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Explicit modeling of multi-period setup times in proportional lot-sizing and scheduling problem with variable capacity

Waldemar Kaczmarczyk

Archives of Control Sciences | 2021 | vol. 31 | No 4 | 883-812 | DOI: 10.24425/acs.2021.139735

Keywords production lot-sizing and scheduling mixed-integer programming

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Abstract

Small bucket models with many short fictitious micro-periods ensure high-quality schedules in multi-level systems, i.e., with multiple stages or dependent demand. In such models, setup times longer than a single period are, however, more likely. This paper presents new mixedinteger programming models for the proportional lot-sizing and scheduling problem (PLSP) with setup operations overlapping multiple periods with variable capacity.
A new model is proposed that explicitly determines periods overlapped by each setup operation and the time spent on setup execution during each period. The model assumes that most periods have the same length; however, a few of them are shorter, and the time interval determined by two consecutive shorter periods is always longer than a single setup operation. The computational experiments showthat the newmodel requires a significantly smaller computation effort than known models.

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Authors and Affiliations

Waldemar Kaczmarczyk

Department of Strategic Management, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland