A hybrid adaptive large neighborhood search heuristic for lot-sizing with setup times

Abstract

This paper presents a hybrid of a general heuristic framework and a general purpose mixed-integer programming (MIP) solver. The framework is based on local search and an adaptive procedure which chooses between a set of large neighborhoods to be searched. A mixed integer programming solver and its built-in feasibility heuristics is used to search a neighborhood for improving solutions. The general reoptimization approach used for repairing solutions is specifically suited for combinatorial problems where it may be hard to otherwise design suitable repair neighborhoods. The hybrid heuristic framework is applied to the multi-item capacitated lot sizing problem with setup times, where experiments have been conducted on a series of instances from the literature and a newly generated extension of these. On average the presented heuristic outperforms the best heuristics from the literature, and the upper bounds found by the commercial MIP solver ILOG CPLEX using state-of-the-art MIP formulations. Furthermore, we improve the best known solutions on 60 out of 100 and improve the lower bound on all 100 instances from the literature.

Nesting problems

“…Bennell and Dowsland (2001) solved the irregular strip packing problem combining tabu search and linear programming. An approach that uses a branch and cut method to explore several large neighbourhood structures in order to solve the lot-sizing problem was presented by Muller et al (2012).…”

Lot sizing with setup carryover and crossover

“…For our study, we assume the same instances which have inspired Süral et al (2009) and Muller et al (2012) data sets. The data set is expanded using the idea of concatenating instances of Muller et al (2012). However, we have increased the planning horizon and the number of products of the original instances.…”

“…Amorim et al (2014) also used the ALNS framework for the VRPTW, considering perishable goods, heterogeneous fleet and multiple time-windows. Muller et al (2012) presented a hybrid ALNS for the lot-sizing problem with setup times using an MILP-solver in the repair phase, instead of a "pure" heuristic.…”

“…The data set is based on the papers of Trigeiro et al (1989), Süral et al (2009) and Muller et al (2012). Süral et al (2009) chose some of the most difficult instances generated by Trigeiro et al (1989), belonging to data subset G: instances G51 to G60 and G66 to G75, being five instances for each combination size (N ×T ) of 12×15, 24×15, 12×30 and 24×30.…”

“…Süral et al (2009) chose some of the most difficult instances generated by Trigeiro et al (1989), belonging to data subset G: instances G51 to G60 and G66 to G75, being five instances for each combination size (N ×T ) of 12×15, 24×15, 12×30 and 24×30. Muller et al (2012) expanded the data set by concatenating instances, generating instances with larger planning horizons. The procedure is simple and the new instances are generated by taking the original and aggregating the same instance to the planning horizon two and three times.…”