Optimal Mixed Batch Shipment Policy with Variable Safety Factor for the Single-Vendor Single-Buyer Production-Inventory System

This study investigates the production and inventory problem involving stochastic demand in a single‐vendor single‐buyer integrated system. The stochastic model is constructed and is controlled by both the reorder and shipping points with mixed geometric and equal batch shipment policy and variable safety factor. The minimum cost model is transformed into the maximum order quantity model. Consequently, the structure of mixed geometric and equal shipments can easily be obtained. The structure of the mixed geometric and equal shipments comprises number of batches, number of geometric shipments, and ratio of equal sized shipments to the size of the first shipment. The problem is solved using the proposed algorithm that determines the economic lot size, the structure of the mixed geometric and equal shipments, and the safety factor. An illustrative example demonstrates the effectiveness of the algorithmic procedures.