Journal of Materials Processing Technology 186 (2007) 60–65 A multicriteria flowshop scheduling problem with setup times Tamer Eren ∗ Kırıkkale University, Faculty of Engineering, Department of Industrial Engineering, 71450 Kırıkkale, Turkey Received 9 March 2006; accepted 4 December 2006 Abstract Most of research in production scheduling is concerned with the minimization of a single criterion. However, scheduling problems often involve more than one aspect and therefore require multicriteria analysis. In this study, a multicriteria two-machine flowshop scheduling problem with setup times is considered. The objective function of the problem is minimization of the weighted sum of total completion time, makespan, maximum tardiness and maximum earliness. An integer programming model is developed for the problem which belongs to NP-hard class. Only small size problems with up to 20 jobs can be solved by the proposed integer programming model. Heuristic methods are also used to solve large size problems. These heuristics are six tabu search based heuristics and random search method. According to computational results, the tabu search based methods are effective in finding problem solutions with up to 1000 jobs. © 2006 Elsevier B.V. All rights reserved. Keywords: Flowshop scheduling; Multicriteria; Setup times; Integer programming; Heuristic methods 1. Introduction Setup times are defined to be the work to prepare the resource (machine), process, or bench for tasks (products). In manufac- turing environments, this includes obtaining tools, positioning work in process material, returning and adjusting tools, cleaning- up, setting the required jigs and fixtures, and inspecting material. The majority of scheduling research on flowshops considers setup times negligible or as part of the processing times. While this might be justified for some applications, many other situa- tions call for explicit separate setup consideration; see Yoshida and Hitomi [1], Sule and Huang [2], Dileepan and Sen [3], Logendran and Sriskandarajah [4], Allahverdi [5], Allahverdi [6], Allahverdi and Aldowaisan [7], and Su and Chou [8]. An important implication of separate setup times is that the setup on a subsequent machine may be performed while the job is still in process on the immediately preceding machine. A recent survey of scheduling research involving setup times is given by Allahverdi et al. [9] and Cheng et al. [10]. Another area of research in the scheduling literature involves the multicriteria problem. The majority of research on schedul- ing problems addresses only a single criterion while the majority ∗ Tel.: +90 318 3573576x1218; fax: +90 318 3572459. E-mail addresses: teren@kku.edu.tr, tameren@hotmail.com. of real-life problems require the decision maker to consider more than a single criterion before arriving at a decision. The schedul- ing literature reveals that the research on multicriteria is mainly focused on the single-machine problem as a result of the diffi- culty of the multiple machines problem. This paper addresses a two-machine flowshop scheduling problem with a multicriteria objective function. The multicriteria scheduling problems are generally divided into three classes. In the first class, one of the multicriteria is considered as the objective to be optimized while the other is considered as a constraint. In the second class of problems, both criteria are considered equally important and the prob- lem involves finding efficient schedules. In the third class of problems, both criteria are weighted differently and an objec- tive function as the sum of weighted functions is defined. The problem considered in this paper belongs to the third class. In this paper, a multicriteria scheduling problem with separate setup times on two-machine flowshop is considered. The objec- tive function of the problem is minimization of the weighted sum of total completion time, makespan, maximum tardiness and maximum earliness. The considered problem is denoted as F2/s ji /α ∑ C + βC max + γ T max + θE max . This multicriteria prob- lem is an NP-hard problem since the simpler single criterion variations of the problem such as F2/s ji / ∑ C are already NP-hard problems [11,12]. 0924-0136/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2006.12.022