Non‐cooperative strategies for production and shipment lot sizing in one vendor–multi‐buyer system

The supply chain structure examined in this paper consists of a single vendor (or manufacturer) with multiple heterogeneous buyers (or retailers). A continuous deterministic model is presented. To satisfy buyers demands, the vendor will deliver the product in JIT shipments to each buyer. The production rate is constant and sufficient to meet the buyers’ demands. The product is shipped in discrete batches from the vendor's stock to buyers’ stocks and all shipments are realized instantaneously. Special production–replenishment policies of the vendor and the buyers are analyzed. That is, the production batch is transferred to each buyer in several sub‐batches in each production distribution cycle (PDC). This paper offers game model without prices, where agents minimize individual costs. It is a non‐cooperative (1+N)‐person game model with agents (a single vendor and N‐buyers) choosing numbers and sizes of transferred batches. The model describes inventory patterns and cost structure of PDC. It is proved that there exist Nash equilibria in several types of sub‐games of the considered game.