On the Role of Authority in Just-In-Time Purchasing Agreements

Transcription

1 Discussion Paper No. A-55 On the Role o Authority in Just-In-Time Purchasing Agreements CHRISTIAN EWERHART and MICHAEL LORTH May 1997

2 On the Role o Authority in Just-In-Time Purchasing Agreements Christian Ewerhart Department o Economics, University o Bonn, and The Boston Consulting Group, Frankurt a. M., Germany Michael Lorth Department o Economics and Business Administration University o Hagen May 1997 Addresses o the authors: Universität Bonn Wirtschatspolitische Abteilung Adenauerallee Bonn, Germany ewerhart@wipol.uni-bonn.de Fachbereich Wirtschatswissenschat FernUniversität Hagen Feithstr. 140 / AVZ II Hagen, Germany michael.lorth@ernuni-hagen.de

3 Abstract This paper analyzes buyer-supplier relationships where the supplier can hand over partial control over his irm to the manuacturer. We show that standard just-in-time purchasing agreements can yield optimal levels o investment in lexible production. I investments in lexibility are socially valuable then it is optimal or the supplier to give up control over the delivery schedule. In this case, schedules o higher volatility chosen by the manuacturer induce more eicient investment incentives on the part o the supplier. Consequently, the supplier deliberately gives up partial control over his irm in order to reach an outcome which is preerred by both supplier and manuacturer. JEL-Classiication: L

4 I. Introduction This paper combines two strands o literature: The economic literature on ownership and authority and the management literature on just-in-time (JIT) manuacturing. The irst line o research is concerned with the concept o authority as deined by Simon (1951) and that o ownership ormalized by Grossman and Hart (1986). The second line o literature, represented or example by Schonberger (198) and Hall (1983), ocuses on the by now well-known management techniques o just-in-time manuacturing and purchasing, which aim at improving both cost structure and product quality in the complete production process. In this paper, we investigate the optimality o simple contracts observed in real-lie buyer-supplier relationships and describe circumstances that avor just-in-time purchasing agreements. Just-in-time purchasing in vertical buyer-seller relationships is considered as an eective method to reduce inventory levels on the part o the buyer. This is desirable since inventories cause costs rom both running the inventory and paying interest on the capital bound in orm o stocks. But at the same time, just-in-time purchasing is commonly seen to be done against the suppliers' interests. According to a recent survey o U.S. and Japanese automotive suppliers by Helper and Sako (1995), more than hal o all mailed suppliers in the United States and about one-third o all mailed Japanese suppliers agreed with the statement that "JIT only transers inventory responsibility rom customers to suppliers." A manuacturer adhering to the just-intime philosophy will ask the supplier or a more lexible orm o delivery. Ideally or him, inputs in orm o materials, parts and other intermediate products are delivered just when they are needed in his production process. For the supplier, this implies a high requency o delivery in conjunction with small, variable batches. Since optimal batch sizes in a supplier's production adapted to conventional purchasing and delivery conditions, are usually signiicantly larger than those needed by the 1

5 manuacturer, the supplier will either have to produce sub-optimal lot sizes or stockpile inventory. (See Helper and Sako (1995) or more empirical evidence.) Just-in-time purchasing is implemented usually by so-called call-orward delivery systems. In such a system, the buyer is given the right to order dierent quantities at dierent times, and to do so very requently. The stream o goods between seller and buyer, or as will say, the delivery schedule is thereore planned and controlled to a large extent by the buyer. Put dierently, a call-orward contract allocates the authority over the delivery schedule to the manuacturer. In a classical purchasing agreement, however, the manuacturer is given ar less reedom in choosing his orders. Usually, he aces restrictions like minimal and maximal order quantities or minimal delivery times. Moreover, he is obliged to keep his internal production running. Thus, although the buyer still orders the goods rom the seller, he controls the delivery o the goods only to a small degree. Hence, in classical agreements, authority over the delivery schedule is primarily given to the seller. Accordingly, in the model, the parties are endowed with the possibility to allocate the authority over the delivery schedule to either the supplier or the buyer. We show that the agreedupon allocation inluences the incentives to invest in lexible production and that transerring the authority over the delivery schedule to the buyer is optimal i this investment is socially important. The model is designed to encompass the case o integrated production. By this, we mean the delivery o goods rom either a shop or work center o one department to another department. Under integrated production, the residual control right over the assets o the irst department is transerred to the manager o the second department. In contrast, non-integrated production means that the supplier o a good is an autonomous irm, and the residual rights o control over the supplier's assets lie in the hands o the supplier's manager. Again, the allocation o control has an impact on the

6 investment incentives o the departments' managers and either integration or nonintegration is optimal. However, we will show that under certain assumptions, it will be optimal to give partial control over a non-integrated supplier to the manuacturer. A second objective pursued through the installation o just-in-time systems is the improvement o product quality. Crémer (1995) shows that product quality is in act improved in just-in-time delivery systems since, given the impossibility o repairs, the supplier has higher incentives to produce goods o a high quality. For reasons o simplicity, we abstract rom quality aspects in the model. The rest o the paper is organized as ollows. In section II, we introduce the basic model and derive the conditions or the socially eicient investment decisions. Section III analyzes the optimality o simple contractual agreements under dierent assumptions. Section IV concludes. The appendix contains technical details o the proos. II. The Basic Model We consider a trade relationship between a supplier and a manuacturer, both o which are administered by a respective manager. We shall concentrate on the decisions to be taken by the supplier s manager and abstract rom those taken by the manuacturer s manager. To run his actory, the supplier s manager has to make two decisions. The irst decision is a speciication o the delivery schedule, which we envisage as very complex. The costs incurred to supplier and manuacturer by dierent schedules, however, are assumed to depend solely on the schedule s "volatility", which is denoted by [ 01,]. High values o indicate a high volatility in the sense that the delivery requency and the variability o the (small) 3

7 batch sizes are high. However, a low value o denotes a non-requent delivery o large batches o almost identical size. The second decision o the supplier covers all other choices except or the choice o the delivery schedule. We assume again that all payo-relevant aspects o the second decision can be represented by a variable q [ 01,], which we shall reer to as the policy variable. To understand the precise nature o q, suppose that the supplier's policy can be adapted to the respective manager's objectives. Suppose urthermore that the higher the value o q the better the supplier's policy is adapted to the manuacturer's aims. q = 1 then means that the supplier's policy is most adapted to the manuacturer's purposes, while q = 0 denotes a completely supplier-oriented policy. Consequently, we assume conlicting interests with respect to the supplier's policy. Summing up, rom a cost-beneit perspective, the decisions to be taken by the supplier s manager may be summarized by the pair (, q). We shall assume that the managers obtain non-alienable beneits as ollows. For the manuacturer, there is a total value Vq ( ) o the traded units that increases in q, i.e. the better the supplier's policy is adapted to the manuacturer's purposes the higher is the manuacturer's value o the product to be delivered. In addition, the manuacturer has to carry convex inventory costs L( ) decreasing in. I the price or the total trade is denoted by p, the manuacturer s manager obtains Vq ( ) L ( ) p. The cost o the supplier s manager consists o a policy dependent cost component Cq( q) increasing in q and a volatility-dependent cost component C ( ) increasing in. Thus, his beneit is given by p C ( q) C ( ). Eicient decisions q and maximize total beneit q ( ) ( ) ( ) ( ) V q L C q C. (1) q 4

8 We suppose that the supplier s manager can reduce his cost components by early speciic investments i q and investment in the lexibility o production i. More precisely, an investment i q leads to sunk costs Kq( i ) or a given policy q. We assume Similarly, an investment i leads to sunk costs K ( i ) q and reduces absolute cost C q Cq qq > 0 and that C q is convex in ( qi, q ). and reduces absolute cost C or a given volatility. In addition, we suppose that investment in the reduction o the volatility-dependent cost component reduces also marginal costs, i.e. C < 0. Finally, we assume that C is convex in (, i ). Figure 1 depicts the time structure. 0 1 manuacturer and supplier write longterm agreement supplier chooses investment levels i and i q manuacturer and supplier re-negotiate about and q t Figure 1. Time structure Eicient investment levels i, i q, and decisions q,, maximize the total ex ante beneit ( ) ( ) q( q ) ( ) q( q) ( ) V q L C i, q C i, K i K i. () The corresponding irst-order conditions are given by ( i, ( i )) K ( i ) C = ( iq q ( iq) ) Kq( iq), (3) Cq, =. (4) q 5

9 III. Optimal Contracts Long-term trading relations naturally involve high transaction costs, e.g. or writing and evaluating nearly complete contracts. Accordingly, long-term contracts like justin-time purchasing agreements tend to be highly incomplete. (C. Schonberger (198) or a description o Japanese and U.S. contracts.) Economic theory emphasizes that in the presence o transaction costs, the allocation o authority and property rights will serve as a substitute or overly detailed contracts. We will thereore determine optimal contracts between supplier and manuacturer under the restriction that contracts can only speciy residual control rights. We will assume that ex ante investments i q and i are not contractible at all. Moreover, we suppose that the supplier s delivery schedule and policy are not contractible ex ante in the sense that the parties are just able to allocate the corresponding control rights. Thereore, a contract written by the parties beore investments are undertaken contains the total payment p, and speciies the allocation o the residual control right over q and that o the authority over. I the individually rational decision o at least one party results in an ineicient choice o the pair ( q, ) then the parties will gain rom re-negotiation and thereore write a new contract that speciies ex post eicient decisions q ( i q ) and ( i ) assume that ( ) ( ) q( q ) + ( ). We will V q L C i, q C i, (5) or all q,, i q and i, i.e. we suppose that trade is always socially eicient. Then the re-negotiation surplus rom re-negotiation to ( q, ) is non-negative and given by (,,, ) = ( ) ( ) q( q, ) (, ) V( q) L( ) Cq( iq q) C ( i ) RS q q V q L C i q C i { },,. (6) 6

10 We assume that the surplus is shared among the parties such that the supplier obtains a raction α. When choosing his individually rational levels o investment, the supplier anticipates re-negotiation. He thereore maximizes ( ) ( ) ( ) ( ) ( ) p C i, q C i, + α RS q i, i,, q, (7) q q q where the pair ( q, ) may depend on the allocation o control rights speciied in the initial contract. Using the Envelope Theorem, the corresponding irst-order condition on i is given by ( i i ) K ( i ) C C ( ) ( i, ), ( ) 1 α α =. (8) The interpretation o this ormula is as ollows. The right-hand side mirrors the marginal cost o investment, the let-hand side the marginal reduction in cost. The two components o the let-hand side represent the two eects o an investment i. Firstly, a marginal investment lowers the cost C in the case when re-negotiation ails. This has two implications. On the one hand, the threat point in the bargaining, > 0. On the other hand, the re- process will shit down by C ( i ) negotiation surplus RS q ( iq) ( i ) q ( ),,, increases by the same amount, but only a ( ) share α o it is given to the supplier. As a second eect investment inluences the re- negotiation surplus by decreasing the actual cost C i, ( i ) share α is given to the supplier., and, as above, a In the same way we can derive the irst-order condition with respect to i q as ( iq q iq ) Kq( iq) Cq Cq ( ) ( iq q) ( ) 1 α, α, =. (9) q q The interpretation o this ormula is similar to that o equation (8). Thus, since a dierent allocation o control rights in general inluences the choice o q and, it 7

11 can be seen rom ormulas (8) and (9) that the incentives to invest or the supplier depend on these allocations. There are two control rights to be allocated by the contract which will be treated separately. The control over the delivery schedule. I the supplier controls then he will choose as low as possible since a high volatility increases his production cost. Thus, in this case, = 0. As igure shows, this change in the threat point distorts the incentives to invest such that i < i. α =1 0< α < 1 K ' ( i ) α =0 C ( i, ( i )) C ( i, 0) i ( α) i Figure. Under-investment in case o supplier control over the delivery schedule We give a ormal proo o this and the ollowing assertions in the appendix. I the manuacturer controls the delivery schedule, then he will avoid inventory costs by 8

12 choosing = 1. The supplier's incentives to make speciic investments will again be distorted but in the opposite direction. See igure 3 or a graphical illustration o this eect. In sum, supplier control o will generally lead to under-investment in lexibility while manuacturer control will result in over-investment. α =0 0< α < 1 α =1 K ' ( i ) C ( i, 1) C ( i, ( i )) i i ( α) Figure 3. Over-investment in case o manuacturer control over the delivery schedule Proposition 1. I the manuacturer controls the delivery schedule then the supplier has a higher incentive to invest in lexible production. Thus, i a too high level o investment in lexibility is socially less harmul than a too low level, then the manuacturer s manager should control the delivery schedule. 9

13 The control over the supplier s policy. As beore the supplier s policy may be controlled by either the supplier s manager himsel or by the manuacturer s manager. Similar to the analysis above, there will be distorting eects on the investment incentives o the supplier s manager. Proposition. (Grossman-Hart) I the manuacturer controls the supplier's policy then the supplier has a lower incentive to make speciic investments than under nonintegration. Thus, i a too low level o relationship-speciic investments i q in the policy q is socially more harmul than a too high level, then the supplier's manager should have control over the supplier s policy. The contracts to be written may be o our types (see table 1). Manuacturer controls Supplier controls Manuacturer controls q Integrated Production Buered Integrated Production Supplier controls q Call-orward Delivery System (Just-in-Time Purchasing) Classical Purchasing Contract Table 1. Types o contracts between supplier and manuacturer. Corollary 1. I speciic investments as well as investments in lexibility are important, then the parties will choose a just-in-time purchasing agreement. 10

14 IV. Conclusion The paper investigated the role o authority and control in the special case where suppliers can hand over partial control over their irm to the manuacturer. We have shown that standard just-in-time purchasing agreements can lead to optimal incentives to invest in lexible production. The reason underlying this eect is that i investments in lexibility are socially important then it may be optimal or the supplier to give up control over the delivery schedule since this leads to schedules o higher volatility chosen by the manuacturer. This in turn causes more eicient investment incentives on the part o the supplier. Thus, in this case, the supplier deliberately gives up partial control over his irm in order to reach an outcome that both supplier and manuacturer preer. For reasons o tractability, the model used to derive our results neglects the complicated time structure o order and delivery in manuacturing. A desirable dynamic extension o the model meets resistance. For example, one could want to include that the parties re-negotiate repeatedly over the per-period delivery schedule instead bargaining once and or all over the delivery schedule's volatility. This would mean to model explicitly the periodical planning o the supplier's production, given incomplete inormation about uture orders by the manuacturer. However, this by itsel is already an intricate optimization problem (c. Holt et al. (1960)). 11

15 Appendix We give a proo or proposition 1. (The proo o proposition is almost identical and is thereore dropped.) We show that giving the control rights about to the supplier lowers the investment level i ( α ) deined as the solution to ( i i ) K ( i ) C C ( ) ( i, ), ( ) 1 α α =. (A1) Note irst that i α = 1, equation (A1) is identical to equation (3) that characterizes the socially eicient i. Thus, it suices to show that ( ) i α decreases in α. Total dierentiation o (A1) with respect to i and α yields di ( ) dα α = C α C ( i ( i )) + i ( i ) ( ) C ( i, ) i, ( i ) C + C ( ) ( i ) ( α).,, ( i ) K ( i ) + 1, + (A) Since C < 0, the numerator is positive or = 0 and negative or = 1. We show that the denominator is positive. For this, consider the irst-order condition characterizing ( i ), i.e. C ( ( i )) i ( i ) L = ( ),. (A3) Total dierentiation o (A3) with respect to i and yields d di ( i ) C i =. (A4) L C + 1

16 Thus, since C is convex the expression in parentheses in the denominator o (A) is positive. Hence, the denominator o (A) is positive, proving the assertion. Q.E.D. Reerences Crémer, Jacques (1995): "Towards an economic theory o incentives in just-in-time manuacturing," European Economic Review, 39, Grossman, Sanord J., and Oliver D. Hart (1986): "The Costs and Beneits o Ownership: A Theory o Lateral and Vertical Integration," Journal o Political Economy, 94, Hall, Robert W. (1983): "Zero Inventories," Dow Jones-Irwin, Homewood, Illinois. Helper, Susan R., and Mari Sako (1995): "Supplier Relations in Japan and the United States: Are they converging?," Sloan Management Review, Spring 1995, Holt, Charles C., Franco Modigliani, John F. Muth, Herbert A. Simon (1960): "Planning Production, Inventories, and Work Force," Prentice-Hall, Englewood Clis, N.J. Schonberger, Richard J. (198): "Japanese Manuacturing Techniques: Nine Hidden Lessons in Simplicity," Free Press, New York. Simon, Herbert A. (1951): "A Formal Theory o the Employment Relationship", Econometrica, 19,