Cooperation and profit allocation in distribution chains

We study the coordination of actions and the allocation of profit in distribution chains under decentralized control. We consider distribution chains in which a single supplier supplies goods for replenishment of stocks of several retailers who, in turn, sell these goods to their own separate markets. The goal of the supplier and the retailers is to maximize their individual profits. Since the optimal joint profit under centralized control is larger than the sum of the individual optimal profits under decentralized control, cooperation among firms by means of coordination of actions may improve individual profits. The effects of cooperation are studied by means of cooperative games. For each distribution chain we define a corresponding cooperative game and study its properties. Among others we show that such games are balanced. Based on the nice core structure a stable solution concept for these games is proposed and its properties are interpreted in terms of the underlying distribution chain. \u

Non-cooperative joint replenishment under asymmetric information

Cataloged from PDF version of article.We consider jointly replenishing n ex-ante identical firms that operate under an EOQ like setting using a non-cooperative game under asymmetric information. In this game, each firm, upon being privately informed about its demand rate (or inventory cost rate), submits a private contribution to an intermediary that specifies how much it is willing to pay for its replenishment per unit of time and the intermediary determines the maximum feasible frequency for the joint orders that would finance the fixed replenishment cost. We show that a Bayesian Nash equilibrium exists and characterize the equilibrium in this game. We also show that the contributions are monotone increasing in each firm’s type. We finally conduct a numerical study to compare the equilibrium to solutions obtained under independent and cooperative ordering, and under full information. The results show that while information asymmetry eliminates free-riding in the contributions game, the resulting aggregate contributions are not as high as under full information, leading to higher aggregate costs. 2013 Elsevier B.V. All rights reserved

Finding a Nash equilibrium in noncooperative N-person games by solving a sequence of linear stationary point problems

Game Theory;Nash Equilibrium

Cooperation in Supply Chain Networks: Motives, Outcomes, and Barriers

This paper analyzes the phenomenon of cooperation in modern supply chains in the light of Game Theory. We first provide a discussion on the meaning of cooperation in supply chains, its motives, outcomes and barriers. We then highlighted the applicability of Cooperative Game Theory as methodology for analyzing cooperation in supply chains. Second, we review recent studies that analyze the cooperation in supply chains by means of cooperative game theory. A special emphasis will be given inventory centralizations games. Finally, gaps in the literature are identified to clarify and to suggest future research opportunities

Coordinating the Optimal Discount Schedules of Supplier and Carrier

Transportation is important in making supply chain decisions. With the careful consideration of transportation expenses, the performance of each supply chain member, as well as the entire supply chain, could be improved significantly. The purpose of this research is: 1) to explore and identify the various situations that relate to replenishment and transportation activities; and 2) to reveal the strength of the connection between purchase quantity and transportation discounts, and integrate the two discounts to enhance supply-chain coordination. The problem is analyzed and categorized into four representative cases, depending on transportation. To aid the supplier or the carrier to determine the discount that should be offered, in light of the buyer's reaction to that discount, decision models are proposed under three different circumstances. First, assuming a single product, we investigate the quantity discounts from the supplier's perspective, via a noncooperative game-theoretical approach and also a joint decision model. Taking into account the price elasticity of demand, this analysis aids a sole supplier in establishing an all-unit quantity discount policy in light of the buyer's best reaction. The Stackelberg equilibrium and the Pareto-optimal solution set are derived for the noncooperative and joint-decision cases, respectively. Our research indicates that channel efficiency can be improved significantly if the quantity discount decision is made jointly rather than noncooperatively. Moreover, we extend our model in several directions: (a) the product is transported by a private fleet; (b) the buyer may choose to offer her customers a different percentage discount than that she obtained from the supplier; and (c) the case of multiple (heterogeneous) buyers. Numerical examples are employed, here and throughout the thesis, to illustrate the practical applications of the models presented and the sensitivity to model parameters. Secondly, we consider a situation with a family of SKUs for which the supplier will offer a quantity discount, according to the aggregate purchases of the product group. Management of those items is based on the modified periodic policy. From the supplier's point of view, what are the optimal parameters (breakpoint and discount percentage)? For deterministic demand, we discuss the cases in which demand is both constant and price-sensitive. First as a noncooperative Stackelberg game, and then when the two parties make the discount and replenishment decisions jointly, we illustrate the impact of price-sensitivity and joint decision making on the supplier's discount policy. The third approach studies the case in which transportation of the goods by a common carrier (a public, for-hire trucking company) is integrated in the quantity discount decisions. In reality, it is quite difficult for the carrier to determine the proper transportation discount, especially in the case of LTL (less-than-truckload) trucking. This is not only because of the "phantom freight" phenomenon, caused by possible over-declaration of the weight by the shipper, but also due to the fact that the discount relates to both transportation and inventory issues. In this research, we study the problem of coordinating the transportation and quantity discount decisions from the perspectives of the parties who offer the discounts, rather than the ones that take them. By comparison of the noncooperative and cooperative models, we show that cooperation provides better overall results, not only to each party, but also to the entire supply chain. To divide the extra payoffs gained from that cooperation, we further conduct a coalition analysis, based upon the concept of "Shapley Value." A detailed algorithm and numerical examples are provided to illustrate the solution procedure. Finally, the thesis concludes with comprehensive remarks. We summarize the contributions of this thesis, show the overall results obtained here, and present the directions that our research may take in the future

Large Newsvendor Games

We consider a game, called newsvendor game, where several retailers, who face a random demand, can pool their resources and build a centralized inventory that stocks a single item on their behalf. Profits have to be allocated in a way that is advantageous to all the retailers. A game in characteristic form is obtained by assigning to each coalition its optimal expected profit. A similar game (modeled in terms of costs) was considered by Muller et al. (2002), who proved that this game is balanced for every possible joint distribution of the random demands. In this paper we consider newsvendor games with possibly an infinite number of newsvendors. We prove in great generality results about balancedness of the game, and we show that in a game with a continuum of players, under a nonatomic condition on the demand, the core is a singleton. For a particular class of demands we show how the core shrinks to a singleton when the number of players increases.newsvendor games, nonatomic games, core, balanced games.

Cooperation on capacitated inventory situations with fixed holding costs

[Abstract] In this paper we analyze a situation in which several firms deal with inventory problems concerning the same type of product. We consider that each firm uses its limited capacity warehouse for storing purposes and that it faces an economic order quantity model where storage costs are irrelevant (and assumed to be zero) and shortages are allowed. In this setting, we show that firms can save costs by placing joint orders and obtain an optimal order policy for the firms. Besides, we identify an associated class of costs games which we show to be concave. Finally, we introduce and study a rule to share the costs among the firms which provides core allocations and can be easily computed.Ministerio de Ciencia e Innovación; MTM2011-23205Galicia. Consellería de Economía e Industria; INCITE09-207-064-PRComunidad Valenciana. Generalidad; ACOMP/2014Ministerio de Ciencia e Innovación; MTM2011-27731-C0

E-Fulfillment and Multi-Channel Distribution – A Review

This review addresses the specific supply chain management issues of Internet fulfillment in a multi-channel environment. It provides a systematic overview of managerial planning tasks and reviews corresponding quantitative models. In this way, we aim to enhance the understanding of multi-channel e-fulfillment and to identify gaps between relevant managerial issues and academic literature, thereby indicating directions for future research. One of the recurrent patterns in today’s e-commerce operations is the combination of ‘bricks-and-clicks’, the integration of e-fulfillment into a portfolio of multiple alternative distribution channels. From a supply chain management perspective, multi-channel distribution provides opportunities for serving different customer segments, creating synergies, and exploiting economies of scale. However, in order to successfully exploit these opportunities companies need to master novel challenges. In particular, the design of a multi-channel distribution system requires a constant trade-off between process integration and separation across multiple channels. In addition, sales and operations decisions are ever more tightly intertwined as delivery and after-sales services are becoming key components of the product offering.Distribution;E-fulfillment;Literature Review;Online Retailing

Experiments for Satellite and Material Recovery from Orbit. Volume III - Experiment Missions Final Report

Experiment missions for OSO satellite rendezvous, capture, material recovery, refurbishment, and extravehicular operation wor