ELSEVIER European Journal of Operational Research 110 (1998) 525-547 EUROPEAN JOURNAL OF OPERATIONAL RESEARCH Theory and Methodology Hybrid heuristics for the capacitated lot sizing and loading problem with setup times and overtime decisions Linet Ozdamar *, ~evket Ilker Birbil Department of Systems Engineering, Yeditepe University. Gayrettepe, Emekli Subay Evleri 2315. Istanbul, Turkey Received 1 February 1997; accepted 1 July 1997 Abstract The capacitated lot sizing and loading problem (CLSLP) deals with the issue of determining the lot sizes of product families/end items and loading them on parallel facilities to satisfy dynamic demand over a given planning horizon. The capacity restrictions in the CLSLP are imposed by constraints specific to the production environment considered. When a lot size is positive in a specific period, it is loaded on a facility without exceeding the sum of the regular and overtime capacity limits. Each family may have a different process time on each facility and furthermore, it may be technolog- ically feasible to load a family only on a subset of existing facilities. So, in the most general case, the loading problem may involve unrelated parallel facilities of different classes. Once loaded on a facility, a family may consume capacity during setup time. Inventory holding and overtime costs are minimized in the objective function. Setup costs can be included if setups incur costs other than lost production capacity. The CLSLP is relevant in many industrial applica- tions and may be generalized to multi-stage production planning and loading models. The CLSLP is a synthesis of three different planning and loading problems, i.e., the capacitated lot sizing problem (CLSP) with overtime decisions and setup times, minimizing total tardiness on unrelated parallel processors, and, the class scheduling problem, each of which is NP in the feasibility and optimality problems. Consequently, we develop hybrid heuristics involving powerful search techniques such as simulated annealing (SA), tabu search (TS) and genetic algorithms (GA) to deal with the CLSLP. Results are compared with optimal solutions for 108 randomly generated small test problems. The procedures developed here are also compared against each other in 36 larger size problems. © 1998 Elsevier Science B.V. All rights reserved. 1. Introduction In the literature, lot sizing and scheduling deci- sions are usually treated independently for simpli- fying the overall decision-making problem. In the " Corresponding author. Fax: 90 216 387 9108; e-mail: ozdamar@yeditepe.edu.tr. classical hierarchical decision-making context, it is suggested that lot sizing decisions take place in the medium range planning level whereas schedul- ing decisions are dealt with in the short term plan- ning level (Hax and Candea, 1984). Lot sizing models are grouped together within the single stage/multi-stage capacitated lot sizing model (CLSP) which assumes that demand is 0377-2217/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PHS0377-221 7(97)00269-5