Evaluating orders allocation within networks of firms

ARTICLE IN PRESS

Int. J. Production Economics 86 (2003) 233–249

Evaluating orders allocation within networks of firms A. Hammami*, P. Burlat, J.P. Campagne Ecole Nationale Sup!erieure des Mines de Saint Etienne, 158 cours Fauriel, Saint Etienne 42023, France Received 7 January 2002; accepted 26 February 2003

Abstract In a context of profound transformation of the relations between firms, an organizational paradigm is developing rapidly: the network. Networks of firms are specific co-ordination modes between market and hierarchy, and need collaborative tools to regulate their activities fairly and to limit opportunism. This paper exposes a method to calculate satisfying routes for customers’ orders within manufacturing networks of SMEs. This method aims at designing the routing of activities, so as to meet the customers’ needs in terms of cost, quality and delivery time (short-term performance constraints), and to promote learning processes and skills exchanges within the network (long-term performance criteria). The method is illustrated with a case study. r 2003 Elsevier B.V. All rights reserved. Keywords: Performance analysis; Networks; Learning; Optimization problems; Allocation

1. Introduction This article deals with ‘‘networks of firms’’, i.e. virtual industrial structures linked with horizontal agreements (unlike the ‘‘firm network’’ managed by a mainspring firm controlling a vertical industrial architecture). Those networks are made of independent firms virtually linked together to achieve a goal. Different types of networks can be identified according to the nature of the relations that federate their members, e.g. Poulin et al. (1994): purchasing network (economies of scale for purchases and supplies), production network (joint production), new market-oriented network (shar*Corresponding author. Tel.: 33-4-77-42-6636; fax: 33-4-7742-6666. E-mail address: [email protected] (A. Hammami).

ing new business services to increase turn over), quality certification network (sharing quality experts to obtain ISO 9000 certification), data exchange standardization network (constructing and adopting common norms to exchange data), etc. These types of networks are not mutually exclusive. For example, a group may correspond to a production network and at the same time to a purchasing network. Networks are particular organizations by the way they are a hybrid form between market and hierarchy. Indeed, inside networks coordination is not carried out through a hierarchical organization (as in the firm) or through price mechanism (as on the market), but through cooperation and interaction between independent firms. For this reason, networks need specific coordination tools to link together activities processed by different firms and to federate independent goals.

0925-5273/03/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0925-5273(03)00066-5

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

234

1.1. Networks of SMEs In that context, our research focuses on manufacturing networks of SMEs. Networks of SMEs are specific because the shareholder and the manager of a SME are often the same person. Co-ordination is then a relevant problem for networks of SMEs, where each partner strongly preserves its independence and often runs its own decision-making processes among the network. Furthermore, different kinds of opportunism (Williamson, 1975) may appear among networks of SMEs, such as *

*

* *

only apparent co-operation (limited effort, lower-quality goods, service below standard, etc.), catch of an excessive share of joint profits (overvalued switching costs, overvaluation of the added value brought), excessive exploitation of a joint resource, personal appropriation of the resources created in common or by other.

Consequently, collaborative decision aid models are required within networks to collaborate fairly and to limit opportunism. 1.2. Learning processes within networks Meanwhile, investigations have shown that acquisition of know-how and experience constitutes the first goal (60%) of co-operation between manufacturers, before economies of scale (Hannoun and Guerrier, 1996). Our own observations and investigations about networking also led us to presume that knowledge exchanging is the main reason for independent firms to join networks (Burlat and Peillon, 2001). Therefore, we assume that the tools to co-ordinate activities must both prevent opportunism and enable learning processes within networks. Consequently, the objective for this paper is to present a method to distribute customers’ orders among the partners of a network. This method aims at co-ordinating activities within a network, so as to meet the customers needs in terms of cost, quality and delivery time (short-term performance constraints), and to promote learning processes and

skills exchanges within the network (long-term performance criteria). The main problem consists in integrating those distinct kinds of objectives in a unique coherent decision aid procedure. We first introduce supporting literature dealing with such decision aid procedures (Section 2). Then we expose the models we use (Section 3). We discuss short-term performance constraints (Section 4) and long-term learning criteria (Section 5) to guide the routing decision process. A synoptic summarizes the method (Section 6), and a case study is presented (Section 7). Finally, we offer further perspectives about this research (conclusion).

2. Supporting literature To study the order allocation problem, we were inspired by research works on the vendor selection problem because of the similarities of both problems. Moreover, the vendor selection problem is widely studied. Hence, the scientific literature is rich in works not only about selection criteria but also about selection methods, their application environment, their advantages, limitations and solutions sets. This section begins with a confrontation of the vendor selection and the order allocation problems. Then, we introduce an overview of the vendor selection problem. A typology of the approaches used for modeling this problem is presented. Finally, we explain the extension of the vendor selection problem as it applies to the order allocation problem. 2.1. Vendor selection problem/order allocation problem The vendor selection problem is associated with deciding how one vendor should be selected from a number of potential alternatives (Dickson, 1966). We define the order allocation problem as the distribution of activities among the partners of a network of firms to satisfy customers’ orders. Thus, it differs from a vendor selection problem by the presence of dependent activities linked up by anteriority constraints.

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

The vendor selection and the order allocation problems are both selection problems. They have often the same selection criteria. However, the order allocation problem is more complicated because the activities are co-dependent: the selection of a partner to carry out an activity depends on the selection of partners for the previous and next activities.

*

2.2. Typology of modeling approaches Several selection criteria and methods have been developed in literature on supplier selection. Dickson (1966) surveyed 273 purchasing managers who identified 23 selection criteria. Weber et al. (1991) reviewed 74 articles: 47 of the articles address multiple criteria. The most mentioned criteria in both studies are: price, delivery, quality, facilities capacity, geographic location and technical capability. Different analytical methods were used in the vendor selection process. A typology of the approaches used for modeling this problem is presented below. 2.2.1. Traditional methods Traditional methods for vendor selection problem: the categorical method (CM), the cost ratio method (CRM) and linear average or weightedpoint method (WPM) had been studied by Timmerman (1986). *

*

Categorical method (CM): for the CM, the decision maker provides a subjective rating to each vendor on each criterion to convey its actual performance. A composite ranking is then calculated. This method is simple, easy and cheap to implement. However, it is a largely intuitive approach relying on personal judgment, ability and experience of the decision maker. Cost ratio method (CRM): is based on cost analysis: a total cost of each purchase is calculated. It is not just the acquisition price, but it includes the buyer’s internal operating costs associated with the quality, delivery and services. This method gives more objective results than the CM. However, it is too complex

235

to implement because of the difficulties in translating all aspects of vendor performance into precise cost figures. Weighted-point method (WPM): considers numerical weights which are assigned to evaluation criteria. The criteria weight is multiplied by a vendor performance score. These products are then totaled to determine a final rating for each vendor. The WPM is less subjective than the CM. However, the decision maker still exercises considerable judgment in determining the weights for the evaluation criteria. The WPM requires that the performance measures be expressed in the same units.

2.2.2. Mathematical programming methods Economical order quantity models (Chakravarty and Martin, 1988; Hwang et al., 1990) and mixed integer optimization programming (Bender et al., 1985; Narasimhan, 1983; Current and Weber, 1994) have been widely used for modeling the vendor selection problem. Other mathematical programming techniques have been applied to the problem such as goal programming (GP) (Buffa and Wade, 1983; Chaudhry et al., 1991; Hajidimitriou and Georgiou, 2000), compromise programming (CP) and multi-objective programming (MOP) (Weber and Ellram, 1993; Weber, 1996; Weber and Desai, 1996; Weber et al., 1998; Weber et al., 2000a, b). *

*

Goal programming (GP): is a mathematical programming technique where rather than attempting to maximize or minimize an objective function directly, the algorithm seeks to minimize the deviations from each goal. The deviations from each goal are minimized according to priority weights assigned to the goal. The GP differs from the other mathematical programs by promoting the satisfaction of objectives rather than an optimization philosophy. Compromise programming (CP): this technique seeks to minimize the deviation from an ideal solution (a fictional solution which fits all criteria perfectly). The deviation from the ideal solution is minimized according to priority weights assigned to evaluation criteria.

ARTICLE IN PRESS 236 *

A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

Multi-objective programming (MOP): is a mathematical program that has a stack of objective functions instead of only one. Hence, it allows various criteria to be evaluated in their own units of measurement. A MOP model provides the decision maker with a set of noninferior solutions rather than a single optimal solution, so he can analyze the impacts of different criteria on the decision.

2.2.3. Cost-based methods These methods: activity-based costing (Roodhooft and Konings, 1996; Degraeve and Roodhooft, 1998) and the total cost of ownership (Ellram, 1995; Degraeve et al., 2000) quantify all the costs associated with the purchasing process throughout the entire value chain of the firm. 2.2.4. Multi-criteria decision aid methods (MCDM) Several MCDM were used for modeling the vendor selection problem such as the analytic hierarchy process (AHP) (Narasimhan, 1983; Nydick and Hill, 1992; Barbarosoglu and Yazgac, 1997; Phuong Ta and Yin Har, 2000), or the interpretive structural modeling (ISM) (Mandal and Deshmukh, 1994). These methods have to be applied to a set of feasible solutions (all constraints are respected). The MCDM provides the manager with different ways of preferences modeling. Besides, most MCDM give a classification of solutions. *

Analytic hierarchy process (AHP): is one of the most used MCDM for vendor selection modeling. The AHP structures the problem as a hierarchy of criteria, sub-criteria and alternatives. Pair-wise comparisons are then processed to determine the criteria weights. The alternatives are also compared in a pair-wise fashion with regard to each criterion. A final score is then determined for each alternative. The AHP method has the advantage of structuring the problem in a hierarchical way. The AHP, although very efficient for small problems, becomes difficult to use for extensive problems because of the number of pair-wise comparisons needed.

*

Interpretive structural modeling (ISM): is an interactive methodology that uses the decision maker judgment to build relationships among specific items that define the problem. The ISM method has been used in vendor selection problems to show the inter-relationship between the criteria.

2.2.5. Statistical methods Recently, several papers based on statistical methods were published for modeling the vendor selection problem: Mummalaneni et al. (1996) used statistical analysis, Verma and Pullman (1998) suggested a discrete choice analysis experiment model, and Petroni and Braglia (2000) offered a model based on principal component analysis. Other techniques have been applied to the vendor selection problem: Human judgment models (Patton, 1996), neural networks (Siying et al., 1997) combined methods such as the combination of linear programming and AHP (Gohdsypour and O’Brien, 1988) or WPM and Monte-Carlo simulation (Thompson, 1990). The vendor selection method can be adapted to model the order allocation problem by taking into account, e.g. in the form of precedence constraints, the dependence between the activities. Many other methods can be used to model the order allocation problem such as multi-attribute decision methods (Electre, Promethee, Topsis, Evamix, SMART, AHP, etc.) which provide the decision maker with a classification of solutions. However, these methods are very efficient only if there are no constraints in the problem formulation. Besides, two different techniques can give different results when applied to the same problem, even with the same assumptions and with the same decision maker.

3. Modeling procedure First, we expose our conceptual model and our hypothesis to describe networks of SMEs. Then we present the modeling procedure, introducing successively the technological map, the competencies map and the product/actor attainment graph.

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

3.1. Conceptual model and hypothesis Our conceptual model to describe networks is based on four elementary entities: actor, activity, resource and competency (Hammami et al., 2001). Actor: is a partner of the network. It is usually a firm. When it is necessary, the accuracy of the model can be improved. In this case, an actor will be a service or even a person within a firm. Activity: is any action described by a verb. A chain of activities is made of several co-ordinated activities directed at a goal. Resource: is an entity required to support the achievement of activities (e.g. machines, tools, computers, software applications, etc.). We usually focus on bottleneck resources. Competency: is the ability of an actor to mobilize intangible resources (knowledge, social and psychological aptitudes, etc.) and material resources available in his environment (tools, instruments, information, etc.), in order to achieve the goals of an activity characterized by a specific context. We note that, in this paper, we use a more restrictive definition for competency. We consider competency as the ability of an actor to achieve an activity using a resource. Ergo, a competency is always built up through a (actor, activity, resource) trio (see Fig. 1). Our observations about networking lead to accept the following hypothesis for the allocation problem: 1. An activity can be achieved by one or several actors of the network. In the case where many actors contribute to the achievement of an activity Ai ; each partner Pj will achieve a quantity Qi;j :

237

2. An actor can offer several bids to accomplish an activity. A bid is characterized by a due date, a cost and a quality level. 3. An actor can offer bids for coupled activities (i.e. a bid may include several activities). A bid for coupled activities is supposed to be more relevant than many bids for single activities. 4. The actors are competitors for some activities and complementary for other activities. 3.2. Technological map The technological map describes the way a product is processed. It is made of (see Fig. 2): 1. the product attainment graph, 2. the activities/competencies table. 3.2.1. Product attainment graph This is the logical succession of activities to process the product. This graph is made of production activities (machine, assemble, etc.) as well as administrative activities (plan, report, purchase, control subcontractors, etc.). It includes bifurcation, parallelism and anteriority constraints within activities. The attainment graph conforms to the IDEF3 formalism (Mayer et al., 1995). In the following example, both A2 and A3 activities have to be done, whereas one activity out of A4 or A5 has to be selected (Fig. 3). 3.2.2. Activities/competencies table Table 1 lists the set of competencies usually corresponding to an activity. The activities/ competencies table is built in conformity with Product

Actor uses achieves Competency

Technological map

Resource

Activity

requires

Fig. 1. Actor, resource, activity and competency relations.

Product attainment graph

Activities / competencies table

Fig. 2. Technological map.

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

238

A2 A1

&

A4

Table 2 Example of competencies map

A5

Partner Competency Activity Resource Expert level Competency weight Number of do

X A3

Fig. 3. Product attainment graph.

Table 1 Example of activities/competencies table Activities

Corresponding competencies

Ai A1

Designation Purchase

A2

y

Ck C1 C4 C12 y y

Designation Negotiate Budget Plan y y

a generic competency frame ROME. This frame makes it possible to standardize the description of skills among all the actors of the network. 3.3. Competencies map For each partner of the network, a competencies map gives the list of skills the partner possesses. This map also contains an expert level (between 0 and 4) and a learning policy for each competency. The level of expertise refers to the following definition (ROME): Level Level Level Level Level

0: 1: 2: 3: 4:

no competency, aware but not functional, able to work with, mastery, expertise, ability to improve the activity execution.

The learning policy of a partner Pj concerning the competency Ck is characterized by a weight between 0 and 1 named aj;k (the higher aj;k ; the more significantP this competency is regarding the firm policy and k ajk ¼ 18j). Our model focuses onto learning by doing (the simple fact to do the activity several times enables

Pj Ck (plan) Ai (purchase) Rm (MRP software) ej;k (3) aj;k (0.7) Di;k;m (10)

to improve the competency). For each partner Pj and for each triplet (competency, activity, expert level), we define the number of ‘‘do’’ to reach the further expert level. This number of ‘‘do’’ refers to the number of times the activity must be processed within the firm before changing the expert level. For example, the partner Pj has got the competency Ck (Plan), concerning the activity Ai (Purchase); its expert level ej;k is 3, and Pj aims to reach level 4 after 10 orders using the resource Rm (Table 2): 3.4. Product/actor attainment graph After designing the technological map, the partners bid to carry out one or several activities. Blending partners’ bids with the product attainment graph enables us to build the product/actor attainment graph which represents all the possible routes of activities through the partners of the network. In the following example, activities A5 and A6 can be made either by partners P1 and P2 ; but P1 does not want to process A6 if A5 has been previously done by P2 (Fig. 4). 3.5. Extended product/actor attainment graph According to the actors mobilized for a given route, logistic and administrative additional activities are automatically generated. When consecutive activities are processed by different partners, a transport activity and a co-ordination activity are generated in the product/actor attainment graph. Both transport and co-ordination activities increase costs and cycle times. They are modeled with ‘‘T’’ triangles (Fig. 5).

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

*

A6

A5 P1

X

A5

Zoom in

A5

P1 A6 P2

P1

4.1. Inviting bids

P2

Fig. 4. Product/actor attainment graph.

A5

A6

P1

P1

A5

T

A6

P1

P2

A5

A6

P2

P2

Fig. 5. A cut of the extended product/actor attainment graph.

4. Short-term constraints: Cost, quality and delivery time Short-term performance is mainly assessed in terms of lead time, cost and quality (C.f. Section 2.2). It expresses the simultaneous satisfaction of customers and company expectations. This satisfaction can be formulated *

*

as the respect of time and quality constraints imposed by the customer within limits of target costs, as the attainment of a minimal margin when the customer associates different values to the same product according to its lead time and/or its quality level. It is noted that:

*

network will encourage learning processes within the set of acceptable solutions. in the context of network of firms, others constraints (not indicated here) can be added, such as objectives of distribution of activities between companies or minimal level of activity per company.

A6

P2

X

239

the objective of short-term performance is expressed in the search of acceptable solutions rather than the search for optimal solution. The

When a customer’s order occurs, the partners of the network are invited to make proposals according to the list of required activities for this product (product attainment graph). For each product, the final customer will require a delivery time, a quality level and a price. Requiring a quality level imposes that each activity is committed to a company at least guaranteeing this level of quality (if the customer requires an ISO certification, all the companies implied in the attainment of the product must be certified). Due dates for all activities are generated so as to meet the target delivery time for the final product. This leads to associate with each activity an earliest start time and a latest finish time. These dates are calculated thanks to the product attainment graph and to average duration for each activity. The total margin of each activity is shared onto the critical path and onto the longest path including this activity. This makes it possible to define a time interval to achieve each activity. Bids requirements and partners’ submission for each activity are consequently expressed as in Table 3. As indicated in Section 3.4, a partner’s submission may relate to one activity or to a group of activities (e.g. partner P1 can offer a proposal for A5 and a tender for both A5 and A6 ).

Table 3 Inviting bids Criteria

Bids requirements

Partner’s submission

Time

Earliest start time latest finish time No requirement Minimal quality level

Start time duration

Cost Quality

Cost Quality level

ARTICLE IN PRESS 240

A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

4.2. Partners’ submissions construction

Table 4 Cost coefficients example

We want to focus on the necessity for the inviting bids procedure. Actually, the model retained for the benchmarking of short-term performances cannot be static. Indeed, the performance when accomplishing an activity is contextual, i.e. it depends not only on the qualification level of the actor, but also on the instantaneous load of the resource used. Moreover, the impact of the instantaneous load is relative because the performance is based on multiple criteria. Ergo, to qualify the impact of this load in terms of cost, quality or lead time, it is necessary to express this load, for a single resource, into different units: hours labor, hours machine, number of operations. For example, in a non-critical resource, processing an activity can require increasing the work time. This decision will have impacts in terms of cost and eventually quality. However, it will not affect the lead time of the final product. On the contrary, the achievement of an activity on a bottleneck resource affects the lead time of the product, but not its cost nor its quality. To conclude, the cost function is not linear. When a workstation is underloaded, then the addition of a supplemental activity will not induce significant extra costs (the fixed cost associated to the permanent personnel of the unit being independent of its load). On the other hand, modifying the structure and/or working conditions produces high costs. Let us consider an enterprise performing an activity on a resource Rm in a workshop using polyvalent manpower. When overtime is required in this workshop, the production cost will increase. Let:

Load level (Lm ) Coefficient

* * * *

Lm the manpower load in the workshop, n1 the capacity without overtime, n2 the capacity with overtime, n3 the capacity with an extra night shift.

Table 4 gives an example of cost coefficients according to manpower load in this workshop. For the same activity, the lead time will depend on the load on the resource Rm (Table 5).

on1 1

n1 oLm on2 1.25

n2 oLm on3 1.4

Table 5 Lead times example Activity level Lead time (day)

oq1

q1oAoq2 q2oAoq3

> q3

1

2

4

3

All these tables are managed by each partner. Their answers in terms of cost, time and quality are based upon their estimated workload and are then contextual. 4.3. Selecting satisfactory solutions: Mathematical model Next, partners’ proposals are aggregated in the form of a product/actor attainment graph. We now describe the mathematical selection process to obtain a set of non-dominated solutions. For many reasons, we selected an MOP model for the short-term selection problem. First, the MOP permits the decision maker to take into account many criteria. Second, since we do not have to aggregate criteria in one objective function, we evaluate the criteria in their own measurement units. Finally, the MOP provides the decision maker with a set of satisfactory solutions according to the different selection criteria. 4.3.1. Mathematical model Variables DD due date of the last activity QLi required quality level for activity i STrij start time offered in bid r to carry out activity i by partner j STi start time for selected activity i Drij duration offered in bid r to carry out activity i by partner j Di duration for selected activity i

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

Crij

cost offered in bid r to carry out activity i by partner j cost for selected activity i standard additional cost due to automatic additional activities generated between activities i1 and i2 cost of additional activities generated between activities i1 and i2 quality level offered in bid r to carry out activity i by partner j quality level for activity i after bid’s selection number of activities binary variable: brij ¼ 1 if bid number r offered to carry out activity i by partner j is selected; brij ¼ 0 otherwise cost of the product total quality level

Ci ACi1,i2

Ci1,i2 Qrij Qi N brij

C TQL

Constraints Anteriority constraints: If activity m has to be carried out after activity i then STm XSTi þ Di

8m; i:

Due date constraint: For the latest activity (activity N)

241

We have to select one bid for each activity: XX brij ¼ 1 8i: r

j

The cost of additional activities: If i1 ai2 ; j1 aj2 ; XXXX ACi1 ;i2 br1 i1 j1 br2 i21 j2 ; Ci1 ;i2 ¼ r1

r2

j1

j2

otherwise Ci1 ;i2 ¼ 0: The cost of the product: N N X N X X Ci þ Ci1 ;i2 : C¼ i1 ¼1 i2 ¼1

i¼1

The finish time: D ¼ STN þ DN : The total quality level: N X Qi : TQL ¼ i¼1

Objective functions Minimize the cost: Min C: Maximize the total quality level: Max TQL:

STN þ DN pDD: Quality constraint:

5. Long-term optimization: Learning criteria

Qi XQLi :

Assuming that skills exchange is one of the main long-term reasons for networking, the model will now focus onto learning processes within the network. According to the network policy, the partners determine orders of priority to improve proficiencies. We have to transform these priorities into weights of criteria. To do so, we use the group AHP method (AHP applied to group decisions (Saaty, 1980). This method fits collective decision-making processes where weights of criteria have to be determined.

Start time of activity i: XX STi ¼ STrij brij 8i: r

j

Duration of activity i: XX Di ¼ Drij brij 8i: r

j

Quality level for activity i: XX Qi ¼ Qrij brij 8i: r

j

Cost of activity i: XX Ci ¼ Crij brij r

j

5.1. Group AHP method 8i:

In the AHP, the problem is modeled as a hierarchy. Each level in the hierarchy requires

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

242

pair-wise comparisons using a ratio scale such as the one required by Saaty ð1=9; 1=8; y; 1=2; 1; 2; y; 9Þ: A preference matrix A is then constructed through pair-wise comparisons. Matrix A has to be reciprocal such that aij ¼ 1=aji (aij ¼ 1 means that Ci and Cj have equal importance regarding the network policy, aij ¼ 9 means than Ci is much more important than Cj ):

C1 A ¼ C2 Cn

C1

0

1 B 1 B a12 B B @

1 a1n

C2

Cn

a12



1



 

 

a1n

1

C  C: C  C A 1

A1

A2

AG

VG

. . AP

Individual judgments matrices

Matrix of aggregate judgments

Normalized principal eigenvector

Fig. 6. AIJs in group AHP.

The relative priorities are given by the normalized right principal eigenvector V: AV ¼ lmax V :

A1

V1

In a group decision, the individual preferences are synthesized to form a group preference in one of the following two ways (Peniwati, 1996):

A2

V2

*

*

Aggregation of individual judgments (AIJ) The entire group is supposed to be very cohesive and assumed to think alike. Therefore, it works as a single entity. Hence, individual judgments (represented by matrices A1 ; A2 ; y; Ap ) are combined in a common judgment matrix (AG ) and one priority vector is determined for the group (VG ). The AIJ applied to group AHP is in Fig. 6. Aggregation of individual preferences (AIP) AIP is used when the problem is in a context where individuals are acting in their own right within different value systems. Since we are concerned with each individual’s resulting priorities, individual judgments (represented by matrices A1 ; A2 ; y; Ap ) are processed to find individual priorities which are determined by the normalized principal eigenvectors V1 ; V2 ; y; Vp of matrices A1 ; A2 ; y; Ap : The individual priorities (V1 ; V2 ; y; Vp ) are then combined into one group priority vector (VG ). The AIP applied to group AHP is presented in Fig. 7.

VG

. . AP

Individual judgments matrices

Individual priorities eigenvectors

Group aggregate priorities

Fig. 7. AIPs in group AHP.

5.2. Partners preferences aggregation In the networks we observed so far, the partners were rather cohesive. So, we used the AIJ method to find the eigenvector (VG ) characterizing the learning policy for the network: 0 1 aG;1 Ba C B G;2 C VG ¼ B C: @ ^ A aG;n

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

But, we also decided to take into account the individual learning policies we defined for each partner, regarding their own enterprise. These individual learning policies have been introduced in Section 3.3 and named ajk in the competencies map. To do so, we propose to aggregate for each competency k; aGk and the ajk of each partner j: X aAggregation;k ¼ dG aGk þ dj ajk ; j



P where dG and dj are weights dG þ j dj ¼ 1 that balance the importance of the network versus the partners. This aggregation enables us to take into account both collective and individual preferences. 5.3. Final evaluation To select the optimal solution according to learning criteria, we use the WPM (c.f. Section 2.2.). The WPM method requires the performance measures to be expressed in the same units, which is the case at this step of our resolution procedure (cost, quality and delivery time criteria have been treated previously). We first calculate a score for each non-inferior solution. This score describes the proficiencies improvement of the network after processing the order. This score is a deviation calculated as below: ! XXX efutur  eactual jk jk Score ¼ aAggregation;k ; Di;k;m i j k is the expert level partner Pj aims to where efutur jk reach for competency Ck ; and eactual is the actual jk expert level of partner Pj concerning competency Ck : We select the alternative that obtained the best score.

6. Synoptic The approach we introduced is summarized in the synoptic displayed in Fig. 8.

243

7. Case study This case study is a simplified version of a real industrial case introduced below. After a modification in the purchasing policy of their main contractors and following cuts in the number of suppliers, seven subcontractors from the mechanical engineering industries set up, in 1995, a network named Me! canergie. The Me! canergie group combines a boilermaker plant, a sheet-metal machine shop and five mechanical engineering firms. Here, the basic goal leading the firms to networking is commercial: each firm aims at increasing its sales by reaching new customers. The network then recruits a sales manager. The quest for clientele becomes not only regional but national. In our simplified model, we consider three actors among the seven: two mechanical engineering firms named M1 and M2 and the boilermaker named B3: It is noted that these three partners are complementary for some activities and concurrent for others. A main problem for this network is to dispatch fairly between the partners the activities to process orders, so that the customers needs can be met and the learning policy can be achieved. This network will first be analyzed according to its activities. These activities refer both to the technical work to process products and to the logistic operations like purchase of materials, planning, or delivery.

7.1. The product attainment graph In the case study, the product attainment graph (Fig. 9) has been simplified by grouping activities together. The activities needed to provide the required product are: purchase (P), machining (M), assembly (A), subcontracting control (SC) and delivery (D). Additional transport activities will not be added in this present case because the partners are close together.

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

244

Actions

Concepts

Product

Network of firms

Technological map

Product attainment graph

Activities / competencies table

Competencies map

Inviting Bids Partners' submissions

Product / Actor Attainment graph

Automatic generation of additional activities

Extended Product / Actor Attainment graph Short term selection (Quality, Delivery, Cost)

Set of admissible solutions

Learning Policy

Long term selection

Optimal Configuration

Fig. 8. Modelling procedure.

7.2. An activities/competencies table The activities/competencies table (Table 6) was drawn up thanks to the interviews carried out with the partners of the network of firms.

SC P

&

& M

A

Fig. 9. Product attainment graph.

D

7.3. Competencies map The competencies maps of partners M1; M2 and B3 are presented in Table 7.

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

7.4. Product/actor attainment graph

Each partner submits to process activities given in Table 9. We note that numerical values are assigned to the quality levels, so as to maximize the total quality level in the resolution procedure. Thanks to partners submissions, we can now design the product/actor attainment graph (Fig. 10).

We now propose to invite bids for each activity as in Table 8. Table 6 Activities/competencies table Activities 1

2

Required competencies Purchase (P)

Subcontracting control (SC)

C1 C2 C3

Plan Negotiate Approach customs

C4

Have technical know-how

C2

Negotiate

3

Machining (M)

C5 C6 C7

Machine Measure Interpret design diagram

4

Assembly (A)

C8

Assemble

5

Delivery (D)

C1 C3

Plan Approach customs

245

7.5. Results 7.5.1. Short-term selection We applied the mathematical model of Section 4.3 to find the set of feasible and non-inferior solutions. These solutions are summarized in Table 10. The graphical representation of the set of feasible solutions is shown in Fig. 11. The noninferior solutions are linked together by segments (Table 11). 7.5.2. Long-term selection The set of non-inferior solutions found in the previous step is now analyzed according to the

Table 7 Competencies map Partner

M1

Competency Activity Resource Expert level Competency weight Number of do

C1 P R1 e1;1 ¼ 3 a1;1 ¼ 0:2 4

Partner

M2

Competency Activity Resource Expert level Competency weight Number of do

C1 P R9 e2;1 ¼ 3 a2;1 ¼ 0:4 3

Partner

B3

Competency Activity Resource Expert level Competency weight Number of do

C5 M R15 e3;5 ¼ 3 a3;5 ¼ 0:4 10

C1 D R2

4

C1 D R10

5

R16

20

C2 P R3 e1;2 ¼ 2 a1;2 ¼ 0:3 3

C2 SC R4

0

C2 P R11 e2;2 ¼ 2 a2;2 ¼ 0:2 0

C3 P R12 e2;3 ¼ 2 a2;3 ¼ 0:3 1

C6 M R17 e3;6 ¼ 3 a3;6 ¼ 0:4 5

C7 M R18 e3;7 ¼ 4 a3;7 ¼ 0:2 0

C3 P R5 e1;3 ¼ 3 a1;3 ¼ 0:1 5

C3 D R13

2

C3 D R6

0

C8 A R14 e2;8 ¼ 3 a2;8 ¼ 0:1 4

C4 SC R7 e1;4 ¼ 2 a1;4 ¼ 0:2 5

C8 A R8 e1;8 ¼ 4 a1;8 ¼ 0:2 0

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

246 Table 8 Inviting bids

P

Activity

P

SC

M

A

D

Mean activity time (days) Earliest start time (days) Latest finish time (days) Required quality level

5 0 6 Q1

1 6 13 Q2

3 6 10 Q1

2 10 13 Q2

1 13 15 Q2

M1

P

X

&

M1

P

M2

SC

Table 9 Partners’ submissions Partner

M1

Activity Bid (br;i;j Þ Start time (STr;i;j ) Duration (Dr;i;j ) Cost h (Cr;i;j ) Quality level (Qr;i;j )

P b1;1;1 0 5 300 Q1ð3Þ

Partner

M2

Activity Bid (br;i;j ) Start time (STr;i;j ) Duration (Dr;i;j ) Cost h (Cr;i;j ) Quality level (Qr;i;j )

P b1;1;2 1 6 310 Q1(3)

P b2;1;1 0 6 280 Q1ð3Þ

SC b1;2;1 7 2 200 Q2ð2Þ

A b1;4;1 10 3 100 Q2ð2Þ

D b1;5;1 13 1 50 Q1ð3Þ

M

D b1;5;2 13 1 40 Q2(2)

M b1;3;3 6 3 220 Q1(3)

A B3

M1 X

X M

B3 A b1;4;2 10 2 120 Q1(3)

M1

A

B3

M2

D

M b2;3;3 7 3 220 Q1(3)

learning policy of the network. To do so, the WPM is applied. The competencies weights we obtained are summarized in Table 12. In our case study, alternative number 12 is the optimal one as mentioned in Table 13. The obtained scores enable us to classify the possible alternatives, and consequently to choose the most promising one. In other words, they permit to select the assignment of activities to the actors that satisfy logistic and customer needs and guarantees the highest competencies development.

8. Conclusion: Implications and future work The purpose of this paper was to present a decision aid procedure blending short-term constraints and learning mechanisms objectives within networks of firms. First, we surveyed the methods mainly used to solve the vendor selection and the

M1 X D M2

Fig. 10. Product/actor attainment graph.

order allocation problems. Then, we proposed a procedure based on four modeling concepts: product/attainment graph, activities/competencies table, competencies map and product/actor attainment graph. Next, we presented our mathematical model to select the set of non-dominated routes according to short-term constraints. Finally, a long-term optimization based on AHP and WPM methods led to meeting the learning aims within the network. This study motivated additional research that is now underway. We plan to overcome some of the limitations of the current model. First, we envision to include stochastic parameters into the model, so as to represent better the reality of networks and to evaluate the reliability of selected routes. Second, we are examining the use of new ways for preference modeling. Next, we plan to study the case where several partners contribute together to carry out the same activity, each one achieving a part of this activity. This last improvement will

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

247

Table 10 Feasible and non-inferior solutions Alternatives 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

b1;1;1 b2;1;1 b1;1;2

1 0 0

0 1 0

0 0 1

1 0 0

0 1 0

1 0 0

0 1 0

0 0 1

1 0 0

0 1 0

1 0 0

0 1 0

0 0 1

1 0 0

0 1 0

1 0 0

0 1 0

0 0 1

1 0 0

0 1 0

b1;2;1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

b1;3;3 b2;3;3

1 0

1 0

1 0

0 1

0 1

1 0

1 0

1 0

0 1

0 1

1 0

1 0

1 0

0 1

0 1

1 0

1 0

1 0

0 1

0 1

b1;4;1 b1;4;2

1 0

1 0

1 0

1 0

1 0

0 1

0 1

0 1

0 1

0 1

1 0

1 0

1 0

1 0

1 0

0 1

0 1

0 1

0 1

0 1

b1;5;1 b1;5;2

1 0

1 0

1 0

1 0

1 0

1 0

1 0

1 0

1 0

1 0

0 1

0 1

0 1

0 1

0 1

0 1

0 1

0 1

0 1

0 1

TQL Cost

13 870

13 850

13 880

13 870

13 850

14 890

14 870

14 900

14 890

14 870

12 860

12 840

12 870

12 860

12 840

13 880

13 860

13 890

13 880

13 860

Fig. 11. Graph of feasible solutions.

make it possible to include new forms of learning in the model. The model will not only work for learning by doing, but also for learning by interacting (Lundvall, 1992) (learning by interacting requires a strong interaction among partners to transfer the savoir-faire from one to another, and is a relevant learning mode within networks). To promote

learning by interacting, coupled bids from at least two actors shall be selected with priority. Finally, we also project improving the modeling of the learning policy. The learning policy should not only deal with increase of competencies but it must also mirror changes where an actor decides to develop, maintain or even abandon a given competency. To do so, for each competency Ck ; the policy of each partner Pj of the network will be analyzed as in Table 14. In this example, partner P1 wants to acquire Ck and to share it with other partners of the network, whereas P3 wants to outsource it. This table will give criteria to select orders routes according to more accurate learning objectives: as previously, an order needing the activation of the Ck competency will be routed if possible through the P2 or P4 firms so that these firms may develop this competency. But this order will also avoid partner P3 : Furthermore, a coupled bid from P1 and P2 will be favored so as to promote learning by interacting. By the way, this table may also reveal difficulties among the network: in this example, P1 wants to acquire a competency that P4 does not want to share.

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249

248 Table 11 Set of non-inferior solutions Alternative TQL Cost Activities allocation

Activity

2 13 850 Partner

Pð1Þ SCð2Þ Mð3Þ Að4Þ Dð5Þ

M1 M1 B3 M1 M1

Bid

5 13 850 Partner

2 1 1 1 1

M1 M1 B3 M1 M1

Bid

7 14 870 Partner

2 1 2 1 1

M1 M1 B3 M2 M1

Bid

10 14 870 Partner

2 1 1 1 1

M1 M1 B3 M2 M1

Bid

12 12 840 Partner

1 2 1 1

M1 M1 B3 M1 M2

Bid

15 12 840 Partner

Bid

2 1 1 1 1

M1 M1 B3 M1 M2

2 1 2 1 1

Table 12 Aggregation of competencies weights

aG;k (group) a1;k (M1) a2;k (M2) a3;k (B3) aaggregation,k

Coefficient

C1

C2

C3

C4

C5

C6

C7

C8

dG ¼ 0:7 d1 ¼ 0:1 d2 ¼ 0:1 d3 ¼ 0:1 dG +Sdj ¼ 1

0.2 0.2 0.4 0 0.20

0.1 0.3 0.2 0 0.12

0.1 0.1 0.3 0 0.11

0 0.2 0 0 0.02

0.2 0 0 0.4 0.18

0.1 0 0 0.4 0.11

0.1 0 0 0.2 0.09

0.2 0.2 0.1 0 0.17

Table 13 Final evaluation Alternative Score

2 0.16

5 0.15

7 0.20

Table 14 Competencies analysis Ck competency

P1

P2

P3

P4

Acquire Develop Share Outsource Abandon

1 0 1 0 0

0 1 1 0 0

0 0 0 1 0

0 1 0 0 0

References Barbarosoglu, G., Yazgac, T., 1997. An application of the analytic hierarchy process to the supplier selection problem. Production and Inventory Management Journal 38 (1), 15–21.

10 0.19

12 0.23

15 0.22

Bender, P.S., Brown, R.W., Isaac, M.H., Shapiro, J.F., 1985. Improving purchasing productivity at IBM with a normative decision support system. Interfaces 15, 106–115. Buffa, F.P., Jackson, M.W., 1983. A goal programming model for purchase planning. Journal of Purchasing and Materials Management 19 (3), 27–34. Burlat, P., Peillon, S., 2001. Skills networks and local dynamics. In: McNaughton, R.B., Green, M.B. (Eds.), Global Competition and Local Networks. Ashgate Publishing Limited, London. Chakravarty, A.K., Martin, G.E., 1988. An optimal joint buyer–seller discount pricing model. Computers and Operations Research 15 (3), 271–281. Chaudhry, S., Forst, F., Zydiak, J., 1991. A multicriteria approach to allocating order quantity among vendors. Production and Inventory Management Journal 32 (3), 82–86. Current, J., Weber, C., 1994. Application of facility location modeling constructs to vendor selection problems. European Journal of Operational Research 76, 387–392.

ARTICLE IN PRESS A. Hammami et al. / Int. J. Production Economics 86 (2003) 233–249 Degraeve, Z., Roodhooft, F., 1998. Determining sourcing strategies: A decision model based on activity and cost driver information. Journal of Operational Research Society 49 (8), 781–789. Degraeve, Z., Labro, E., Roodhooft, F., 2000. An evaluation of vendor selection models from a total cost of ownership perspective. European Journal of Operational Research 125, 34–58. Dickson, G.W., 1966. An analysis of vendor selection systems and decisions. Journal of Purchasing 2 (1), 5–17. Ellram, L.M., 1995. Total cost of ownership: An analysis approach for purchasing. Journal of Physical Distribution and Logistics 25 (8), 4–23. Gohdsypour, S.H., O’Brien, C., 1988. A decision support system for supplier selection using an integrated analytic hierarchy process and linear programming. International Journal of Production Economics 56–57, 199–212. Hajidimitriou, Y.A., Georgiou, A.C., 2000. International site selection decisions using multi-objective methods. American Business Review 18 (2), 87–95. Hammami, A., Burlat, P., Campagne, J.P., 2001. Contribution a" la Conception et au Pilotage d’une Entreprise R!eseau. 3e Conf!erence Francophone de MOd!elisation et SIMulation MOSIM’01, Avril 2001, Troyes (France). Hannoun, M., Guerrier, G., 1996. Le partenariat industriel Paris, Minist"ere de l’Industrie. de la Poste et des T!el!ecomunications, SESSI, Paris. Hwang, H., Moon, D.H., Shinn, S.W., 1990. An EOQ model with quantity discounts for both purchasing price and freight cost. Computers and Operations Research 17 (1), 73–78. Lundvall, B.A., 1992. National Systems of Innovation. Towards a Theory of Innovation and Interactive Learning. Pinter Publishers, London. Mandal, A., Deshmukh, S.G., 1994. Vendor selection using interpretive structural modelling (ISM). International Journal of Operations and Production Management 14 (6), 52–59. Mayer, R., Menzel, C., Painter, M., Witte, P., Blinn, T., Perakath, B., 1995. Information integration for concurrent engineering (IICE) IDEF 3 process description capture: Method report. Armstrong Laboratory, University Drive East College Station, Texas. Mummalaneni, V., Dubas, K.M., Chao, C., 1996. Chinese purchasing managers ‘ preferences and trade-offs in supplier selection and performance evaluation. Industrial Marketing Management 25 (2), 115–124. Narasimhan, R., 1983. An analytical approach to supplier selection. Journal of Purchasing and Materials Management 19 (4), 27–32. Nydick, R.I., Hill, R.P., 1992. Using the analytic hierarchy process to structure the supplier selection procedure. International Journal of Purchasing and Materials Management 28 (2), 31–36. Patton, W.W., 1996. Use of human judgment models in industrial buyer’s vendor selection decisions. Industrial Marketing Management 25, 135–149.

249

Peniwati, K., 1996. The analytic hierarchy process: The possibility theorem for group decision making. Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process, Vancouver, BC, pp. 202–214. Petroni, A., Braglia, M., 2000. Vendor selection using principal component analysis. The Journal of Supply Chain Management 36 (2), 63–69. Phuong Ta, H., Yin Har, K., 2000. A study of bank selection decisions in singapore using the analytical hierachy process. International Journal of Bank Marketing 18 (4), 170–180. Poulin, D., Montreuil, D., Gauvin, S., 1994. L’entreprise r!eseau—B#atir aujourd’hui l’organisation de demain. PubliRelais, Montr!eal. ROME: R!epertoire Op!erationnel des M!etiers et de l’Emploi, Agence Nationale Pour l’Emploi, (ANPE), France. Roodhooft, F., Konings, J., 1996. Vendor selection and evaluation: An activity based costing. European Journal of Operational Research 102, 97–102. Saaty, T.L., 1980. The Analytic Hierarchy Process. McGrawHill, New York. Siying, W., Jinlong, Z., Zhicheng, L., 1997. A supplier selecting system using a neural network. International Conference on Intelligent Processing Systems, IEEE, New York, pp. 468–471. Thompson, K.N., 1990. Vendor profile analysis. Journal of Purchasing and Materials Management 26 (1), 11–18. Timmerman, E., 1986. An approach to vendor performance evaluation. Journal of Purchasing and Materials Management 22 (4), 2–8. Verma, R., Pullman, M.E., 1998. An analysis of the supplier selection process. Omega 26 (6), 739–750. Weber, C.A., 1996. A data envelopment analysis approach to measuring vendor performance. Supply Chain Management: An International Journal 1 (1), 28–39. Weber, C.A., Desai, A., 1996. Determination of paths to vendor market efficiency using parallel coordinates representation: A negotiation tool for buyers. European Journal of Operational Research 90, 142–155. Weber, C.A., Ellram, L.M., 1993. Supplier selection using multi-objective programmaing: A decision support system. International Journal of Physical Distribution and Logistics Management 23 (2), 3–14. Weber, C.A., Current, J.R., Benton, W.C., 1991. Vendor selection criteria and methods. European Journal of Operational Research 50 (1), 2–18. Weber, C.A., Current, J.R., Desai, A., 1998. Non-cooperative negociation strategies for vendor selection. European Journal of Operational Research 108, 208–223. Weber, C.A., Current, J.R., Desai, A., 2000a. An optimization approach to determining the number of vendor to employ. Supply Chain Management: An International Journal 5 (2), 90–98. Weber, C.A., Current, J.R., Desai, A., 2000b. VenDOR: A structured approach to vendor selection and negotiation. Journal of Business Logistics 21 (1), 135–167. Williamson, O.E., 1975. Markets and Hierarchies: Analysis and Antitrust Implications. The Free Press, New-York.