Single machine scheduling problem with interval processing times to minimize mean weighted completion time Ali Allahverdi a,n , Harun Aydilek b , Asiye Aydilek c a Department of Industrial and Management Systems Engineering, Kuwait University, P.O. Box 5969, Safat, Kuwait b Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait c Department of Economics and Finance, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait article info Available online 14 June 2014 Keywords: Scheduling Single machine Mean completion time Uncertainty Heuristics abstract The single resource scheduling problem is commonly applicable in practice not only when there is a single resource but also in some multiple-resource production systems where only one of the resources is bottle neck. Thus, the single resource (machine) scheduling problem has been widely addressed in the scheduling literature. In this paper, the single machine scheduling problem with uncertain and interval processing times is addressed. The objective is to minimize mean weighted completion time. The problem has been addressed in the literature and efficient heuristics have been presented. In this paper, some new polynomial time heuristics, utilizing the bounds of processing times, are proposed. The proposed and existing heuristics are compared by extensive computational experiments. The conducted experiments include a generalized simulation environment and several additional representative distributions in addition to the restricted experiments used in the literature. The results indicate that the proposed heuristics perform significantly better than the existing heuristics. Specifically, the best performing proposed heuristic reduces the error of the best existing heuristic in the literature by more than 75% while the computational time of the best performing proposed heuristic is less than that of the best existing heuristic. Moreover, the absolute error of the best performing heuristic is only about 1% of the optimal solution. Having a very small absolute error along with a negligible computational time indicates the superiority of the proposed heuristics. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Scheduling decisions directly affect production costs and cus- tomer satisfaction. This is because the right scheduling decisions help reduce production costs as a result of better resource utilization. This leads to shorter delivery time to customers, and hence, increased customer satisfaction. Scheduling jobs (tasks) on a single machine (resource) is widely applicable in real life. Moreover, in many applications of multiple- machine production systems, one machine is bottle neck, and hence, the right scheduling decision on that particular machine greatly affects the performance of the production system. There- fore, the problem of scheduling on a single machine is important, and hence, numerous researchers addressed this problem. There are many applications of the single machine scheduling problem where job processing times are known with certainty, e.g., Vilà and Pereira [14], Valente and Schaller [13], Kianfar and Moslehi [4]. Therefore, the vast majority of research on the single machine scheduling problem has been devoted to the case of deterministic problem where job processing times are treated as known and fixed values. Some researchers addressed the problem where job processing times are modeled as stochastic random variables with certain mean and variance, e.g., Iranpoor et al. [3]. For some scheduling environments, the exact probability distri- butions for processing times may not be known. A solution obtained by assuming a certain probability distribution may not be even close to the optimal solution for the realized processing times. It has been observed that although it is hard to obtain the exact probability distributions of processing times before scheduling, it is relatively easier to obtain the upper and lower bounds of processing times in many practical cases. Therefore, the bounds of processing times can be utilized in finding a solution for the scheduling problem. This problem is known as uncertain scheduling problem with bounded or interval processing times, Sotskov et al. [10]. Scheduling problems with uncertain and bounded processing times have also been addressed in the literature for other schedul- ing environments such as flowshops. For example, Allahverdi and Aydilek [1] addressed the two-machine flowshop scheduling problem with interval processing times with the objective of Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/caor Computers & Operations Research http://dx.doi.org/10.1016/j.cor.2014.06.003 0305-0548/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail addresses: ali.allahverdi@ku.edu.kw (A. Allahverdi), aydilek.h@gust.edu.kw (H. Aydilek), aydilek.a@gust.edu.kw (A. Aydilek). Computers & Operations Research 51 (2014) 200–207