Planning Horizons for the Dynamic Lot Size Model with Backlogging

Joseph D. Blackburn · Howard Kunreuther

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Supply Chain and Inventory Management Management and Optimization Techniques Optimization and Mathematical Programming

Abstract

Planning horizons are developed for the dynamic economic lot site model with backlogging when the marginal production cost is either constant or variable. The inventory holding and backlogging cost functions are assumed to be concave. An efficient forward algorithm generalizes the Eppen-Gould-Pashigian procedure and enables us to place bounds on the optimal production plan should a horizon not be found.

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References

2004Dynamic Version of the Economic Lot Size Model 1969A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System—A Network Approach 1969Extensions of the Planning Horizon Theorem in the Dynamic Lot Size Model 1964Some Generalizations of an Inventory Planning Horizon Theorem

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1993Chapter 1 Single-Product, single-Location models 1993The dynamic lot-sizing model with backlogging: A simpleo(n logn) algorithm and minimal forecast horizon procedure 1979Coordinated replenishments of items under time‐varying demand: Dynamic programming formulation 1976The Assortment Problem with Nonlinear Cost Functions 1998Infinite Horizon Production Planning in Time-Varying Systems with Convex Production and Inventory Costs 1986Rolling Planning Horizons: Error Bounds for the Dynamic Lot Size Model 1988Multiproduct dynamic lot-sizing model with coordinated replenishments 2012A polynomial algorithm for a lot-sizing problem with backlogging, outsourcing and limited inventory

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