Capacitated lot sizing problem with periodic carbon emission constraints and multiple resources

Koca, Esra and Koksalan, G. Irmak (2023) Capacitated lot sizing problem with periodic carbon emission constraints and multiple resources. International Journal of Production Research . ISSN 0020-7543 (Print) 1366-588X (Online) Published Online First

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We study the single item capacitated lot sizing problem with multiple resources and periodic carbon emission constraints that impose an upper bound for the average emission per product produced in any period. Although the uncapacitated version of this problem can be solved in polynomial time, generalisation of the problem including the resource capacities is NP-Hard, in general. We present important structural properties for the optimal solutions of the problem. We consider the special cases with two resources and under non-speculative costs, construct the piecewise linear total production cost function when the resource capacities, and the emission and cost parameters are time-invariant, and develop a polynomial time dynamic programming algorithm (DP) to solve them. Then, we generalise the procedure to construct the total production cost function and the DP for the general setting with fixed number of capacitated resources. We test our algorithm for different problem instances, and compare it with a commercial solver and a DP available in the literature for solving the lot sizing problem with piecewise concave production cost functions. The results reveal that our DP outperforms the other one, and it performs better than the commercial solver when the number of breakpoints of the total production cost function is small.
Item Type: Article
Uncontrolled Keywords: complexity analysis; dynamic programming; multi-resource capacitated lot sizing; periodic carbon emission constraints; Production planning
Divisions: Faculty of Engineering and Natural Sciences > Academic programs > Industrial Engineering
Faculty of Engineering and Natural Sciences
Depositing User: Esra Koca
Date Deposited: 07 Aug 2023 15:25
Last Modified: 07 Aug 2023 15:25

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