Capacitated lot-sizing and production sequence problem with setups complexity

• Published in: Scientia Iranica. Transaction E, Industrial engineering Vol. 32; no. 4; pp. 1 - 12
• Main Authors: Behnamian, Javad, Ghomi, Seyed Mohammad Taghi Fatemi, Karimi, Behrooz, Moludi, Marzieh Fadaei
• Format: Journal Article
• Language: English
• Published: Tehran Sharif University of Technology 01.08.2025
• Subjects: Complexity; Genetic algorithms; Integer programming; Linear programming; Lot sizing; Lower bounds; Maintenance costs; Manufacturing; Mixed integer; Nonlinear programming; Optimization; Production planning; Scheduling
• DOI: 10.24200/sci.2022.57019.5025

This paper considered the multi-product multi-level multi-period capacitated lot-sizing and sequencing problem with setup carry-over and sequence-dependent family setup times and costs. A formulation of the problem was provided as a mixed-integer nonlinear programming model. To propose this formulation, first, the mixed-integer nonlinear of the problem was linearized, and then converted to a mixed-integer linear program. To solve large-size instances of the problem, then, a lower bound was provided. The results confirmed the efficiency of the proposed model compared to previous models in terms of the runtime and the number of defined variables and constraints. Since this problem is NP-hard and adding other factors such as family setups, setup carry over and sequence-dependent setups increase its complexity, in this paper, a Genetic Algorithm (GA) was applied in large-size dimensions and its results were compared with the proposed lower bound. The numerical results showed that there is no significant difference between the results of the proposed GAand lower bound, and, so, the GAhad been able to approach the optimal solution.