A Stackelberg game in a production-distribution system with multiple buyers

This paper investigates the coordination of deliveries between a vendor (or manufacturer) and multiple heterogeneous buyers (or retailers) in a two-level supply chain with a decentralized decision process. A continuous deterministic model is presented. To satisfy the buyers’ demands, the vendor delivers the product in JIT shipments to each buyer. The buyers’ demands (continuous) have to be satisfied by the vendor. The production rate is constant and sufficient to meet the buyers’ demands. The product is delivered in discrete batches from the vendor’s stock to the buyers’ stocks and all shipments are realized instantaneously. A special class of production-delivery-replenishment policies of the vendor and the buyers are analyzed. In a competitive situation, the objective is to determine schedules, which minimize the individual average total cost of production, shipment and stockholding in the production-distribution cycle (PDC). This paper presents a game theoretic model without prices, where agents minimize their own costs. It is a non-cooperative (1 + n)-person constrained game with agents (a single vendor and n buyers) choosing the number and sizes of deliveries. The model describes inventory patterns and the cost structure of PDC. It is proven that there exist equilibrium strategies in the considered Stackelberg sub-games with the vendor as the leader. Solution procedures are developed to find the Stackelberg game equilibrium.