Invited Review Parallel machine scheduling with additional resources: Notation, classification, models and solution methods Emrah B. Edis a,⇑ , Ceyda Oguz b , Irem Ozkarahan c a Celal Bayar University, Department of Industrial Engineering, Muradiye, 45140 Manisa, Turkey b Koç University, College of Engineering, Sariyer, 34450 Istanbul, Turkey c Troy University, Computer Science, P.O. Drawer 4419, Montgomery, AL 36104, USA article info Article history: Received 31 December 2010 Accepted 22 February 2013 Available online 7 March 2013 Keywords: Scheduling Parallel machines Additional resources Integer programming abstract Majority of parallel machine scheduling studies consider machine as the only resource. However, in most real-life manufacturing environments, jobs may require additional resources, such as automated guided vehicles, machine operators, tools, pallets, dies, and industrial robots, for their handling and processing. This paper presents a review and discussion of studies on the parallel machine scheduling problems with additional resources. Papers are surveyed in five main categories: machine environment, additional resource, objective functions, complexity results and solution methods, and other important issues. The strengths and weaknesses of the literature together with open areas for future studies are also emphasized. Finally, extensions of integer programming models for two main classes of related problems are given and conclusions are drawn based on computational studies. Ó 2013 Elsevier B.V. All rights reserved. 1. Introduction Scheduling models and algorithms are most widely used in manufacturing applications for efficient production. Parallel ma- chine scheduling (PMS) problems are among the most studied areas in scheduling literature. While Cheng and Sin (1990) give a comprehensive analysis of PMS research, Mokotoff (2001) presents a survey for the makespan minimization on identical parallel ma- chines. More recently, Pfund et al. (2004) review the literature re- lated to traditional unrelated parallel machine scheduling problems. In most of the PMS studies, the only resource considered is the machine. However, in most real-life manufacturing environ- ments, jobs also require, beside machines, certain additional re- sources, such as automated guided vehicles, machine operators, tools, pallets, dies and industrial robots, for their handling and pro- cessing (Slowinski, 1980; Blazewicz et al., 1983; Ventura and Kim, 2000). Thus, the study of PMS with additional resources is a signif- icant area of research. Consistent with the definition given by Blazewicz et al. (2004), we call an additional resource processing resource if it is required together with a machine (processor) during the processing of a job. Otherwise, i.e., if the resource is required either before or after the processing of a job, then it is called input–output resource. The additional resources are further classified with respect to their renewability (resource constraints) and divisibility (resource divisi- bility)(Slowinski, 1980; Blazewicz et al., 2007). From the viewpoint of resource constraints (Slowinski, 1980; Blazewicz et al., 2007): – A resource is renewable, if its only total usage at every moment is constrained. Once it is used for a job, it may be used again for another job. – A resource is non-renewable, if its total consumption is constrained. In other words, once it is used by some job, it cannot be available for any other job. – A resource is doubly constrained, if it is both renewable and non-renewable. From the viewpoint of resource divisibility (Slowinski, 1980; Blazewicz et al., 2007): – Discrete resources can be allocated to jobs in discrete units from a given finite set of possible allocations. – Continuous resources can be allocated to jobs in arbitrary amounts within an interval. This paper gives a review and discussion of studies related to PMS problems with additional resources, where the additional re- sources are processing, discrete and renewable. While the prob- lems are investigated with respect to their main characteristics, the strengths and the weaknesses of the literature, open areas and future needs of the studies are also given. 0377-2217/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ejor.2013.02.042 ⇑ Corresponding author. Address: Celal Bayar University, Department of Indus- trial Engineering (Celal Bayar Universitesi Endustri Muhendisligi Bolumu), Mur- adiye Kampusu, 45140 Manisa, Turkey. Tel.: +90 236 2012207; fax: +90 236 2412143. E-mail addresses: emrah.edis@cbu.edu.tr (E.B. Edis), coguz@ku.edu.tr (C. Oguz), iozkarahan@troy.edu (I. Ozkarahan). European Journal of Operational Research 230 (2013) 449–463 Contents lists available at SciVerse ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor