On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

Drift or shift? Continuity, change, and international variation in knowledge production in OR/MS

With the aim of contributing to the debate around OR/MS as a discipline, this study provides a historical comparative investigation of publicly available knowledge production in the field. The empirical investigation is based on a content analysis of 300 randomly selected articles from six major journals in the field. We have found: (1) since the late 1950s to the present day there has been no significant change in the types of published research in OR/MS in North America; (2) from the late 1950s to the present day, there have been significant differences in types of published research in OR/MS internationally. The imputed imbalance between theory and applications in published work had already occurred in the early stages of the development of OR/MS in North America and has since remained very much the same. Furthermore, research in the United Kingdom has been distinctly different from that dominant in North America and elsewhere. There are also indications that outside North America and the United Kingdom there is an emerging turn towards applications-oriented research. Over the last two or three decades there has been a significant increase overall in the share of articles published by academic authors