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Organization structure and cooperative market relations
OMEGA, The Int. Jl of Mgmt Sei., Vol. 4, No. 5, 1976. Pergamon Press. Printed in Great Britain
Organization Structure and Cooperative Market Relations HELMY H BALIGH RICHARD M BURTON (Received September 1975; in revised form April 1976)
A linear model is used as the vehicle for analyzing some of the interactions between an organization's cooperative market relations (product forms) and its structure (decomposition and coordination). Normative implications for organizational choice, and a set of conclusions concerning the nature of organizational change and growth for practical use are developed. The concept of product form as a description of cooperative market relations is the basis for relating the activities of the firm to its market environment. The decision on product form is viewed as a decision on the resource usage vector, and hence as a decision on the nature of the linear programming model formulated. The decision on the decomposition of this linear model and on the solution procedure are viewed as decisions on organization structure. They are viewed as decisions on the partitioning of the organization's decision variables into divisions and on the mechanisms used to coordinate these divisions.
THE DECISIONS ON DECOMPOSITION, COORDINATION, AND PRODUCT FORM DECISION p r o b l e m s o n certain aspects o f o r g a n i z a t i o n structure have been widely a n d c o n v e n i e n t l y discussed in t h e c o n t e x t o f the d e c o m p o s i t i o n a n d s o l u t i o n p r o c e d u r e s o f a linear p r o g r a m m i n g m o d e l [1, 3, 5, 8]. T h e p r o c e d u r e followed in solving a linear m o d e l d e t e r m i n e s elements o f the o r g a n i z a t i o n ' s structure viz. the w a y the o r g a n i z a t i o n is d e c o m p o s e d , a n d the m e c h a n i s m s used for its c o o r d i n a t i o n [1, 3, 5, 8, 10]. These analyses, however, have started w i t h a given linear m o d e l a n d c o n c e n t r a t e d only o n the s o l u t i o n procedure. I n this p a p e r we c o n s i d e r b o t h the decision o n the linear p r o g r a m m i n g s o l u t i o n p r o c e d u r e a n d the decisions on the n a t u r e o f the m o d e l a n d m o d i fications in it. W h e r e a s the decision o n a solution p r o c e d u r e is a decision o n o r g a n i z a t i o n structure, the decision on the n a t u r e o f the m o d e l f o r m u l a t e d is a decision o n the firm's p o t e n t i a l c o o p e r a t i v e relations. T h e latter is a decision on
The authors are grateful for the help they received in making revisions of the paper from several of their colleagues in GSBA. 583
Baligh, BurtonmOrganization Structure
relations of the organization to its environment. Our analysis of these relations is thus a limited focus variation of the general analysis of the relation between structure of the organization and its environment. The literature on this topic includes the work of Thompson [11, 12] which focuses on the relation of uncertainty to decision structures. Lawrence and Lorsch's [9] contingency models focus on relations between environmental uncertainty and internal structure and degree of decentralization. Burns and Stalker's [4] investigation of electronics firms demonstrates the influence of technological uncertainty and rapid innovation on structure. Finally there is Chandler's [6] historic analysis of the general relations between structure and strategy. Decisions on the organization's cooperative market relations, i.e. on the nature of this one boundary between it and its environment, we term decisions on product form [2]. Product form is discussed in terms of the resource amounts necessary to obtain it. It is a concept that is easily and clearly developed in terms of the linear model, and represents a description of the firm's cooperative relations with its environment. Decisions on product form are decisions on the nature of the linear programming model, and decisions on organization structure are decisions on the decomposition and solution procedures of this model. It is the relations of these two kinds of decisions that is the topic of the paper. The practical significance of the paper lies in its contribution to comprehensive planning for an organization. It points out some of the needs of organizational structure which arise from changes in the firm's relations with its market environment. It identifies the effects which the existing organizational structure has on the development of changes in the firm's relations with its markets. By showing the nature of the interconnection between the two decisions on organization structure and product form the paper identifies general ramifications of each alone. It supplies relations that must be specifically identified if planning is to become more comprehensive. These practical implications will become more apparent through our use of a simple example. We shall use the case of an organization which manufactures and sells two product lines--tires and batteries, to illustrate our analysis of the possible effects of changes in the product form in each line on organization structure and vice versa. The analysis uses the linear model of the firm which isJ max 27 S'jx~ y=l J s.t. 27 ak~xj<_A~ k = l . . . . . K. j=l xl>_0 j = l ..... d. I where s'j - sj - e~ z C~blj, i=1 584
Omega, VoL 4, No. 5
and xj akj bu Ak Cl
/,j sj
= = = = --=
S'j
=--
number of units o f p r o d u c t j ; amount of fixed resource k required for a unit of j ; amount of variable resource/required for a unit o f j ; upper bound of fixed resource, k, k = 1. . . . . K; unit variable cost for input, i; entry price, or purchase price, for process,j; exit price, or selling price, forprocessj; net contribution to p r o f i t , j = 1. . . . . J.
Further, let aj = (a~j, a 2 j , . . . , a k i . . . . ,axj) and bj = (bu,b2 J . . . . . b u . . . . ,bu). The vector (Sj,Pj,aj,bj) is associated with the j t h process or activity. The jth product's form is described by such a vector, and the firm's cooperative market relations may thus be described by a set of vectors. Any change in these cooperative market relations or product forms would be reflected by changes in the set or in the components of its vector elements. An initial formulation of a linear model entails a decision on a given set of potential product forms which the firm is to consider. The solution of the model involves picking a subset of these to implement. The decision on the process by which this linear model is solved repeatedly to meet parameter changes involves decisions on the decomposition of the model and on the mechanisms to use to coordinate the segment solutions. These decisions are decisions on organization structure. Alterations in potential cooperative market relations mean changes in the form of the linear model to be solved and hence possible changes in structure. Table 1 contains a summary of the relations between types of product form sets and organization structures.
SEPARABLE PRODUCT FORMS In the case of independence or separable product forms, the set of product forms and the related linear model are given by the figure obtained from Fig. 1 XI Variables
xo
Objective
[---1[
Xl÷d
Xj
Xl
J Af .A m Am÷l
Constraint sei" (Intertwine cl) 5 " "
Near separability)
FIG. 1. 585
AK
Lit O0
optimal costly solution procedure inefficient
feasible optimal solution costly solution procedure efficient (?)
not feasible
not feasible
optimal less costly solution procedure efficient
feasible
feasible optimal solution costly solution procedure efficient (?)
feasible
Centralized
feasible nonoptimal solution less costly solution procedure efficient (?)
feasible optimal solution costly solution procedure efficient (?)
feasible optimal solution costly solution procedure efficient (D
feasible but unnecessary
feasible but unnecessary
feasible nonoptimal solution less costly solution procedure efficient (?)
Budgeting approach
feasible optimal solution costly solution procedure efficient (?)
feasible optimal solution costly solution procedure efficient (D
feasibly but unnecessary
Pricing approach, i.e. transfer pricing
Entries refer to the following: a. Feasibility of structure; b. Nature of model solution produced by structure; c. Cost of solution procedure; d. Efficiency of structure.
non-separable
I n t eor rtwined:(!
separable
Sparable Technological interdependence of product forms associated with a chosen set of cooperative market relations
Natural decomposition
Structure Arbitrary resource allocation for decomposition
TABLE 1. FEASIBILITY A N D OUTCOMES OF ORGANIZATION STRUCTURE GIVEN INTERDEPENDENCE OF P R O D U C T FORMS
e~
0~
-¢
Omega, Vol. 4, No. 5 ~hen we ignore altogether the boxes marked (near separability) and (intertwined). This is a case, for example, of a firm that sells tires {xl ..... x,}and batteries{xz+~ ..... xs}. The J variables can be partitioned such that variables 1 through l use inputs 1 through m only; and similarly, variables l+1 through J use inputs m + l through K only. The set of potential cooperative market relations chosen is that reflected by the particular processes, x~ ..... xj, and the forms of their corresponding vectors (S~,P~,aj,bj). This formulation of the problem is naturally decomposable into 2 problems, tire problems and battery problems. Let division 1 be assigned responsibility for {x~,...,x~} given resources {A~..... Am}. Similarly, division 2 sets {xz+ ~..... x j} given resources{Am+ 1..... Ax}. The coordination issue between divisions 1 and 2, tires and batteries, is non-existent--they set no dependent variables and share no common resources. Consider a change in product form of a simple kind, e.g. it is proposed that Sj --->Sj + ASj and that a~j --~ a~j + Aa w More cord, or more rubber could be added to a tire. Or, thicker plates are put in a battery. If both ASj and Aatj > 0, then the change involves putting a larger effort into the product and receiving a larger selling price for it. This product form change could be thought of as a 'quality' change. We suggest that minor adjustments in quality, not involving new technology, have minor, if any, organizational implications. For any proposed change, two issues arise: first, is the change desired, and second, does the change in product form require an organizational change as well ? The proposal that asj --->aij -I- Aatj brings about a trivial change in formulation, for i _< m, and the question on the organization structure has an obvious answer. There is no change in the organization structure. The firm expands the model to include the alternative process given by: (S~ + ASs, Pj, (alj,...,a u + Aau ..... amj, 0,...,0 ..... 0), bj), and solves the new but still naturally decomposable problem. A marginal approach, not involving a new total solution would be to compare the marginal revenue, ASj, with the marginal cost, Aalj • Al where Al is the shadow price (dual variable value) of the current optimal solution. Only if the marginal revenue exceeds the marginal cost, is the proposed product form change desirable.
NEAR SEPARABILITY The nearly separable case is more complex. It is described by the figure obtained from Fig. 1 when only the box marked intertwined is ignored. Consider the 1st process for division 1, and let S~ ~ $1 -b AS1 be the price change and am+ ~. ~ = 0 --> am+ a.~ > 0. This change eliminates the previous simplicity, and the natural decomposition; the first division changes its product such that it 587
Baligh, Burton--Organization Structure requires the use of a resource, m + W , which is currently used by, and the responsibility of, the second division. Ignoring the organizational issue for the moment, we could proceed as before to analyze the profitability of the proposed change by either incorporating the proposal into the total firm model, or by comparing the marginal revenue ASt for the new tire with the marginal cost, am+a. 1 "Am+l. The first calculation is not possible with a naturally decomposed structure, although the second calculation is. If the change is desirable at this level of analysis, i.e. AS1 > am ÷ 1.1 " A,, + x the next step is implementation and that involves changing the organization structure and incurring further costs. It is possible to ignore the fact that the m + l st resource used by divisions 1 and 2 is really the same, and thus, the tire division would procure its own electrolysis setup, and the battery division would remain with Am+ ~. This is an arbitrary resource allocation structure. The change in cooperative market relations is associated with a particular change in formulation of the model. Clearly, this reduces the coordination cost, but would increase the resource cost as it would only be by accident that an optimal allocation of the m-+-I st resource, electrolysis capacity, would be independently attained. Galbraith's [7] "creation of self-contained tasks" is an identical approach. Other organization structures to be considered may be resource guided (budgeting) or price-guided (transfer pricing) or centralized. In either of the first two cases, it is necessary to set up a central coordinator who must consider the best allocation of the m + 1st resource between the divisions. The centralized organization has been considered previously, and there remains a comparison among only the other two. The resource guided organization [5, 8] would operate in the following manner. An initial allocation of the m + pt resource would be made to divisions 1 and 2. Using this trial allocation, they would then make plans and determine the marginal value of the m--kP t resource, and report the value back to the central coordinator. The central coordinator would adjust the allocation giving the division with the higher marginal benefit a little more, the other a little less. Continuing this procedure, it is sufficient for an optimal allocation that the central coordinator terminate the process when both divisions obtain the same marginal benefit from the resource. Clearly, this planning process is costly. There is the required central coordinator. Each division must plan at least once, and possibly for a large number of trials. The number depends critically upon how 'good' the initial trial allocation is. The closer it is to the best allocation, the fewer trials required. This process is costly and time consuming. The price guided system [3] would proceed as follows: The central coordinator 'owns' the mq-1 st resource and sells it to the divisions. The central coordinator would compare the demand against the amount available. If the demand exceeds the availability, he would raise the price; and vice versa. The central coordinator would stop where the demand did not exceed the avail588
Omega, Vol. 4, No. 5
ability (i.e. the market is cleared). This system could involve a large number of iterations, depending upon how well the price is set. Our remarks concerning the trade-offs in the resource guided system apply here as well. A question remains concerning the relative desirability of the resource guided system visa vis the price guided system. This is an empirical question concerning their relative efficiencies and the answer depends upon the particular situation.
INTERTWINED PRODUCT FORMS The simplest intertwined situation would involve a product say Xo, whose production requires inputs from all K resources, i.e. (So, Po, ao, bo) is such that ako > 0, y k. The problem is described by the whole of Fig. 1. For the tire and battery firm, a product using all the resources of both divisions may be a battery covered in a tire rubber casing for protection. Here, the array of possible organization structures is the same as the nearly separable situation and the analysis of the previous section applies. However, the relative efficiences of different structures may not be the same. It is quite clear that in this case the central coordinator has a larger problem--he has either more resources to budget, or more transfer prices to set. In either of the budgeting or transfer price situations, it is likely that this set of cooperative market relations will involve more costly coordinated solution procedures, and higher returns to such procedures than will the set of nearly separable cooperative market relations. As a result, the problem of finding the best structure in the intertwined case can be expected to be more critical to the organization's well being than in the nearly separable case.
CAPITAL BUDGETING, COOPERATIVE MARKET RELATIONS AND ORGANIZATION STRUCTURE In the separable product form section, we considered the change in product form reflected by Aatj ~ 0 with a price change ASj. As a short-run consideration, we require AS~ > Aatj" At for the change to be profitable. Thus, for a single period of unit length the differential cash flow is ASj -- Aatj" At. Let us assume this obtains for all time periods. Then, the present value of this change is: T AS~--Aao •;~t 27 t = 0 (1 +r)' 589
Baligh, Burton--Organization Structure Where T is the life of the new organization and r is the discount rate. This present value must be higher than any one time cost required in changing the product form or the organization's structure. Let R be the one time cost of changing the organization structure and product form of xl, giving us the near separability form. The differential cash flow is ASt
-- am+l,1
" hm+t
-- w
where w is the recurring added operating costs for the new organization. Then, if the present value T
27 t=0
AS1 -- a,n+t,t
" Am+t -- w
(1 + r)'
is greater than the initial cost R, the change is profitable. Clearly, there exists a different set of one time costs R and differential operating costs w for each organizational structure, whether it is centralized, arbitrarily decomposed or decomposed and coordinated by a budgeting or pricing approach. These form a set of exclusive and exhaustive structures from which to choose one to accompany a product form change. The best choice is the one for which the present value exceeds the initial costs by the greatest amount. Thus, for each product form the best structure over the long run is identified, and the information necessary to compare different pairs of product form change and best organization structure is supplied. It is our observation that capital budgeting analysis of new products frequently ignores organizational issues and the costs involved in making organizational changes, if they are required. ORGANIZATION STRUCTURE AND THE POTENTIAL SET OF COOPERATIVE MARKET RELATIONS Knowledge of the complexity of solving certain kinds of formulated linear models may be used in the process of model formulation. The anticipated needs of structures may be used to alter the set of potential cooperative market relations in the initial formulation. In the process of choosing a structure, one may deliberately remove potential cooperative relations from consideration, i.e. change the initial formulation, since the presence of some such elements in the set may make solution procedures of all types (all structures) much more costly. The decision to remove such cooperative market relations may well precede any attempt at model solution. For example, our tire and battery firm produces two sets of products that allow for a natural decomposition of the production divisions, i.e. car tires and batteries of various kinds and sizes. The retail marketing of the two sets of products in the organization's own retail stores involves the use of resources common to both, as suggested in Fig. 2, e.g. resources Ar+l ..... Ak. These resources, involving distribution, retail advertising, space, etc., are many in 590
Omega, Vol. 4, No. 5 number, and the coordination of their use by both products involves high costs. When the two sets of products are sold only at wholesale, these resources are few or zero in number and the costs of coordinating the marketing efforts of the two products are low. Any advantages to retailing of the products may well be more than counter-balanced by the increased costs of coordination. The firm may choose to stay out of the cooperative market relations involved in retailing. By so choosing it has allowed the requirements of structure to determine its cooperative market relations. The organization structure and implemented set of cooperative market relations have an effect on the area which elements of the organization search for alterations of potential cooperative market relations. Suppose the firm had found it profitable to sell car tires and batteries at retail in its own stores, and had created a division to coordinate the marketing of both kinds of products. Under these conditions the retail stores division would seek new cooperative market relations in the form of new products which would improve the assortment of goods in its retail stores. It might seek automobile accessories to sell in its retail stores. If the firm had chosen to sell its car batteries and tires at wholesale, the car tire division may seek to use its expertise in its new cooperative relations and maintain its independence of the battery division by manufacturing airplane tires. In this case the absence of the retailing division reduces the pressure in the firm for the search for products compatible with retail marketing of tires and car batteries. The search and pressures are much more likely to be for those products compatible with the production of car batteries and car tires. Independent divisions may be expected to seek changes in product forms that maintain their independence. Further, the absence of a central coordination unit is likely to mean that no pressure exists to expand the interdependence between divisions, and hence the operations of such a central unit. Suppose the formulation were the intertwined one described by Fig. 1. Here x t
xt _ ~
Objective [
x~
I At
Constraint set
Am
~r+[
AK FIG. 2.
591
Baligh, Burton--Organization Structure a centralized structure is costly, and a decentralized structure with Xo in either of two divisions or comprising a division by itself is likely to involve many solution iterations for coordination. A decentralized structure without coordination, i.e. a solution procedure that produces a feasible but non-maximizing solution, may be best. Whatever estimate one may have regarding the best structure for this formulation one should consider the possibility of altering the formulation by removing Xo from the set of potential cooperative market solutions altogether. This would yield a set of separable product forms. Thus, using the procedures outlined earlier a decision may be made to formulate the simpler model, leaving out of consideration the cooperative relations involved in Xo and to choose a decentralized structure given that certain parameters, e.g. price of Xo, are within certain ranges. It may also be planned to alter the formulation and the structure if the product Xo'S revenues and variable costs enter other ranges. One can conclude that, because of its effects on structure, a product form such as that given by Xo in Fig. 1 is not likely to be organizationally viable unless it is a major contributor to the firm's profit. The larger the number of such products the more likely that any one will be viable given any contribution it makes to profits. If the initial formulation had a set of product forms with a large set of shared resources (markets) of the form described in Fig. 2, and the structure were centralized, then the central decision unit is likely to search for forms that would improve the use of the shared resources even if it added complexities by removing a partial natural decomposition. The addition of Xo product forms is more likely to follow from the structure given in Fig. 2. Such forms are those to which the central decision unit owes its existence, and which involve it in a 'least learning' expansion process. The extent to which the new form will remove partial natural decompositions may well be expected to depend on the political power relationships between the central coordination unit and the divisions representing the partial natural decomposition. Not only is the area of search likely to be dependent on structure as a result of the behavior of individuals, but formulations turned up by the search will be compared with an eye to the fact that structure changes tend to involve large setup costs. To go from a centralized structure to a decentralized one requires people to be involved in computation, whereas before they had not been so engaged. To go from less coordinated decentralized to more coordinated decentralized structures requires an increase in the information processing done by individuals, and an increase in their number, and in the specificity of the decision rules to which they must adhere. Structural inertia may specify future market developments unless these are explicitly planned. Meanwhile planned future market developments cannot ignore these structural requirements, and the costs they may entail. These are the costs of re-educating decision makers and overcoming structural inertia. 592
Omega, 1Iol. 4, No. 5 SUMMARY The paper develops a conceptually operational view of both structure and the cooperative market relations that makes the two decision problems compatible for simultaneous treatment. The vehicle used is a tire and battery firm viewed as a linear activity analysis model. The decision on cooperative market relations is cast as one involving a choice of a potential set of product forms. The choice is equivalent to the choice of the formulation of a linear model of the firm, or some small set of such formulations. From this set of potential relations there will emerge a subset of cooperative relations which the organization will choose to have with its market environment. The particular manner in which a given model formulation affects the costs and returns to various structures has been analyzed. These costs and returns are those of different methods of solution, i.e. structures. The manner in which a structure may be used to choose from a set of potential cooperative market relations (model formulations) has been identified. Using a capital budgeting framework, we are able to suggest a normative criterion for the comparison of proposed changes in product form and organization structure and in long run capital expenditure on resources fixed in the short run. Finally the demands of structure costs, i.e. solution procedure costs, on problem formulations and hence on the potential and therefore chosen cooperative relation sets has been investigated and identified. REFERENCES 1. ATK1NSD (1974) Managerial decentralization and decomposition in mathematical programming. OpL Res. Q. 25(4), 615-624. 2. BALIGrt HH and RICI~ARTZLE (1967) Vertical Market Structures. Allyn and Bacon, Boston. 3. BAUMOLW and E~IAN T (1964) Decomposition, pricing for decentralization and external economies. Mgmt Sci. 11(1), 1-32. 4. BURNS T and STALKER GM (1961) The management of innovation. Tavistock, London. 5. BURTONRM, DAMONWW and LOU6HRIIX~EDW (1974) The economics of decomposition: resource allocation vs. transfer pricing. Decis. Sci. 5(3), 297-310. 6. CHANDLERA n , JR (1962) Strategy and Structure: Chapters in the History of the American Industrial Enterprise. MIT, Cambridge, MA. 7. GALBRArm JAY (1973) Designing Complex Organizations. Addison Wesley, Reading, MA. 8. KORNAIJ and LIPTAKTh (1965) Two-level planning. Eeonometrica 33(1), 141-169. 9. LAWRENCEPR and LORSCHJay W (1969) Developing Organizations: Diagnosis and Action. Addison-Wesley, Reading, MA. 10. MARSCHAKJ (1955) Elements for a theory of teams. Mgmt Sci. 1(2), 127-137. 11. THOMPSONJD (1964) Decision-making, the firm, and the market, in New Perspectives in Organization Research (Eds. COOPERWVg, LEAvrrr HJ and SHELLYMW). John Wiley, New York. 12. THOMPSONJD (1967) Organizations in Action. McGraw-Hill, New York. CORRESPONDENCE: Professor H H Baligh, Graduate School of Business Administration, Duke University, Durham, NC 27706, USA.
&DDRESS FOR
593
Organization Structure and Cooperative Market Relations HELMY H BALIGH RICHARD M BURTON (Received September 1975; in revised form April 1976)
A linear model is used as the vehicle for analyzing some of the interactions between an organization's cooperative market relations (product forms) and its structure (decomposition and coordination). Normative implications for organizational choice, and a set of conclusions concerning the nature of organizational change and growth for practical use are developed. The concept of product form as a description of cooperative market relations is the basis for relating the activities of the firm to its market environment. The decision on product form is viewed as a decision on the resource usage vector, and hence as a decision on the nature of the linear programming model formulated. The decision on the decomposition of this linear model and on the solution procedure are viewed as decisions on organization structure. They are viewed as decisions on the partitioning of the organization's decision variables into divisions and on the mechanisms used to coordinate these divisions.
THE DECISIONS ON DECOMPOSITION, COORDINATION, AND PRODUCT FORM DECISION p r o b l e m s o n certain aspects o f o r g a n i z a t i o n structure have been widely a n d c o n v e n i e n t l y discussed in t h e c o n t e x t o f the d e c o m p o s i t i o n a n d s o l u t i o n p r o c e d u r e s o f a linear p r o g r a m m i n g m o d e l [1, 3, 5, 8]. T h e p r o c e d u r e followed in solving a linear m o d e l d e t e r m i n e s elements o f the o r g a n i z a t i o n ' s structure viz. the w a y the o r g a n i z a t i o n is d e c o m p o s e d , a n d the m e c h a n i s m s used for its c o o r d i n a t i o n [1, 3, 5, 8, 10]. These analyses, however, have started w i t h a given linear m o d e l a n d c o n c e n t r a t e d only o n the s o l u t i o n procedure. I n this p a p e r we c o n s i d e r b o t h the decision o n the linear p r o g r a m m i n g s o l u t i o n p r o c e d u r e a n d the decisions on the n a t u r e o f the m o d e l a n d m o d i fications in it. W h e r e a s the decision o n a solution p r o c e d u r e is a decision o n o r g a n i z a t i o n structure, the decision on the n a t u r e o f the m o d e l f o r m u l a t e d is a decision o n the firm's p o t e n t i a l c o o p e r a t i v e relations. T h e latter is a decision on
The authors are grateful for the help they received in making revisions of the paper from several of their colleagues in GSBA. 583
Baligh, BurtonmOrganization Structure
relations of the organization to its environment. Our analysis of these relations is thus a limited focus variation of the general analysis of the relation between structure of the organization and its environment. The literature on this topic includes the work of Thompson [11, 12] which focuses on the relation of uncertainty to decision structures. Lawrence and Lorsch's [9] contingency models focus on relations between environmental uncertainty and internal structure and degree of decentralization. Burns and Stalker's [4] investigation of electronics firms demonstrates the influence of technological uncertainty and rapid innovation on structure. Finally there is Chandler's [6] historic analysis of the general relations between structure and strategy. Decisions on the organization's cooperative market relations, i.e. on the nature of this one boundary between it and its environment, we term decisions on product form [2]. Product form is discussed in terms of the resource amounts necessary to obtain it. It is a concept that is easily and clearly developed in terms of the linear model, and represents a description of the firm's cooperative relations with its environment. Decisions on product form are decisions on the nature of the linear programming model, and decisions on organization structure are decisions on the decomposition and solution procedures of this model. It is the relations of these two kinds of decisions that is the topic of the paper. The practical significance of the paper lies in its contribution to comprehensive planning for an organization. It points out some of the needs of organizational structure which arise from changes in the firm's relations with its market environment. It identifies the effects which the existing organizational structure has on the development of changes in the firm's relations with its markets. By showing the nature of the interconnection between the two decisions on organization structure and product form the paper identifies general ramifications of each alone. It supplies relations that must be specifically identified if planning is to become more comprehensive. These practical implications will become more apparent through our use of a simple example. We shall use the case of an organization which manufactures and sells two product lines--tires and batteries, to illustrate our analysis of the possible effects of changes in the product form in each line on organization structure and vice versa. The analysis uses the linear model of the firm which isJ max 27 S'jx~ y=l J s.t. 27 ak~xj<_A~ k = l . . . . . K. j=l xl>_0 j = l ..... d. I where s'j - sj - e~ z C~blj, i=1 584
Omega, VoL 4, No. 5
and xj akj bu Ak Cl
/,j sj
= = = = --=
S'j
=--
number of units o f p r o d u c t j ; amount of fixed resource k required for a unit of j ; amount of variable resource/required for a unit o f j ; upper bound of fixed resource, k, k = 1. . . . . K; unit variable cost for input, i; entry price, or purchase price, for process,j; exit price, or selling price, forprocessj; net contribution to p r o f i t , j = 1. . . . . J.
Further, let aj = (a~j, a 2 j , . . . , a k i . . . . ,axj) and bj = (bu,b2 J . . . . . b u . . . . ,bu). The vector (Sj,Pj,aj,bj) is associated with the j t h process or activity. The jth product's form is described by such a vector, and the firm's cooperative market relations may thus be described by a set of vectors. Any change in these cooperative market relations or product forms would be reflected by changes in the set or in the components of its vector elements. An initial formulation of a linear model entails a decision on a given set of potential product forms which the firm is to consider. The solution of the model involves picking a subset of these to implement. The decision on the process by which this linear model is solved repeatedly to meet parameter changes involves decisions on the decomposition of the model and on the mechanisms to use to coordinate the segment solutions. These decisions are decisions on organization structure. Alterations in potential cooperative market relations mean changes in the form of the linear model to be solved and hence possible changes in structure. Table 1 contains a summary of the relations between types of product form sets and organization structures.
SEPARABLE PRODUCT FORMS In the case of independence or separable product forms, the set of product forms and the related linear model are given by the figure obtained from Fig. 1 XI Variables
xo
Objective
[---1[
Xl÷d
Xj
Xl
J Af .A m Am÷l
Constraint sei" (Intertwine cl) 5 " "
Near separability)
FIG. 1. 585
AK
Lit O0
optimal costly solution procedure inefficient
feasible optimal solution costly solution procedure efficient (?)
not feasible
not feasible
optimal less costly solution procedure efficient
feasible
feasible optimal solution costly solution procedure efficient (?)
feasible
Centralized
feasible nonoptimal solution less costly solution procedure efficient (?)
feasible optimal solution costly solution procedure efficient (?)
feasible optimal solution costly solution procedure efficient (D
feasible but unnecessary
feasible but unnecessary
feasible nonoptimal solution less costly solution procedure efficient (?)
Budgeting approach
feasible optimal solution costly solution procedure efficient (?)
feasible optimal solution costly solution procedure efficient (D
feasibly but unnecessary
Pricing approach, i.e. transfer pricing
Entries refer to the following: a. Feasibility of structure; b. Nature of model solution produced by structure; c. Cost of solution procedure; d. Efficiency of structure.
non-separable
I n t eor rtwined:(!
separable
Sparable Technological interdependence of product forms associated with a chosen set of cooperative market relations
Natural decomposition
Structure Arbitrary resource allocation for decomposition
TABLE 1. FEASIBILITY A N D OUTCOMES OF ORGANIZATION STRUCTURE GIVEN INTERDEPENDENCE OF P R O D U C T FORMS
e~
0~
-¢
Omega, Vol. 4, No. 5 ~hen we ignore altogether the boxes marked (near separability) and (intertwined). This is a case, for example, of a firm that sells tires {xl ..... x,}and batteries{xz+~ ..... xs}. The J variables can be partitioned such that variables 1 through l use inputs 1 through m only; and similarly, variables l+1 through J use inputs m + l through K only. The set of potential cooperative market relations chosen is that reflected by the particular processes, x~ ..... xj, and the forms of their corresponding vectors (S~,P~,aj,bj). This formulation of the problem is naturally decomposable into 2 problems, tire problems and battery problems. Let division 1 be assigned responsibility for {x~,...,x~} given resources {A~..... Am}. Similarly, division 2 sets {xz+ ~..... x j} given resources{Am+ 1..... Ax}. The coordination issue between divisions 1 and 2, tires and batteries, is non-existent--they set no dependent variables and share no common resources. Consider a change in product form of a simple kind, e.g. it is proposed that Sj --->Sj + ASj and that a~j --~ a~j + Aa w More cord, or more rubber could be added to a tire. Or, thicker plates are put in a battery. If both ASj and Aatj > 0, then the change involves putting a larger effort into the product and receiving a larger selling price for it. This product form change could be thought of as a 'quality' change. We suggest that minor adjustments in quality, not involving new technology, have minor, if any, organizational implications. For any proposed change, two issues arise: first, is the change desired, and second, does the change in product form require an organizational change as well ? The proposal that asj --->aij -I- Aatj brings about a trivial change in formulation, for i _< m, and the question on the organization structure has an obvious answer. There is no change in the organization structure. The firm expands the model to include the alternative process given by: (S~ + ASs, Pj, (alj,...,a u + Aau ..... amj, 0,...,0 ..... 0), bj), and solves the new but still naturally decomposable problem. A marginal approach, not involving a new total solution would be to compare the marginal revenue, ASj, with the marginal cost, Aalj • Al where Al is the shadow price (dual variable value) of the current optimal solution. Only if the marginal revenue exceeds the marginal cost, is the proposed product form change desirable.
NEAR SEPARABILITY The nearly separable case is more complex. It is described by the figure obtained from Fig. 1 when only the box marked intertwined is ignored. Consider the 1st process for division 1, and let S~ ~ $1 -b AS1 be the price change and am+ ~. ~ = 0 --> am+ a.~ > 0. This change eliminates the previous simplicity, and the natural decomposition; the first division changes its product such that it 587
Baligh, Burton--Organization Structure requires the use of a resource, m + W , which is currently used by, and the responsibility of, the second division. Ignoring the organizational issue for the moment, we could proceed as before to analyze the profitability of the proposed change by either incorporating the proposal into the total firm model, or by comparing the marginal revenue ASt for the new tire with the marginal cost, am+a. 1 "Am+l. The first calculation is not possible with a naturally decomposed structure, although the second calculation is. If the change is desirable at this level of analysis, i.e. AS1 > am ÷ 1.1 " A,, + x the next step is implementation and that involves changing the organization structure and incurring further costs. It is possible to ignore the fact that the m + l st resource used by divisions 1 and 2 is really the same, and thus, the tire division would procure its own electrolysis setup, and the battery division would remain with Am+ ~. This is an arbitrary resource allocation structure. The change in cooperative market relations is associated with a particular change in formulation of the model. Clearly, this reduces the coordination cost, but would increase the resource cost as it would only be by accident that an optimal allocation of the m-+-I st resource, electrolysis capacity, would be independently attained. Galbraith's [7] "creation of self-contained tasks" is an identical approach. Other organization structures to be considered may be resource guided (budgeting) or price-guided (transfer pricing) or centralized. In either of the first two cases, it is necessary to set up a central coordinator who must consider the best allocation of the m + 1st resource between the divisions. The centralized organization has been considered previously, and there remains a comparison among only the other two. The resource guided organization [5, 8] would operate in the following manner. An initial allocation of the m + pt resource would be made to divisions 1 and 2. Using this trial allocation, they would then make plans and determine the marginal value of the m--kP t resource, and report the value back to the central coordinator. The central coordinator would adjust the allocation giving the division with the higher marginal benefit a little more, the other a little less. Continuing this procedure, it is sufficient for an optimal allocation that the central coordinator terminate the process when both divisions obtain the same marginal benefit from the resource. Clearly, this planning process is costly. There is the required central coordinator. Each division must plan at least once, and possibly for a large number of trials. The number depends critically upon how 'good' the initial trial allocation is. The closer it is to the best allocation, the fewer trials required. This process is costly and time consuming. The price guided system [3] would proceed as follows: The central coordinator 'owns' the mq-1 st resource and sells it to the divisions. The central coordinator would compare the demand against the amount available. If the demand exceeds the availability, he would raise the price; and vice versa. The central coordinator would stop where the demand did not exceed the avail588
Omega, Vol. 4, No. 5
ability (i.e. the market is cleared). This system could involve a large number of iterations, depending upon how well the price is set. Our remarks concerning the trade-offs in the resource guided system apply here as well. A question remains concerning the relative desirability of the resource guided system visa vis the price guided system. This is an empirical question concerning their relative efficiencies and the answer depends upon the particular situation.
INTERTWINED PRODUCT FORMS The simplest intertwined situation would involve a product say Xo, whose production requires inputs from all K resources, i.e. (So, Po, ao, bo) is such that ako > 0, y k. The problem is described by the whole of Fig. 1. For the tire and battery firm, a product using all the resources of both divisions may be a battery covered in a tire rubber casing for protection. Here, the array of possible organization structures is the same as the nearly separable situation and the analysis of the previous section applies. However, the relative efficiences of different structures may not be the same. It is quite clear that in this case the central coordinator has a larger problem--he has either more resources to budget, or more transfer prices to set. In either of the budgeting or transfer price situations, it is likely that this set of cooperative market relations will involve more costly coordinated solution procedures, and higher returns to such procedures than will the set of nearly separable cooperative market relations. As a result, the problem of finding the best structure in the intertwined case can be expected to be more critical to the organization's well being than in the nearly separable case.
CAPITAL BUDGETING, COOPERATIVE MARKET RELATIONS AND ORGANIZATION STRUCTURE In the separable product form section, we considered the change in product form reflected by Aatj ~ 0 with a price change ASj. As a short-run consideration, we require AS~ > Aatj" At for the change to be profitable. Thus, for a single period of unit length the differential cash flow is ASj -- Aatj" At. Let us assume this obtains for all time periods. Then, the present value of this change is: T AS~--Aao •;~t 27 t = 0 (1 +r)' 589
Baligh, Burton--Organization Structure Where T is the life of the new organization and r is the discount rate. This present value must be higher than any one time cost required in changing the product form or the organization's structure. Let R be the one time cost of changing the organization structure and product form of xl, giving us the near separability form. The differential cash flow is ASt
-- am+l,1
" hm+t
-- w
where w is the recurring added operating costs for the new organization. Then, if the present value T
27 t=0
AS1 -- a,n+t,t
" Am+t -- w
(1 + r)'
is greater than the initial cost R, the change is profitable. Clearly, there exists a different set of one time costs R and differential operating costs w for each organizational structure, whether it is centralized, arbitrarily decomposed or decomposed and coordinated by a budgeting or pricing approach. These form a set of exclusive and exhaustive structures from which to choose one to accompany a product form change. The best choice is the one for which the present value exceeds the initial costs by the greatest amount. Thus, for each product form the best structure over the long run is identified, and the information necessary to compare different pairs of product form change and best organization structure is supplied. It is our observation that capital budgeting analysis of new products frequently ignores organizational issues and the costs involved in making organizational changes, if they are required. ORGANIZATION STRUCTURE AND THE POTENTIAL SET OF COOPERATIVE MARKET RELATIONS Knowledge of the complexity of solving certain kinds of formulated linear models may be used in the process of model formulation. The anticipated needs of structures may be used to alter the set of potential cooperative market relations in the initial formulation. In the process of choosing a structure, one may deliberately remove potential cooperative relations from consideration, i.e. change the initial formulation, since the presence of some such elements in the set may make solution procedures of all types (all structures) much more costly. The decision to remove such cooperative market relations may well precede any attempt at model solution. For example, our tire and battery firm produces two sets of products that allow for a natural decomposition of the production divisions, i.e. car tires and batteries of various kinds and sizes. The retail marketing of the two sets of products in the organization's own retail stores involves the use of resources common to both, as suggested in Fig. 2, e.g. resources Ar+l ..... Ak. These resources, involving distribution, retail advertising, space, etc., are many in 590
Omega, Vol. 4, No. 5 number, and the coordination of their use by both products involves high costs. When the two sets of products are sold only at wholesale, these resources are few or zero in number and the costs of coordinating the marketing efforts of the two products are low. Any advantages to retailing of the products may well be more than counter-balanced by the increased costs of coordination. The firm may choose to stay out of the cooperative market relations involved in retailing. By so choosing it has allowed the requirements of structure to determine its cooperative market relations. The organization structure and implemented set of cooperative market relations have an effect on the area which elements of the organization search for alterations of potential cooperative market relations. Suppose the firm had found it profitable to sell car tires and batteries at retail in its own stores, and had created a division to coordinate the marketing of both kinds of products. Under these conditions the retail stores division would seek new cooperative market relations in the form of new products which would improve the assortment of goods in its retail stores. It might seek automobile accessories to sell in its retail stores. If the firm had chosen to sell its car batteries and tires at wholesale, the car tire division may seek to use its expertise in its new cooperative relations and maintain its independence of the battery division by manufacturing airplane tires. In this case the absence of the retailing division reduces the pressure in the firm for the search for products compatible with retail marketing of tires and car batteries. The search and pressures are much more likely to be for those products compatible with the production of car batteries and car tires. Independent divisions may be expected to seek changes in product forms that maintain their independence. Further, the absence of a central coordination unit is likely to mean that no pressure exists to expand the interdependence between divisions, and hence the operations of such a central unit. Suppose the formulation were the intertwined one described by Fig. 1. Here x t
xt _ ~
Objective [
x~
I At
Constraint set
Am
~r+[
AK FIG. 2.
591
Baligh, Burton--Organization Structure a centralized structure is costly, and a decentralized structure with Xo in either of two divisions or comprising a division by itself is likely to involve many solution iterations for coordination. A decentralized structure without coordination, i.e. a solution procedure that produces a feasible but non-maximizing solution, may be best. Whatever estimate one may have regarding the best structure for this formulation one should consider the possibility of altering the formulation by removing Xo from the set of potential cooperative market solutions altogether. This would yield a set of separable product forms. Thus, using the procedures outlined earlier a decision may be made to formulate the simpler model, leaving out of consideration the cooperative relations involved in Xo and to choose a decentralized structure given that certain parameters, e.g. price of Xo, are within certain ranges. It may also be planned to alter the formulation and the structure if the product Xo'S revenues and variable costs enter other ranges. One can conclude that, because of its effects on structure, a product form such as that given by Xo in Fig. 1 is not likely to be organizationally viable unless it is a major contributor to the firm's profit. The larger the number of such products the more likely that any one will be viable given any contribution it makes to profits. If the initial formulation had a set of product forms with a large set of shared resources (markets) of the form described in Fig. 2, and the structure were centralized, then the central decision unit is likely to search for forms that would improve the use of the shared resources even if it added complexities by removing a partial natural decomposition. The addition of Xo product forms is more likely to follow from the structure given in Fig. 2. Such forms are those to which the central decision unit owes its existence, and which involve it in a 'least learning' expansion process. The extent to which the new form will remove partial natural decompositions may well be expected to depend on the political power relationships between the central coordination unit and the divisions representing the partial natural decomposition. Not only is the area of search likely to be dependent on structure as a result of the behavior of individuals, but formulations turned up by the search will be compared with an eye to the fact that structure changes tend to involve large setup costs. To go from a centralized structure to a decentralized one requires people to be involved in computation, whereas before they had not been so engaged. To go from less coordinated decentralized to more coordinated decentralized structures requires an increase in the information processing done by individuals, and an increase in their number, and in the specificity of the decision rules to which they must adhere. Structural inertia may specify future market developments unless these are explicitly planned. Meanwhile planned future market developments cannot ignore these structural requirements, and the costs they may entail. These are the costs of re-educating decision makers and overcoming structural inertia. 592
Omega, 1Iol. 4, No. 5 SUMMARY The paper develops a conceptually operational view of both structure and the cooperative market relations that makes the two decision problems compatible for simultaneous treatment. The vehicle used is a tire and battery firm viewed as a linear activity analysis model. The decision on cooperative market relations is cast as one involving a choice of a potential set of product forms. The choice is equivalent to the choice of the formulation of a linear model of the firm, or some small set of such formulations. From this set of potential relations there will emerge a subset of cooperative relations which the organization will choose to have with its market environment. The particular manner in which a given model formulation affects the costs and returns to various structures has been analyzed. These costs and returns are those of different methods of solution, i.e. structures. The manner in which a structure may be used to choose from a set of potential cooperative market relations (model formulations) has been identified. Using a capital budgeting framework, we are able to suggest a normative criterion for the comparison of proposed changes in product form and organization structure and in long run capital expenditure on resources fixed in the short run. Finally the demands of structure costs, i.e. solution procedure costs, on problem formulations and hence on the potential and therefore chosen cooperative relation sets has been investigated and identified. REFERENCES 1. ATK1NSD (1974) Managerial decentralization and decomposition in mathematical programming. OpL Res. Q. 25(4), 615-624. 2. BALIGrt HH and RICI~ARTZLE (1967) Vertical Market Structures. Allyn and Bacon, Boston. 3. BAUMOLW and E~IAN T (1964) Decomposition, pricing for decentralization and external economies. Mgmt Sci. 11(1), 1-32. 4. BURNS T and STALKER GM (1961) The management of innovation. Tavistock, London. 5. BURTONRM, DAMONWW and LOU6HRIIX~EDW (1974) The economics of decomposition: resource allocation vs. transfer pricing. Decis. Sci. 5(3), 297-310. 6. CHANDLERA n , JR (1962) Strategy and Structure: Chapters in the History of the American Industrial Enterprise. MIT, Cambridge, MA. 7. GALBRArm JAY (1973) Designing Complex Organizations. Addison Wesley, Reading, MA. 8. KORNAIJ and LIPTAKTh (1965) Two-level planning. Eeonometrica 33(1), 141-169. 9. LAWRENCEPR and LORSCHJay W (1969) Developing Organizations: Diagnosis and Action. Addison-Wesley, Reading, MA. 10. MARSCHAKJ (1955) Elements for a theory of teams. Mgmt Sci. 1(2), 127-137. 11. THOMPSONJD (1964) Decision-making, the firm, and the market, in New Perspectives in Organization Research (Eds. COOPERWVg, LEAvrrr HJ and SHELLYMW). John Wiley, New York. 12. THOMPSONJD (1967) Organizations in Action. McGraw-Hill, New York. CORRESPONDENCE: Professor H H Baligh, Graduate School of Business Administration, Duke University, Durham, NC 27706, USA.
&DDRESS FOR
593