Minimising total weighted earliness and tardiness penalties on identical parallel machines using a fast ruin-and-recreate algorithm Shih-Wei Lin a,b , Kuo-Ching Ying c * , Yen-I Chiang a and Wen-Jie Wu a a Department of Information Management, Chang Gung University, Taoyuan, Taiwan; b Stroke Center, Linkou Chang Gung Memorial Hospital, Taoyuan, Taiwan; c Department of Industrial Engineering and Management, National Taipei University of Technology, Taipei, Taiwan (Received 30 September 2015; accepted 6 May 2016) This paper studies the scheduling problem of minimising total weighted earliness and tardiness penalties on identical parallel machines against a restrictive common due date. This problem is NP-hard in the strong sense and arises in many just-in-time production environments. A fast ruin-and-recreate (FR&R) algorithm is proposed to obtain high-quality solutions to this complex problem. The proposed FR&R algorithm is tested on a well-known set of benchmark test problems that are taken from the literature. Computational results provide evidence of the efficiency of FR&R, which consistently outperform existing algorithms when applied to benchmark instances. This work provides a viable alternative approach for efficiently solving this practical but complex scheduling problem. Keywords: scheduling; metaheuristics; parallel machines; total weighted earliness and tardiness; common due date 1. Introduction The parallel machine scheduling problem is one of the most studied classical scheduling problems and has a wide range of applications in both the manufacturing and the service industries (Lin, Lu, and Ying 2011; Lin and Ying 2014). This study focuses on the identical parallel machines scheduling problem (IPMSP), in which all the jobs must be completed by a restrictive common due date (CDD). A CDD problem is called restrictive if the position of the CDD influences the optimal sequence of jobs; otherwise, it is referred to as unrestrictive. The situation of an unrestrictive CDD occurs if the position of the CDD is a decision variable or if it is larger than the sum of the processing times of all jobs (Baker and Scudder 1990). The objective of this study is to minimise the total weighted earliness and tardiness penalties, commonly encountered in just-in-time (JIT) manufacturing systems where neither early nor late process completion is favourable (Mason, Jin, and Jampani 2009). In the standard classification scheme of Graham et al. (1979), the problem can be denoted as Pjdj ¼ d r j P j ða j E j þ b j T j Þ, where P designates the identical parallel machine environment; dj ¼ d r means that all the jobs have a restrictive CDD and P j ða j E j þ b j T j Þ denotes the fact that the objective is to minimise the total weighted earliness and tardiness penalties. This scheduling problem is NP-hard (Cheng 1989) in the strong sense, and is an extension of the NP-hard single-machine scheduling problem (Garey, Tarjan, and Wilfong 1988). Despite the complexity of IPMSPs, some exact methods such as dynamic programming (Doğramaci 1984) and branch-and-bound (B&B) algorithms (Elmaghraby and Park 1974; Barnes and Brennan 1977; Azizoglu and Kirca 1998; Yalaoui and Chu 2002; Tanaka and Araki 2008) for solving small-scale IPMSPs have been proposed. The majority of the exact methods are constrained to solve generalised IPMSPs with equal processing times and/or CDDs. Since the computational time increases in a non-polynomial manner with the size of the problem, the computational burden of exact methods are prohibitive for large IPMSPs. Most studies of the relevant literature focuses on performance metrics that are based on the minimisation of makespan and/or total tardiness. Notably, the use of makespan and/or total tardi- ness to evaluate schedules neglects undesired effects such as the incurring of inventory carrying costs, storage and insur- ance costs, and product deterioration when jobs are completed before their due date. To satisfy practical requirements, criteria that involve both earliness and tardiness costs must be considered in solving IPMSPs. Although numerous algo- rithms have been proposed for solving different IPMSPs, only a few studies have focused on the problem of minimising total weighted earliness and tardiness penalties (Alvarez-Valdes, Tamarit, and Villa 2015). *Corresponding author. Email: kcying@ntut.edu.tw © 2016 Informa UK Limited, trading as Taylor & Francis Group International Journal of Production Research, 2016 http://dx.doi.org/10.1080/00207543.2016.1190041 Downloaded by [National Taipei University of Technology] at 01:02 28 May 2016