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

Jack Frederick Williams

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Supply Chain and Inventory Management Scheduling and Optimization Algorithms Optimization and Mathematical Programming

Abstract

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.

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References

2004Optimal Policies for a Multi-Echelon Inventory Problem 1969Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems 1973Economic Lot Size Determination in Multi-Stage Assembly Systems 1975Optimal and System Myopic Policies for Multi-Echelon Production/Inventory Assembly Systems 1973A Simple Continuous Review Deterministic One-Warehouse N-Retailer Inventory Problem 1972A Facilities in Series Inventory Model with Nested Schedules 1972An informal survey of multi‐echelon inventory theory 1973Dynamic Lot Size Models for Multi-Stage Assembly Systems

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1988Analysis of Multistage Production Systems 2004Integrated Production and Distribution Operations 1982Note—On the Optimality of Integer Lot Size Ratios in “Economic Lot Size Determination in Multi-Stage Assembly Systems”2017Methodological approaches to supply chain design 1986Multi-Stage Lot-Sizing for General Production Systems 2006

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