An evaluation of heuristics for scheduling a non-delay permutation flow shop with family setups to minimize total earliness and tardiness J Schaller 1 and JMS Valente 2 1 Eastern Connecticut State University, Willimantic, CT, USA; and 2 Universidade do Porto, Porto, Portugal This paper presents several procedures for developing non-delay schedules for a permutation flow shop with family setups when the objective is to minimize total earliness and tardiness. These procedures consist of heuristics that were found to be effective for minimizing total tardiness in flow shops without family setups, modified to consider family setups and the total earliness and tardiness objective. These procedures are tested on several problem sets with varying conditions. The results show that variable greedy algorithms are effective when solving small problems, but using a genetic algorithm that includes a neighbourhood defined by the sequence of batches of jobs belonging to the same set-up family is effective when solving medium- or large-sized problems. The results also show that if setup times can be reduced a significant reduction in total earliness and tardiness could result. Journal of the Operational Research Society (2013) 64, 805–816. doi:10.1057/jors.2012.94 Published online 22 August 2012 Keywords: scheduling; flow shop; heuristics; family setups 1. Introduction In many operations obtaining economies of scale is a critical element in achieving success. Economies of scale are efficiencies in production in which per-unit production costs increase at a slower rate than production volume. In scheduling, efficiencies that lead to economies of scale are gained by grouping similar jobs together. The motivation for grouping sometimes relates to change-over times, or setup times, on the machines. For example, jobs may belong to families where the jobs in each family tend to be similar in some way, such as their required tooling. As a result of this similarity, a job does not need a setup when following another job from the same family, but a known ‘family setup time’ is required when a job follows a member of some other family. Typically, there are a large number of jobs, but a relatively small number of families. The widespread adoption of lean production methods has caused customers to view early delivery of products as well as tardy delivery to be undesirable. Early deliveries result in unnecessary inventory that ties up cash as well as space and resources needed to maintain and manage inventory. Therefore, an important consideration when sequencing and scheduling a set of jobs is completing each job on the customer’s due date. To address these considerations, this paper seeks to identify and compare methods for sequencing a set of jobs in a permutation flow shop with significant family setup times that will minimize the total earliness and tardiness of the jobs. Most research on flow shops has assumed the sequence of jobs to process will be the same on each machine. These schedules are referred to as permutation schedules. This is done for two reasons. First, it simplifies the computational effort and second, it is often not practical to change the sequence of jobs from one machine to the next. In this research only permutation schedules are considered. Formally, suppose there is a set of n jobs belonging to F setup families to be processed in a flowshop consisting of M machines. Let f j and d j represent the setup family and the due date of job j ( j ¼ 1, . . . ,n) respectively. Let p jm , S jm , and C jm represent the processing time, setup time, and completion time of job j ( j ¼ 1, . . . , n) on machine m (m ¼ 1, . . . , M), respectively. The earliness of job j, E j , is defined as: E j ¼ max {d j C jM , 0}, for j ¼ 1, . . . , n and the tardiness of job j, T j , is defined as: T j ¼ max {C jM d j , 0}, for j ¼ 1, . . . , n. The objective function, Z, can be expressed as: Z ¼ P j ¼ 1 n Ej þ T j . Since the objective in the problem is non-regular, inserting idle time into a schedule for the jobs can help to reduce the earliness of some jobs and thus improve the objective. Journal of the Operational Research Society (2013) 64, 805–816 © 2013 Operational Research Society Ltd. All rights reserved. 0160-5682/13 www.palgrave-journals.com/jors/  Correspondence: J Schaller, Department of Business Administration, Eastern Connecticut State University, 83 Windham St., Willimantic, CT 06226-2295, USA.