An Optimal Mixed Batch Shipment Policy for Multiple Items in a Single-Supplier Multiple-Retailer Integrated System

This study addresses mixed batch shipment policy with common replenishment cycle for multiple items in a single-supplier multiple-retailer integrated system. The supplier produces multiple items on a single facility under a common replenishment cycle and delivers products to retailer utilizing a mixed batch shipment policy. The objective is to determine the optimal replenishment cycle, the number of shipments, and the structure of mixed shipment, all of which minimize the integrated total cost per unit time. The single-item isolation model is constructed first, and the single-item isolation model is then integrated into the single-item integration model. Moreover, the single-item integration model is integrated into the multi-item integration model. The minimum total cost model is transformed into a maximum replenishment cycle model to optimize the structure of the mixed batch shipment. The replenishment cycle division method is then developed to obtain the optimal solutions to the subject problem. Examples are presented to illustrate the procedures involved in the replenishment cycle division method.