xerox, clearly the best company, was the one that determined the size of the group (six firms) by specifically inviting these firms to join in a particular project. It is not clear, however, if the strong unanimity implied by the present model was present in these examples. 15Note that it is difficult to predict the relative group sizes across different groups in this model because they depend partly on the number of firms possessing comparable w~'sfor each group, and because the effect of a decrease in wi's(say, from the first group to the second group) on the marginal utility in Eq.(10) is ambiguous. 16Also, they may have incentives to provide inadequate or even false information if they are in the same benchmarking group. This may be another reason why inter-industry benchmarking is often observed.
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We also consider a case in which S u > 0 and S~i > 0. In this case there is a tendency for the firms to benchmark together. For example, it is reasonable to expect that groups are formed among firms that guarantee high degrees of learning. This implies that the process or area under study may have to be reasonably similar, or of comparable size, for the benchmarking partners. Another instance of the presence of special mutual benefits is a case where a group of firms prefer to engage in several benchmarking projects over time or over different functional areas, because a long-term relationship can increase the net benchmarking benefit for each member due to the preexisting knowledge about other members and mutual trust that has developed. 17 The relative importance and the interaction among the effects of various special benefits (costs) and the general tendency to segregate observed in Proposition 2 may be complex and deserve further study. For example, when the kind of operation being benchmarked is unique in an industry with a high degree of competition, a trade-off exists between providing learning opportunities (by benchmarking with similar firms) and preserving proprietary information (by benchmarking with firms in different industries).18 Also, if a firm's size proxies for its desirability as a benchmarking partner, we would expect to observe, ceteris paribus, that firms organize into benchmarking groups of similar sizes. That may be due to certain operational attributes, or simply due to the ability of larger firms to devote more resources to benchmarking, relative to smaller companies. In a recent Wall Street Journal story (1993) it has been observed that small firms' executives created a network of what can be described as informal benchmarking. One reason cited was that they felt that best learning about improvement of their operations came from discussions with other small firms. On the surface of the story, it seems that the (preferred) segregation occurred due to high degrees of learning among small firms. Our present discussion, however, suggests that it may have occurred partly because small firms preferred but were not able (were not accepted) to benchmark with large firms.
5. Determinants of group size and firm participation In this section we examine how the equilibrium is affected by changes in the parameters of our model. In particular, we analyze how the average group size and the number of firms participating in cooperative benchmarking are affected by various factors of the benefits and costs of benchmarking. We also relate cooperative benchmarking and innovation by discussing how today's
~TSee Spendolini (1992) for a discussion of the development and advantages of benchmarking networks. lSSee Leibfried and McNair (1992) for a discussion of competitive and industry benchmarking.
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innovative environment affects benchmarking benefits and costs and equilibrium group formation. Consider N + 1 firms from any i (the ith best) to i + N and call them for notational simplicity firms 1, 2 . . . . . N , N + 1. Suppose that firms 1, 2 . . . . . N have formed a group and are considering whether to add firm N + 1 to the group. The existing members will agree to the addition if and only if the marginal net benefit of adding firm N + 1 is nonnegative, i.e., (10) is nonnegative. Given the properties of the equilibrium characterized by Proposition 2, any change that increases (decreases) expression (10) tends to increase (decrease) both the average group size and the number of firms participating in cooperative benchmarking. We consider below the effects of changes in the levels of cN, ct, w, and in the distribution of w{s.
Proposition 3. Group size and the number of firms participatin9 in cooperative benchmarkin9 tend to increase as learnin9 becomes more efficient, as technology becomes more complementary, or as the marginal cost of benchmarking is reduced. That is, OMUN+ I/O~ > O, OMUN+ I/Ow > O, and ~UN+ I/~CN < O. For Proposition 3 it is easy to see that (10) is decreasing in CNand is increasing in ~ and w. A reduction in the cost of benchmarking tends to increase group size and facilitates benchmarking in general. The same occurs when firms can more efficiently transform the new information obtained through benchmarking, into improvements of their own operations (an increase in ~). Recall that w is the amount of total technological information that potentially exists. A greater w (given wi's fixed) can then be interpreted as greater complementarity or a greater dimension of the technology of the operation being benchmarked, because it implies less overlap among firms' technologies. Complementarity is important in understanding why the best performer would benchmark with inferior partners, because it allows two (or more) firms to successfully learn from each other. To see this, suppose wl = w, i.e., the best firm possesses all potentially available technologies. Then, the firm never engages in benchmarking activities. If w is thought to be much greater than any single wi, then each firm has more incentives to benchmark. This happens, for example, when the operation being benchmarked has sufficiently many dimensions to allow mutual learning. When a group of firms engage in a study of a broadly defined function (e.g., facilities management, customer satisfaction), the number of subareas to be included almost guarantees the existence of complementarity. It also arises across multiple benchmarking projects or across multiple benchmarking rounds
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over time. That is, firms that engage together in several benchmarking projects (in different areas) can learn from one another even when in each area there is little complementarity. 19 Or firms that engage in several rounds of benchmarking (over time) in the same functional area can expect to reverse their positions in the future from the imitated to the imitator and vice versa, even when in each round only one of them benefits. This can happen in an area or an industry in which technological innovations are frequent or demand is unstable. A change in the distribution of wi's among firms also affects the equilibrium. In expression (10) increases in wl, w2 . . . . . wN for a fixed wN+ 1, or a decrease in wN+ 1 alone, reduces (10). In practitioners' jargon, this increases the benchmarking (performance) gap (Camp, 1989) between the existing members and the candidate firm. A greater benchmarking gap reduces the chance that firm N + 1 is accepted as a new partner because the addition provides fewer opportunities to learn for the existing members. Therefore, a greater benchmarking gap increases the chance of segregation. The implications of Proposition 3 can be tested empirically. For example, differences in benchmarking group size across different functional areas may be observed and linked to the characteristics of the functions being benchmarked. As a general observation the International Benchmarking Clearinghouse' survey (IBC, 1992) indicates that on average a benchmarking firm would study between three and four partners. Elnathan, Lin, and Conway (1992) indicate a lower level of participants' satisfaction from a benchmarking project with 25 participants, relative to one with six participants. Our final discussion of this section concerns the relationships among today's business environment, innovation, and cooperative benchmarking. Improvements of the operations of a firm can be attained by adopting a better process or a product either gradually (e.g., continuous improvements) or by a rather drastic change (e.g., reengineering). The information about or the right for a new process or a product can be either internally developed (e.g., R&D), purchased (e.g., a patent), exchanged (e.g., a joint venture), or shared (cooperative benchmarking). If innovation is broadly defined as doing things in new and improved ways, most improvements are innovations at the firm level. Information obtained through cooperative benchmarking is typically not new globally, and the global novelty of, say, an adopted process is not a primary concern to a firm as long as the process improves the firm's operations. Benchmarking, however, facilitates improvements through the diffusion of existing (global) innovations. Benchmarking also complements innovation by providing the 'nuts and bolts" which are crucial in the transformation of innovative breakthroughs into operating production activities. Finally, learning different ideas
~OForexample, Xerox has conducted many benchmarkingstudies across multiple functionalareas, some of them with the same partners.
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from other firms' operations can spark a new idea that is different from any existing ideas. 2° Within the context of our model, today's changing business environment can be thought of as affecting the benefits and costs of cooperative benchmarking in several ways. We conjecture that the changes in today's business environment tend to increase the benefit and decrease the cost of benchmarking expressed in (7) and (8). First, the complementarity of firms' technologies, measured by the magnitude of w, seems to increase because the rapid pace of technological progress makes different firms' technologies more likely to be different. Second, innovations in information processing reduce benchmarking costs. Third, increased competition forces firms to more actively seek improvements by quickly and efficiently absorbing information obtained through benchmarking (an increase in ~t). By Proposition 3 these changes lead to larger groups and increased participation in cooperative benchmarking. This, in turn, contributes to innovation, accelerates technological progress, and increases competition. 6. Conclusion In this paper we have provided a theoretical analysis of different phases of the cooperative benchmarking activities. We have tried to align our discussions with observed practices, and several empirical implications are derived from the analysis. Proposition 1 establishes that in the presence of uncertainty the level of preliminary information gathering about potential partner firms would depend on the amount of uncertainty involving the benefit and the cost of benchmarking, how easy the choice problem is without any additional information, and the marginal cost of information gathering. In the analysis leading to Proposition 2 we have modeled how benefits and costs arise from cooperative benchmarking and found a unique equilibrium group structure characterized by a segregation by the amount of technological information a firm can offer to its partners. Based on the comparative static results of Proposition 3, we have also discussed group size and the number of firms participating in cooperative benchmarking for different types of operations, and for today's changing business environment. For the future study of benchmarking it would be very useful to understand current benchmarking practices and organizations. Such studies would produce a clearer picture of what factors determine firms' benchmarking benefits and costs and in turn affect their benchmarking decisions. Some of the issues ignored in this study, such as those of truthful revealing of information, its verification, and optimal information sharing mechanisms, may also prove important in explaining current practices and organizations. 2°See, for example, discussion of benchmarking in Hammer and Champy (1993) and Grant Thornton (1993).
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Appendix: Proof of Lemma 1 For the first part of Lemma 1 it suffices to show that E[thelengthofjUEj]=w~
+flaw2+fitfl2w3+
'" + f i ~ f i 2 " " f l N
lW~,
where fl, _ = 1 - ( w i / w ). Set E~ is a subset with length wi of a circle whose circumference is w. The locations of E(s are uniformly distributed over the circle and are mutually independent. Consider the union UM of Ej,, j' = M . . . . . N, and set EM ~, where 1 < M < N. Suppose that UM has expected length xM. Since U u and EM 1 are independently located, the probability that any arbitrary point on the circle is an element of the union of the two sets, UM 1, is XMWM W
1 +__
W
W
1 W
,)
+ W
l t 1 --- W
,
which can be simplified as wM ~/w + tim l(XM/W). Integrating over the entire circle (or multiplying by w), the expected length of UM l is wM-~ +/3M lxM. Applying this result repeatedly, the expected length of the union of all E~'s can be written as Wl + ill(w2 +/~2(w3 + "" + W~,)'"), which is the equation that we want to prove. The second part of the lemma follows from arbitrarily in the above proof. This can also expression for BI6 in L e m m a 1. Suppose i 4:1 by each other in the expression. Deleting the N j terms, which are common, the original expression can be written, respectively, as
the fact that w/'s are indexed be verified directly from the and j :~ 1, j > i, are replaced first i - 2 terms and the last expression and the modified
and
~/~l "1~,
,I-wj +
l~jw,~, + l~jl~,. , w , + ,
+
--- +
l*jl~,+, " / ~
,w,].
The difference in the terms in the parentheses between the two expressions is {Wi
Wi) 4- ([Ji
fJj) {Wi. 1 4- / ~ i - l W i • 2 +
+/~,., "'"/~,j ,(fl~wi- l~iwO.
"'" + /Ji
1 "'" fl)
2Wi
1}
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D. Elnathan, O. Kim / Journal of Accounting and Economics 19 (1995) 345-364
which can be simplified as ( w i -- w))
I
1
-
wi + 1
W
~,+,&
Wi+ 2 ~i + 1 - W
Wj 1 ~i + l ' ' " /~j- 2 - W
2&-,]
by using the definitions of /~'s. N o w note that the first two terms in the parenthesis sum to/~i+ 1, the first three terms sum to/~i+ 1/~i+2, a n d so on. The inside of the parenthesis t h e n b e c o m e s fl~+ 1 ' " flj 2 f l j - 1 -- fli+ 1 "'" /~j 2/~j- 1, which is zero. Therefore, a n y pairwise switching a m o n g the partners does not change the benefit. Since a n y order of the partners can be generated by repeated pairwise switching m a n e u v e r s , the benefit of b e n c h m a r k i n g in L e m m a 1 is i n v a r i a n t to the order in which the partners a p p e a r in the expression.
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