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In the scheduling literature, the studies that consider unavailable periods (UPs) have generally ignored the resources. However, when the resources to be used in unavailable periods are limited and these resources are needed for more than one machine at the same time, the problem of when the resource should be allocated to which machine arises. This decision is important as it can greatly affect the effectiveness of the machine schedule. For this reason, it is necessary to consider not only the UPs, but also the resources used by the UPs. In this study, flow shop scheduling problem with unavailable periods, flexible in a time window, and additional resources is discussed. In the considered problem, since additional resources are required during the unavailable periods and they can serve just one machine at a time, they cannot overlap. A MIP model and a hybrid algorithm that genetic algorithm and modified subgradient algorithm works together, have been developed for the considered problem. The performance of the hybrid algorithm is compared with pure genetic algorithm and Cplex solver of GAMS by using randomly generated test problems. Test results showed that while hybrid algorithm has solution quality advantage, genetic algorithm has solution time advantage. In addition, with the developed hybrid algorithm, GAMS results were improved up to 88%. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.03.016 Byline: Rafail N. Gasimov, Aydin Sipahioglu, Tugba Sarac Keywords: Cutting; 1.5-dimensional assortment problem; Multi-objective programming; Weighted sum scalarization; Conic scalarization; Mixed integer linear programming Abstract: In this paper we study a 1.5-dimensional cutting stock and assortment problem which includes determination of the number of different widths of roll stocks to be maintained as inventory and determination of how these roll stocks should be cut by choosing the optimal cutting pattern combinations. We propose a new multi-objective mixed integer linear programming (MILP) model in the form of simultaneously minimization two contradicting objectives related to the trim loss cost and the combined inventory cost in order to fulfill a given set of cutting orders. An equivalent nonlinear version and a particular case related to the situation when a producer is interested in choosing only a few number of types among all possible roll sizes, have also been considered. A new method called the conic scalarization is proposed for scalarizing non-convex multi-objective problems and several experimental tests are reported in order to demonstrate the validity of the developed modeling and solving approaches. Author Affiliation: Industrial Engineering Department, EskiAehir Osmangazi University, Bademlik 26030, EskiAehir, Turkey Article History: Received 30 April 2005; Accepted 13 March 2006

A multi-objective mixed integer linear programming model called scalarization is proposed to solve cutting stock problems is presented.

One of the most common plastic manufacturing methods is injection molding. In injection molding process, scheduling of plastic injection machines is very difficult because of the complex nature of the problem. For example, similar plastic parts should be produced sequentially to prevent long setup times. On the other hand, to produce a plastic part, its mold should be fixed on an injection machine. Machine eligibility restrictions should be considered because a mold can be usually fixed on a subset of the injection machines. Some plastic parts which have same shapes but different colors are used same mold so these parts can only be scheduled simultaneously if their mold has copies, otherwise resource constraints should be considered. In this study, a multi-objective mathematical model is proposed for parallel machine scheduling problem to minimize makespan, total tardiness, and total waiting time. Since NP-hard nature of problem, this paper presents a two-stage mathematical model and a two-stage solution approach. In the first stage of mathematical model, jobs are assigned to the machines and each machine is scheduled separately in the second stage. The integrated model and two-stage mathematical model are scalarized by using goal programming, compromise programming and Lexicographic Weighted Tchebycheff programming methods. To solve large-scale problems in a short time, a two-stage solution approach is also proposed. In the first stage of this approach, jobs are assigned to machines and scheduled by using proposed simulated annealing algorithm. In the second stage of the approach, starting time, completion time and waiting time of the jobs are calculated by using a mathematical model. The performance of the methods is demonstrated on randomly generated test problems. [ABSTRACT FROM AUTHOR]