Modelling Set-up Times Overlapping Two Periods in the Proportional Lot-Sizing Problem with Identical Parallel Machines
DOI:
https://doi.org/10.7494/dmms.2013.7.1.43Keywords:
production planning, lot-sizing and scheduling, mixed integer programmingAbstract
This paper presents a new mixed integer programming model for the Proportional Lot-Sizing Problem (PLSP) with identical parallel machines and set-up times overlappingtwo periods. The proposed model assumes constant period length and explicitly calculates the distribution of set-up operations among periods. The presented results of computational experiments with standard mip methods prove that the untying set-ups from period borders enables the reduction of the total costs in optimal solutions.References
Haase K., 1994. Lotsizing and scheduling for production planning. No. 408 Lecture Notes in Economics and Mathematical Systems, Springer-Verlag.
Drexl A., Haase K., 1995. Proportional lotsizing and scheduling, International Journal of Production Economics, 40, pp. 73-87.
Kaczmarczyk W., 2011. Proportional lot-sizing and scheduling problem with identical parallel machines, International Journal of Production Research, 49(9), pp. 2605-2623.
Belvaux G., Wolsey L.A., 2001. Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs, Management Science, 47(7), pp. 993-1007.
Suerie C., 2006. Modeling of period overlapping setup times, European Journal of Operational Research, 174(2): 874-886.
Cattrysse D., Salomon M., Kuik R., van Wassenhove L., 1993. A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times, Management Science, 39, 477-486.
Blocher J.D., Chand S., Sengupta K., 1999. The changeover scheduling problem with time and cost considerations: Analytical results and a forward algorithm, Operations Research, 47, pp. 559–569.
Kaczmarczyk W., 2009. Modelling Multi-Period Set-up Times in the Proportional Lot-Sizing Problem, Decision Making in Manufacturing and Services, 3, pp. 15–35.
Drexl A., Kimms A., 1997. Lot sizing and scheduling — survey and extensions, European Journal Operational Research, 99, pp. 221-235.
Wolsey L.A., 2002. Solving Multi-Item Lot-Sizing Problems with an MIP Solver Using Classification and Reformulation, Management Science., 48(12), pp. 1587-1602.
Kimms A., Drexl A., 1998. Proportional lotsizing and scheduling: some Extensions, Networks, 32 (2), pp. 85-101.
Karmarkar U.S., Schrage L., 1985. The Deterministic Dynamic Product Cycling Problem. Operations Research, 33 (2), pp. 326-345.
Wolsey L.A., 1989. Uncapacitated Lot-Sizing Problems With Start-Up Costs, Operations Research, 37 (5), pp. 741-747.
Downloads
Published
How to Cite
Issue
Section
License
Remeber to prepeare, sign and scan copyright statement
The content of the journal is freely available according to the Creative Commons License Attribution 4.0 International (CC BY 4.0)
Accepted 2014-05-15
Published 2014-05-20