A note on 'Stability of the constant cost dynamic lot size model' by K. Richter

Stan van Hoesel*, Albert Wagelmans

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

4 Citations (Scopus)


In a paper by K. Richter the stability regions of the dynamic lot size model with constant cost parameters are analyzed. In particular, an algorithm is suggested to compute the stability region of a so-called generalized solution. In general this region is only a subregion of the stability region of the optimal solution. In this note we show that in a computational effort that is of the same order as the running time of Richter's algorithm, it is possible to partition the parameter space in stability regions such that every region corresponds to another optimal solution.

Original languageEnglish
Pages (from-to)112-114
Number of pages3
JournalEuropean Journal of Operational Research
Issue number1
Publication statusPublished - 6 Nov 1991

Bibliographical note

Funding Information:
We consider the constant cost dynamic lot size problem with set-up cost c > 0, unit holding cost h > 0 and a planning horizon consisting of T periods. Richter (1987) has analyzed the stability region of this model, i.e., the following question was studied: given an optimal solution for the cost parameters c and h, for which other pairs of parameters (c', h') is the solution still optimal? To answer this question, the notion of a generalized solutuion was introduced. A generalized solution can be viewed as a complete description of the output of the well-known dynamic programming algorithm of Wagner and Whitin (1958). The generalized solutions of two different pairs of * This research was partially supported by the Dutch Organi-sation for Scientific Research (NWO) under grant no. 611-304-017.


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