A single-item lot-sizing problem with a by-product and inventory capacities

Abstract

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 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.

Lot-sizing for industrial symbiosis

“…To the best of our knowledge, only Sridhar et al (2014) and Suzanne et al (2020b) have treated production planning problems dealing with by-products from an academic point of view. Sridhar et al (2014) studied a generic non-linear production planning problem, where the ratio of undesirable by-products increases monotonically as a convex function of the cumulative production mixture.…”

“…Sridhar et al (2014) studied a generic non-linear production planning problem, where the ratio of undesirable by-products increases monotonically as a convex function of the cumulative production mixture. Suzanne et al (2020b) proposed a lot-sizing problem, where the by-product is generated in a constant proportion, stored in a limited capacity (constant and time-dependent) and transported to a further destination. They showed that the studied problem is N P -Hard when the capacity is time-dependent, and can be optimally solved in polynomial time when the capacity is constant.…”

“…Being industry-dependent, the industrial symbiosis networks can also include specific intermediate facilities required by the by-product handling systems, e.g. for storage or treatment purposes (Suzanne et al, 2020b). These intermediate facilities can belong to production units, or be provided by third parties, complicating thereby the logistics related to the by-product handling.…”

“…• Introducing and formalizing a lot-sizing problem in the framework of an industrial symbiosis: The addressed problem extends the work of Suzanne et al (2020b), by integrating the receiver production unit in the management of a by-product generated by the supplier production unit. As discussed in Section 2.1, the lot-sizing problem introduced in this paper enriches the joint production planning literature by its novelty and industrial relevance.…”

Effective Algorithms for the Economic Lot-Sizing Problem with Bounded Inventory and Linear Fixed-Charge Cost Structure

“…Later, Veinott [3] proved that ZIO policies could be likewise used to derive optimal plans when the cost structure was concave in general. Since then, a significant number of contributions have been published in the literature considering diverse extensions of this simple model (refer to Brahimi et al [4] and Wolsey [5] for more comprehensive surveys and to [6][7][8][9][10] for more recent contributions).…”