Integrating vendor managed inventory and cooperative game theory to effectively manage supply networks

This chapter discusses the issue of integrating inventory and distribution optimization together with game theory to effectively manage supply networks. Inventory and distribution simultaneously optimization is a challenging problem aiming at coordinating decisions related to inventory management with those related to transportation scheduling. This problem is known as the inventory routing problem (IRP) and is an underlying optimization model for supply networks implementing a vendor managed inventory (VMI) strategy. Game theory, and in particular cooperative games, involves several decision-makers willing to coordinate their strategies and share the payoff. In particular, coalitions of decision-makers can make binding agreements about joint strategies, pool their individual payoffs, and redistribute the total in some specified way. In a supply and distribution context, the manager of a franchising business must decide how much inventory to carry. Naturally, the manager of each sales-points wishes to carry an as low as possible amount of inventory and at the same time have enough inventory to cover all demand and not miss any potential sale. One possibility to achieve these two contrasting goals is to allow cooperation among the sales-points and trade the product at some fair price. Sales-points with an excess inventory may want to sell that surplus to other sales-points in the same cluster or coalition, facing a larger than expected demand. The game consists in determining clusters of sales-points which are willing to cooperate, a fair trade-price, and inventory quantities to be carried by each sales-points to minimize the total costs and maximize the total sales. In other models, the total cost of transportation between a depot and a set of customers must be divided among them and the game considers the synergies in the determination of the individual costs.

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