Lead-time hedging and coordination between manufacturing and sales departments using Nash and Stackelberg games

doi:10.1016/j.ejor.2010.09.001

European Journal of Operational Research

Volume 210, Issue 2, 16 April 2011, Pages 231-240

https://doi.org/10.1016/j.ejor.2010.09.001 Get rights and content

Abstract

In a firm, potential conflict exists between manufacturing and sales departments. Salespersons prefer to order from manufacturing departments in advance so that they can secure products in the amount they need to satisfy customers in time. This time in advance strategy is defined as “lead-time hedging.” While this hedging strategy is good for the sales department to guarantee the right quantity at the right time for customers, it adds additional costs and pressure to the manufacturing department. One scheme to resolve this conflict is to introduce a fair “internal price,” charged by the manufacturing department to the sales department. In this paper, two models involving a fair internal price are introduced. In one model, a Nash game is played to reach an optimal strategy for both parties. In the other model, a Stackelberg game is played in which the manufacturing department serves as the leader. We show that these two models can successfully reduce lead-time hedging determined by the salesperson and can increase the firm’s overall profit, as compared to the traditional model without considering the internal price. More insights have also been analyzed that include the comparisons of the manufacturer’s and the salesperson’s profits among the traditional model, the Nash game model, the Stackelberg game model, and the centralized global optimization model.

Introduction

In today’s rapidly changing business environment, many conflict areas exist between manufacturing and sales departments (Shapiro, 1977). These conflict areas are caused in practice by the sales department pushing the manufacturing department. According to Shapiro (1977), one of the conflict areas between the manufacturing and the sales departments is the production scheduling and distribution. The sales department informs the manufacturing department that customers need products at a time before they actually do. This time in advance is defined as lead-time hedging. This hedging strategy implemented by the sales department reduces the lead-time and pushes the manufacturing department to produce in a shorter amount of time.

To be more specific, let t₀ be the actual due time that one customer needs a product and this information is known by one salesperson. However, instead of telling the manufacturing department the actual due time, the salesperson makes an order at time t₁ and informs the manufacturing department that the customer needs the product at time t₂, which is ahead of t₀. Clearly, from the definition of lead-time, which is referred to the time span between customer ordering and customer receipt of the product, t₀ − t₁ should be the actual maximum allowable lead-time for the manufacturing department to produce the product. But since the manufacturing department is informed that t₂ is the due time, the maximum allowable lead-time becomes t₂ − t₁. In this way, the salesperson pushes the lead-time from t₀ − t₁ to t₂ − t₁. The difference between the two, i.e., t₀ − t₂, is referred to as lead-time hedging amount in this paper.

The reason for the existence of lead-time hedging for salespersons in the sale department is that they are always concerned about whether the manufacturing department can deliver the order in time, due to uncertainties in the production process (e.g., weather conditions, machine breakdown, etc.). If the manufacturing department fails to deliver the product in time, the customer may be lost. Therefore, “lead-time hedging” provides a means of protection against losing customers.

While lead-time hedging is good for salespersons to guarantee the right quantities at the right time for customers, it adds much pressure for the manufacturing department. In order to produce the required quantities in a shorter amount of time, the manufacturing department may need employees to work over time, or even need to increase capacities, both of which add extra cost burden. Thus, it is necessary to introduce a scheme to coordinate two departments in order to maximize the firm’s overall profit.

What scheme should be used to resolve the conflict? What are optimal strategies for the manufacturing and the sales departments under this scheme? How is the entire firm’s profit influenced by the scheme? These are the main questions answered in this paper. To be more specific, the scheme discussed in this paper involves an “internal price”. The manufacturing department charges the sales department a fair internal price to balance the cost pressure. For instance, the internal price increases as the lead-time hedging amount increases. By introducing this internal price, the entire firm’s profit will be increased, as compared to the case in which no coordination scheme is incorporated. Two models are studied. One is a Nash game model, where the manufacturing department and the sales department provide the internal price and the lead-time hedging amount simultaneously. The other is a Stackelberg game model, which gives the manufacturing department a leading role. It is demonstrated that these two models can successfully reduce the lead-time hedging amount determined by the sales department and can increase the firm’s overall profit. In addition, the performance of the Stackelberg game model is better than that of the Nash game model, and the entire firm’s profit of the Stackelberg game model is very close to the centralized global optimal profit.

The remaining part of this paper is organized as follows. Section 2 gives a literature review on previous related research. Section 3 describes the problem, makes assumptions, and provides notation for the problem. In Section 4, a traditional model without any introduced scheme is presented and optimal strategies for this model are studied. In Section 5, an “internal price” scheme is introduced and both departments make decisions simultaneously. A Nash game model is studied to coordinate the system. Section 6 studies a Stackelberg game model in which the manufacturing department plays a leading role. Section 7 provides the comparisons of the three models together with a centralized global optimization model. Numerical studies are used to compare the entire firm’s profit under four models and to verify the previous analytical results. Section 8 concludes our study and demonstrates that the Nash game model and the Stackelberg game model successfully resolve the potential conflict. Finally, future research directions are explored in Section 9.

Section snippets

Literature review

There has been significant research progress in the area on lead-time and pricing decisions. Most previous research focuses on studying the cases in which customer demands are modeled as a function of lead-time or price. Various literature can be classified by three schemes. The first one is on the setting of the problem that a paper is solving. For instance, a paper may address the following questions: Is there a centralized decision maker controlling price and lead time? Or are price and lead

Modeling assumptions and notation

In this paper, a firm with one manufacturing department and one sales department is considered, and a single product is produced by the manufacturing department. The sales department has several orders on hand, denoted as orders 1, 2, … , n. The demand for each order i, denoted as D_i, is given and can be different from each other. As previously described, the sales department sells the products to the customer at sale price, and informs the manufacturing department the due time. In practice, the

A traditional model without coordination

This model estimates the sales department’s profit based on the condition that there is no coordination scheme. This model considers one manufacturing department and one sales department. Each order i, i = 1, 2, … , n, has a given demand D_i selling to customers at a fixed price p. The lead-time hedging amount t_i is chosen when the order is placed by the sales department. A larger t_i will lead to less risk to unfill the order, but will have larger holding cost for the sales department. Thus, the sales

Nash game model

In the traditional model, the sales department has enough power in which they can sacrifice the manufacturing department in order to benefit itself. In this Section, a coordinated scheme is introduced. This scheme gives both parties equal power and helps the manufacturing department mitigate extra costs caused by lead-time hedging, by introducing a fair internal price for the sales department. For instance, the manufacturing department will charge the sales department an internal price.

A Nash

Stackelberg game model

This Section discusses the same scheme as the previous Section, with the difference being that the manufacturing department serves as the leader and a Stackelberg game is incorporated.

In the game, the manufacturing department, as a Stackelberg leader, decides a fair internal price, w, for each order provided by the sales department to maximize the manufacturing department’s total profit, taking into account the expected sales department’ behavior on the first stage. On the second stage, the

Comparative analysis and numerical studies

Solutions in Proposition 1, Proposition 2, Proposition 3, Proposition 4 provide the basis for the traditional, the Nash game, and the Stackelberg game models. In this section, we compare the performances of these three models. In addition, in order to better demonstrate the performances of the two introduced models, the Nash game model and the Stackelberg game model, we also compare their performances with a centralized global optimization model, where the lead-time hedging value is determined

Conclusion

In this paper, we set up a coordination scheme for the manufacturing and the sales departments to solve the lead-time hedging issue. In our approach, an internal price was introduced and two different coordination models, the Nash game model and the Stackelberg game model were studied to solve the conflicts. In the Nash game model, the manufacturing and the sales departments decide the internal price and the lead-time hedging simultaneously. In the Stackelberg game model, the manufacturing

Future research

In future research, we will extend our research scope and study more general settings. For instance, we will incorporate more realistic constraints into our models such as the scarcity of resources for the manufacturing department. We will also consider the case in which the information between the two departments is not perfect and thus, stochastic models and Bayesian game will be studied. Besides these, we will consider the scenarios that incorporate shortage penalty, backlogging costs,

Acknowledgments

The authors thank the editor and the two referees for their helpful suggestions on improving the quality of this paper. This research was partially supported by the U.S. National Science Foundation under Award IIP-0725843.

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Published by Elsevier B.V.

Production, Manufacturing and LogisticsLead-time hedging and coordination between manufacturing and sales departments using Nash and Stackelberg games

Abstract

Introduction

Section snippets

Literature review

Modeling assumptions and notation

A traditional model without coordination

Nash game model

Stackelberg game model

Comparative analysis and numerical studies

Conclusion

Future research

Acknowledgments

Product differentiation and capacity cost interaction in time and price sensitive markets

Manufacturing & Service Operations Management

Supply Chain Management: Strategy Planning and Operations

Pricing and leadtime decisions in decentralized supply chains

Management Science

Lead-time setting, capacity utilization, and pricing decisions under lead-time dependent demand

IIE Transactions

Production, Manufacturing and Logistics
Lead-time hedging and coordination between manufacturing and sales departments using Nash and Stackelberg games