A single-item lot-sizing problem with a by-product and inventory capacities - Suzanne, Elodie; Absi, Nabil; Borodin, Valeria; van den Heuvel, Wilco (European journal of operational research, 2020)
•A single-item lot-sizing problem (ULS-B) dealing with a by-product is studied.•We prove that ULS-B with inventory capacities is weakly NP-Hard.•A pseudo-polynomial dynamic programming (DP) algorithm is proposed for ULS-B.•For ULS-B with constant inventory capacities, a polynomial DP algorithm is developed. The high pace of waste accumulation in landfills and the depletion of scarce natural resources lead us to seek pathways for converting unavoidable production outputs into useful and high added-value products. In this context, we formalize and propose a model for the single-item lot-sizing problem, which integrates the management of unavoidable production residues classified as by-products. During the production process of a main product, a by-product is generated, stored in a limited capacity and transported with a fixed transportation cost. This problem is investigated for two cases of the by-product inventory capacity: time-dependent and constant. We prove that the problem with inventory capacities is NP-Hard. To solve it optimally, we develop a pseudo-polynomial time dynamic programming algorithm. For the case with stationary inventory capacities, a polynomial time dynamic programming algorithm is proposed.