A Tabu-Search Heuristic for the Capacitated Lot-Sizing Problem with Set-up Carryover

Abstract

This paper presents a tabu-search heuristic for the capacitated lot-sizing problem (CLSP) with set-up carryover. This production-planning problems allows multiple items to be produced within a time period, and setups for items to be carried over from one period to the next. Two interrelated decisions, sequencing and lot sizing, are present in this problem. Our tabu-search heuristic consists of five basic move types---three for the sequencing decisions and two for the lot-sizing decisions. We allow infeasible solutions to be generated at a penalty during the course of the search. We use several search strategies, such as dynamic tabu list, adaptive memory, and self-adjusting penalties, to strengthen our heuristic. We also propose a lower-bounding procedure to estimate the quality of our heuristic solution. We have also modified our heuristic to produce good solutions for the CLSP without set-up carryover. The computational study, conducted on a set of 540 test problems, indicates that on average our heuristic solutions are within 12% of a bound on optimality. In addition, for the set of test problems our results indicate an 8% reduction in total cost through set-up carryover.Lot Sizing, Tabu Search, Set-up Carryover

Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches

“…For the standard problems, traditional method or special purpose heuristics seem to outperform the meta-heuristics (Gopalakrishnan et al 2001). On the other hand, metaheuristics provide good results for the more difficult problems such as multi-level or sequence dependent problems, for which the traditional methods fail.…”

“…One of the main reasons for the success of these metaheuristics is their flexibility and ability to handle large and complex problems. As a consequence, these methods are usually developed for extensions of the standard lot sizing problems for which no good special purpose algorithm exists and which are too difficult to solve with commercial integer optimization software: 1) Single level CLSP (Hindi 1996, Kohlmorgen et al 1999, with set up times (Hung et al 1999, Özdamar andBozyel 2000), with set up times and overtime (Özdamar, Birbil and Portmann 2002), with set up times and multiple resources (Hung et al 2003), with set up carry over (Gopalakrishnan et al 2001), with sequence dependencies (Fleischmann and Meyr 1997, Laguna 1999, Meyr 2000, on parallel machines (Özdamar and Birbil 1998), ; 2) Multi level lot sizing without capacities (Kuik and Salomon 1990, Dellaert and Jeunet 2000, Dellaert et al 2000, Tang 2004);…”

“…In the first option, we explicitly include both the integer variables and the production quantities in the representation. (Özdamar and Birbil 1998, Özdamar and Barbarosoğlu 1999, Özdamar and Bozyel 2000, Gopalakrishnan et al 2001, Özdamar, Birbil and Portmann 2002. The second option is to include only the integer variables and discard the production quantities.…”

“…An example is to impose a backlog cost for demand which cannot be met in time The definition of the neighborhood for SA and TS depends on the specific problem at hand and the representation of the solution. In a representation with both integer and continuous variables, moves can be defined on both parts (Gopalakrishnan et al 2001). Neighbor solutions can also be generated by partially or completely shifting the lot of one item Birbil 1998, Özdamar andBarbarosoğlu 1999, Özdamar and representation with only the integer variables, the simplest mechanism only alters the set up variable for one product-period combination.…”

Single machine multi-product capacitated lot sizing with sequence-dependent setups

“…The authors start with the standard CLSP model, use the standard facility location reformulation, and introduce new sets of variables and constraints to model the setup carryover. Gopalakrishnan et al [2001] also address CLSP with setup carryover and present two effective tabu-search heuristics.…”