Group scheduling and due date assignment on a single machine Shisheng Li a , C.T. Ng b,Ã , Jinjiang Yuan a a Department of Mathematics, Zhengzhou University, Zhengzhou, Henan 450001, People’s Republic of China b Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People’s Republic of China article info Article history: Received 4 January 2010 Accepted 16 December 2010 Available online 5 January 2011 Keywords: Single-machine scheduling Group technology Due date assignment Earliness–tardiness abstract We consider a single-machine scheduling problem involving both the due date assignment and job scheduling under a group technology environment. The jobs (orders) of customers are classified into groups according to their production similarities in advance. To achieve production efficiency and save time/money resource, all jobs of the same group are required to be processed contiguously on the machine. A sequence-independent setup time precedes the processing of each group. The due dates are assignable according to one of the following three due date assignment methods: FML-CON, FML-SLK and DIF, where FML-CON means that all jobs within the same group are assigned a common due date, FML-SLK means that all jobs within the same group are assigned an equal flow allowance, and DIF means that each job can be assigned a different due date with no restrictions. The goal is to determine an optimal combination of the due date assignment strategy and job schedule so as to minimize an objective function that includes earliness, tardiness, due date assignment and flow time costs. An Oðn log nÞ time unified optimization algorithm is provided for all of the above three due date assignment methods. & 2010 Elsevier B.V. All rights reserved. 1. Introduction The class of due date assignment problems is a challenging topic, and has attracted much attention in the past few decades due to the increasing interest in Just-In-Time systems. In this type of problems, the due date itself is a decision variable, in contrast to classical scheduling in which due dates are given parameters. The study of due date assignment problems is motivated by the common real-life situation where the due date is determined during sales negotiations with the customer. In order to avoid earliness–tardiness penalties, including the possibility of losing customers, companies are under increasing pressure to quote attainable delivery dates (due dates). At the same time, promising delivery dates too far into the future may not be acceptable to the customer or may force a company to offer price discounts in order to retain the business (Shabtay and Steiner, 2008a). This can be a difficult task, and there is clearly an inherent tradeoff between short due dates, and due dates that can be easily met. Many researches have dealt with scheduling problems on due date determination and earliness–tardiness penalties (see, e.g., Panwalkar et al., 1982; Bector et al., 1988; Adamopoulos and Pappis, 1996; Ng et al., 2003; Gordon et al., 2002a, 2002b; Shabtay and Steiner, 2008a, 2008b; Chang et al., 2009; Moslehi et al., 2009; Shabtay, 2010; Shabtay et al., 2010; Azaron et al., 2011). Earlier reviews of this research were given by Cheng and Gupta (1989) and Baker and Scudder (1990); and recent surveys of this research were provided by Gordon et al. (2004) and Kaminsky and Hochbaum (2004). In manufacturing processes, it is well-known that the produc- tion efficiency can be increased by grouping various parts and products with similar designs and/or production processes. This phenomenon is known as the group technology (GT) in the literature (Ham et al., 1985). With respect to part manufacturing, the main idea of GT is to identify similar parts and classify them into groups to take advantage of their similarities, and then cells of machines are configured and dedicated to the production of specific groups of parts. Many advantages have been claimed through the wide applications of group technology. For instance, changeover between different parts are simplified, thereby redu- cing the costs or time involved; parts spend less time waiting, which results in less work-in-process inventory; parts tend to move through production in a direct route, and hence the manufacturing lead time is reduced (see, e.g., Ham et al., 1985; Tatikonda and Wemmerl ¨ ov, 1992; Potts and Van Wassenhove, 1992; Chen et al., 1997; Ng et al., 2005; Logendran et al., 2005; Allahverdi et al., 2008; Amin-Naseri and Beheshti-Nia, 2009). In this paper, we consider the problem of the simultaneous determination of due date assignment and job scheduling on a single machine under a GT restriction. Generally, we are given a set of independent jobs (orders) that must be processed on a Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.ijpe.2010.12.023 Ã Corresponding author. Fax: + 852 23302704. E-mail address: lgtctng@polyu.edu.hk (C.T. Ng). Int. J. Production Economics 130 (2011) 230–235