A Profit-Equilibrium Model for Retailers and Vendors in the Vendor Managed Inventory Problem

In this paper, we discuss how the availability and flow of products from an unlimited central warehouse to a retailer network through a vendor in a Vendor Managed Inventory (VMI) supply chain is optimized. First, we define a multiple items inventory model as a basis for describing the VMI supply chain. This model includes a single vendor, its separate central warehouse with unlimited space and orders and its competing retailer network. The mutually beneficial relationships between a vendor and its retailers are described as different types of prices, such as marked prices, cost price, selling price, retailers’ price, considering the customer demand functions. In this way, optimizing the availability and flow of product items means optimizing the profit of both the vendor and retailers; this problem could be considered as a Nash game where players are the retailers and vendors. Our approach is to find the Nash equilibrium by combining particle swarm optimization (PSO) and genetic algorithm (GA). The experimented result of the proposed method is compared to the most referred multi-objective optimization algorithm such as PSO and GA. Furthermore, the effect of cost components on VMI parameters is discussed.