A Hybrid Algorithm for Simultaneous Scheduling of Production and Distribution in Multi-Echelon Structures

This paper presents a dynamic programming algorithm for simultaneous determination of production batch sizes in an assembly network and distribution batch sizes in a conjoined distribution (“arborescent”) network. The objective is to minimize average cost per period over an infinite horizon. Costs consist of processing costs at each node and linear holding costs for inventory. Final product demand rates may vary among the retail nodes, but at each retail node the demand rate is assumed to be known, constant, and continuous. All demand must be met; backorders are not permitted. The model can be used for a single product, or for several products that are temporarily combined for distribution, or for scheduling production in a system where several end products are produced from the same intermediate product, as in some biochemical manufacturing processes.