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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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Bibliography

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[12] W. Kaczmarczyk: Modelling multi-period set-up times in the proportional lot-sizing problem. Decision Making in Manufacturing and Services, 3(1-2), (2009), 15–35, DOI: 10.7494/dmms.2009.3.2.15.
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[14] W. Kaczmarczyk: Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods. International Journal of Production Economics, 219(1), (2020), 236–247, DOI: 10.1016/j.ijpe.2019.06.005.
[15] W.Kaczmarczyk: Explicit modelling of multi-period setup times in proportional lot-sizing problem with constant capacity. (2021), Preprint available at Research Square, DOI: 10.21203/rs.3.rs-1086310/v1.
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Authors and Affiliations

Waldemar Kaczmarczyk
1
  1. Department of Strategic Management, AGH University of Science and Technology, Al.Mickiewicza 30, 30-059, Kraków, Poland

Coordinated Production Planning and Scheduling Problem in a Foundry

A. Stawowy J. Duda
Archives of Foundry Engineering | 2017 | vol. 17 | No 3 | DOI: 10.1515/afe-2017-0105
Keywords Heuristics Application of information technology to the foundry industry Mixed integer programming Production planning Scheduling
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Abstract

In the paper, we present a coordinated production planning and scheduling problem for three major shops in a typical alloy casting

foundry, i.e. a melting shop, molding shop with automatic line and a core shop. The castings, prepared from different metal, have different

weight and different number of cores. Although core preparation does not required as strict coordination with molding plan as metal

preparation in furnaces, some cores may have limited shelf life, depending on the material used, or at least it is usually not the best

organizational practice to prepare them long in advance. Core shop have limited capacity, so the cores for castings that require multiple

cores should be prepared earlier. We present a mixed integer programming model for the coordinated production planning and scheduling

problem of the shops. Then we propose a simple Lagrangian relaxation heuristic and evolutionary based heuristic to solve the coordinated

problem. The applicability of the proposed solution in industrial practice is verified on large instances of the problem with the data

simulating actual production parameters in one of the medium size foundry.

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Authors and Affiliations

A. Stawowy
J. Duda

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