Models and Lagrangian heuristics for a two-level lot-sizing problem with bounded inventory

Abstract

International audienceWe consider a two-level dynamic lot-sizing problem where the first level consists of N finished products competing for a single type of purchased raw material in the second level. While the procurement and production capacities are unlimited, the storage capacity of the raw material is limited and must be carefully managed. The goal is to simultaneously determine a replenishment plan for the raw material and optimal production plans for the finished products on a horizon of T periods while minimizing production, purchasing, setup and inventory holding costs. The problem is modeled using mixed-integer linear programs and solved using both a Lagrangian relaxation-based heuristic and a commercial mixed-integer linear programming solver. 123 N. Brahimi et al. Learning capabilities are integrated in the Lagrangian relaxation to update step size in the subgradient algorithm. The computational results show that the Lagrangian heuris-tic outperforms the solver on different formulations, in particular for large problems with long time horizons

Lot-sizing for industrial symbiosis

“…Wolsey (2010, 2012); Hwang et al (2016)), the supplier-retailer problem (see e.g. Brahimi et al (2015); Phouratsamay et al (2018)) and the One Warehouse Multi-Retailer (OWMR) problem (see e.g. Arkin et al (1989); Solyalı and Süral (2012)) which are the most studied.…”

“…Hwang and Jung (2011); Phouratsamay et al (2018) provided algorithms running in a polynomial time to solve a number of different versions of this problem. Note that the case with inventory capacities at the first level is N P -Hard (Jaruphongsa et al (2004); Brahimi et al (2015); Phouratsamay et al (2018)). Jaruphongsa et al (2004) proposed a two-level problem with demand time-window constraints and stationary inventory bounds at the first level.…”

“…By allowing demand splitting, Jaruphongsa et al (2004) solved the problem using a polynomial algorithm based on dynamic programming. Brahimi et al (2015) solved the supplier-retailer problem with inventory capacities using a Lagrangian relaxation. Phouratsamay et al (2018) solved the same problem using a pseudo-polynomial algorithm based on dynamic programming.…”

“…Phouratsamay et al (2018) solved the same problem using a pseudo-polynomial algorithm based on dynamic programming. The problem studied in the current paper is different from Brahimi et al (2015); Phouratsamay et al (2018) in the sense that the inventory capacities are not on the product, which has to meet a demand. Melo and Wolsey (2010) considered a two-level lot-sizing problem, where an intermediate product is created at the first level, required to meet only the demand in the second level.…”

Single-item lot-based supplying and batch production under a bilateral capacity reservation: A partnership structure

“…Indeed, it can be due that the cost of providing and warehousing the products is not beneficial or the available capacity is not adequate to meet entire demands on assigned schedules. In this regard, the backorders are formulated through the variables of newly manufactured products-flow which are at the contrary direction of the ones relating to the inventory flow [8]. In similar cases with the uncapacitated SILSP, the utmost optimal solutions make spanning-tree configurations.…”