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

Journal title

Archives of Control Sciences




vol. 31


No 4


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



production ; lot-sizing and scheduling ; mixed-integer programming

Divisions of PAS

Nauki Techniczne




Committee of Automatic Control and Robotics PAS


[1] I. Barany, T.J. van Roy and L.A. Wolsey: Uncapacitated lot-sizing: The convex hull of solutions. Mathematical Programming Studies, 22 (1984), 32–43, DOI: 10.1007/BFb0121006.
[2] G. Belvaux and L.A. Wolsey: Modelling practical lot-sizing problems as mixed-integer programs. Management Science, 47(7), (2001), 993–1007, DOI: 10.1287/mnsc.47.7.993.9800.
[3] J.D. Blocher, S. Chand and K. Sengupta: The changeover scheduling problem with time and cost considerations: Analytical results and a forward algorithm. Operations Research, 47(7), (1999), 559-569, DOI: 10.1287/opre.47.4.559.
[4] W. Bozejko, M. Uchronski and M. Wodecki: Multi-machine scheduling problem with setup times. Archives of Control Sciences, 22(4), (2012), 441– 449, DOI: 10.2478/v10170-011-0034-y.
[5] W. Bozejko, A. Gnatowski, R. Idzikowski and M. Wodecki: Cyclic flow shop scheduling problem with two-machine cells. Archives of Control Sciences, 27(2), (2017), 151–167, DOI: 10.1515/acsc-2017-0009.
[6] D. Cattrysse, M. Salomon, R. Kuik and L. vanWassenhove: A dual ascent and column generation heuristic for the discrete lotsizing and scheduling problem with setup times. Management Science, 39(4), (1993), 477–486, DOI: 10.1287/mnsc.39.4.477.
[7] K. Copil, M. Worbelauer, H. Meyr and H. Tempelmeier: Simultaneous lotsizing and scheduling problems: a classification and review of models. OR Spectrum, 39(1), (2017), 1–64, DOI: 10.1007/s00291-015-0429-4.
[8] A. Drexl and K. Haase: Proportional lotsizing and scheduling. International Journal of Production Economics, 40(1), (1995), 73–87, DOI: 10.1016/0925-5273(95)00040-U.
[9] B. Fleischmann: The discrete lot-sizing and scheduling problem. European Journal of Operational Research, 44(3), (1990), 337-348, DOI: 10.1016/0377-2217(90)90245-7.
[10] K. Haase: Lotsizing and scheduling for production planning. Number 408 in Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin, 1994.
[11] W. Kaczmarczyk: Inventory cost settings in small bucket lot-sizing and scheduling models. In Total Logistic Management Conference, Zakopane, Poland, November 25-28 2009.
[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.
[13] W. Kaczmarczyk: Proportional lot-sizing and scheduling problem with identical parallel machines. International Journal of Production Research, 49(9), (2011), 2605–2623, DOI: 10.1080/00207543.2010.532929.
[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/
[16] U.S. Karmarkar and L. Schrage: The deterministic dynamic product cycling problem. Operations Research, 33(2), (1985), 326–345, DOI: 10.1287/opre.33.2.326.






DOI: 10.24425/acs.2021.139735