Economic Lot Size Determination in Multi-Stage Assembly Systems

Wallace B. Crowston · Jack Frederick Williams

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Supply Chain and Inventory Management Management and Optimization Techniques Scheduling and Optimization Algorithms

Abstract

We consider the optimal lot size problem for multi-stage assembly systems where each facility may have many predecessors but only a single successor. Assumptions include constant continuous final product demand, instantaneous production, and an infinite planning horizon. Costs at each facility consist of a fixed charge per lot and a linear holding cost. Under the constraint that lot sizes remain time invariant, it is proven that the optimal lot size at each facility is an integer multiple of the lot size at the successor facility. This fact is used in the construction of a dynamic programming algorithm for the computation of optimal lot sizes. The algorithm exploits the concept of echelon stock [Clark, A. J., H. Scarf. 1960. Optimal policies for a multi-echelon inventory problem. Management Sci. 6 (4, July) 475–490; Clark, A. J., H. Scarf. 1962. Approximate solution to a simple multi-echelon inventory problem. Chapter 5. K. J. Arrow et al., eds. Studies in Applied Probability and Management Science. Stanford University Press, Stanford, California.].

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2004Optimal Policies for a Multi-Echelon Inventory Problem 1969A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System—A Network Approach 2012Including sustainability criteria into inventory models 1966A Deterministic Multi-Period Production Scheduling Model with Backlogging 1969Minimum Concave-Cost Solution of Leontief Substitution Models of Multi-Facility Inventory Systems

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1982Improved Heuristics for Multi-Stage Requirements Planning Systems 1986A 98%-Effective Lot-Sizing Rule for a Multi-Product, Multi-Stage Production / Inventory System 1993Models for multi-plant coordination 1975Optimal and System Myopic Policies for Multi-Echelon Production/Inventory Assembly Systems 1973Dynamic Lot Size Models for Multi-Stage Assembly Systems 1975Manufacturing Cycle Time Determination for a Multi-Stage Economic Production Quantity Model 1980Optimal Multi-Level Lot Sizing for Requirements Planning Systems 1985Continuous-Review Policies for a Multi-Echelon Inventory Problem with Stochastic Demand

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