The Single-Product Lot-Sizing Problem with Constant Parameters and Backlogging: Exact Results, a New Solution, and All Parameter Stability Regions

We consider the single-product lot-sizing problem over a finite planning horizon. Demand at each period is constant, and excess demand is completely backlogged. Holding and backlogging costs are proportional to the amount of inventory stocked or backlogged, while ordering cost is fixed, independent of the quantity ordered. The optimal policy targets to minimize the total relevant costs over the planning horizon. The key results of this paper are: (1) an explicit formula for the optimal total cost as a function of the model parameters and the number of cycles of the policy; (2) a new, polynomial-time algorithm which determines the overall optimal policy; and (3) stability regions for any solution considering simultaneous variations on all cost and demand parameters. The proposed algorithm is easy to implement and therefore is suitable for practical use.

[1]  H. Kunreuther,et al.  Planning Horizons for the Dynamic Lot Size Model with Backlogging , 1974 .

[2]  C.P.M. van Hoesel,et al.  Parametric Analysis of Setup Cost in the Economic Lot-Sizing Model without Speculative Motives , 2000 .

[3]  A. Federgruen,et al.  The dynamic lot-sizing model with backlogging: A simple o(n log n) algorithm and minimal forecast horizon procedure , 1993 .

[4]  W. Zangwill.  A Deterministic Multi-Period Production Scheduling Model with Backlogging , 1966 .

[5]  Suresh Chand,et al.  Setup cost stability region for the dynamic lot sizing problem with backlogging , 1992 .

[6]  Knut Richter.  Stability of the constant cost dynamic lot size model , 1987 .

[7]  Albert P. M. Wagelmans,et al.  A note on 'Stability of the constant cost dynamic lot size model' by K. Richter * , 1991 .

[8]  W. Zangwill.  A Backlogging Model and a Multi-Echelon Model of a Dynamic Economic Lot Size Production System---A Network Approach , 1969 .

[9]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[10]  Knut Richter,et al.  Sequential stability of the constant cost dynamic lot size model-searching for monotonicity , 1994 .

[11]  S. Papachristos,et al.  Optimal policy and stability regions for the single product periodic review inventory problem, with stationary demands , 1998, J. Oper. Res. Soc..

[12]  Knut Richter.  Sequential stability of the constant cost dynamic lot size model , 1994 .

[13]  Alok Aggarwal,et al.  Improved Algorithms for Economic Lot Size Problems , 1993, Oper. Res..

[14]  T. Morton.  Note—An Improved Algorithm for the Stationary Cost Dynamic Lot Size Model with Backlogging , 1978 .