98%-Effective Lot Sizing for Series Inventory Systems with Backlogging

Derek R. Atkins · Daning Sun

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

Abstract

For deterministic series inventory systems with backlogging, we show that the continuous relaxation of the best integer frequency policies is a lower bound on all feasible policies. The problem with backlogging can be reduced, in O(n) time, to an equivalent problem without backlogging. Therefore, based on the result of R. O. Roundy (Roundy, R. O. 1983. 94%-Effective lot-sizing in multistage assembly systems. Technical Report 674, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York.), the best integer frequency policy provides a solution which is within 2% of the optimal.

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References

198598%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems 1986A 98%-Effective Lot-Sizing Rule for a Multi-Product, Multi-Stage Production / Inventory System 1985The Joint Replenishment Problem with a Powers-of-Two Restriction 1992Simple Power-of-Two Policies are Close to Optimal in a General Class of Production/Distribution Networks with General Joint Setup Costs

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2007A joint economic lot-size model for an integrated supply network using genetic algorithm 2001Multistage Lot Sizing Problems via Randomized Rounding 1998Stationary Policies in Multiechelon Inventory Systems with Deterministic Demand and Backlogging 2008Note: A Simple Heuristic for Serial Inventory Systems with Fixed Order Costs 199994%-Effective Policies for a Two-Stage Serial Inventory System with Stochastic Demand 2006Echelon-stock () control in two-stage serial stochastic inventory systems 2009A two-echelon inventory/distribution system with power demand pattern and backorders 2000Coordination of Production/Distribution Networks with Unbalanced Leadtimes

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