Fast Solution and Detection of Minimal Forecast Horizons in Dynamic Programs with a Single Indicator of the Future: Applications to Dynamic Lot-Sizing Models

Awi Federgruen · Michal Tzur

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

Abstract

In most dynamic planning problems, one observes that an optimal decision at any given stage depends on limited information, i.e., information pertaining to a limited set of adjacent or nearby stages. This holds in particular for planning problems over time, where an optimal decision in a given period depends on information related to a limited future time horizon, a so-called forecast horizon, only. In this paper we identify a general class of dynamic programs in which an efficient forward algorithm can be designed to solve the problem and to identify minimal forecast horizons. Such a procedure specifies necessary and sufficient conditions for a stage to arise as a forecast horizon. This class of dynamic programs includes the single-item dynamic lot-sizing model with general concave costs, both with and without backlogging, to which special attention is given.

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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 1991A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time 1993Improved Algorithms for Economic Lot Size Problems 1993The dynamic lot-sizing model with backlogging: A simpleo(n logn) algorithm and minimal forecast horizon procedure 1994Minimal Forecast Horizons and a New Planning Procedure for the General Dynamic Lot Sizing Model: Nervousness Revisited

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2007Forecast Horizons for a Class of Dynamic Lot-Size Problems Under Discrete Future Demand 1996Learning in Setups: Analysis, Minimal Forecast Horizons, and Algorithms 2012Forecast and rolling horizons under demand substitution and production changeovers: analysis and insights

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