Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Cooperation in stochastic inventory models with continuous review

Consider multiple companies that continuously review their inventories and face Poisson demand. We study cooperation strategies for these companies and analyse if there exist allocations of the joint cost such that any company has lower costs than on its own; such allocations are called stable cost allocations. We start with two companies that jointly place an order for replenishment if their joint inventory position reaches a certain reorder level. This strategy leads to a simple expression of the joint costs. However, these costs exceed the costs for non-cooperating companies. Therefore, we examine another cooperation strategy. Namely, the companies reorder as soon as one of them reaches its reorder level. This latter strategy has lower costs than for non-cooperating companies. Numerical experiments show that the gametheoretical distribution rule — a cost allocation in which the companies share the procurement cost and each pays its own holding cost — is a stable cost allocation. These results also hold for situations with multiple companies

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

Application of game theory in inventory management

Game theory has been successfully applied in supply chain management problems due to its capacity of modeling situations where companies have to make strategic decisions about their production planning, inventory control and distribution systems. In particular, this article presents the application of game theory in inventory management. First, we presente the basics concepts of non-cooperative and cooperative game theory. Then, we present inventory models by means of game theory. For each model, we provide its configuration, the solution concept implemented, and the existence and uniqueness of the equilibrium used.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Application of game theory in inventory management

Game theory has been successfully applied in supply chain management problems due to its capacity of modeling situations where companies have to make strategic decisions about their production planning, inventory control and distribution systems. In particular, this article presents the application of game theory in inventory management. First, we presente the basics concepts of non-cooperative and cooperative game theory. Then, we present inventory models by means of game theory. For each model, we provide its configuration, the solution concept implemented, and the existence and uniqueness of the equilibrium used.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Game-theoretic learning and allocations in robust dynamic coalitional games

The problem of allocation in coalitional games with noisy observations and dynamic4 environments is considered. The evolution of the excess is modelled by a stochastic differential5 inclusion involving both deterministic and stochastic uncertainties. The main contribution is a6 set of linear matrix inequality conditions which guarantee that the distance of any solution of the7 stochastic differential inclusions from a predefined target set is second-moment bounded. As a direct8 consequence of the above result we derive stronger conditions still in the form of linear matrix9 inequalities to hold in the entire state space, which guarantee second-moment boundedness. Another10 consequence of the main result are conditions for convergence almost surely to the target set, when the11 Brownian motion vanishes in proximity of the set. As further result we prove convergence conditions12 to the target set of any solution to the stochastic differential equation if the stochastic disturbance13 has bounded support. We illustrate the results on a simulated intelligent mobility scenario involving14 a transport network