Although Particle Swarm Optimizers (PSO) have been successfully used in a wide variety of continuous optimization problems, their use has not been as widespread in discrete optimization problems, particularly when adopting non-binary encodings. In this chapter, we discuss three PSO variants (which are applied on a specific scheduling problem: the Single Machine Total Weighted Tardiness): a Hybr...

Lawler [E.L. Lawler, A fully polynomial approximation scheme for the total tardiness problem, Operations Research Letters 1 (1982) 207–208] proposed a fully polynomial approximation scheme for the single-machine total tardiness problem which runs in O n 7 e time (where n is the number of jobs and e is the desired level of approximation). A faster fully polynomial approximation scheme running in...

This paper concerns the single machine total weighted tardiness scheduling with sequence-dependent setup times, usually referred as 1|sij | ∑ wjTj . In this NP-hard problem, each job has an associated processing time, due date and a weight. For each pair of jobs i and j, there may be a setup time before starting to process j in case this job is scheduled immediately after i. The objective is to...

Abstract This paper explores the characteristics of solutions when scheduling jobs in a shop with parallel machines. Three classical objective functions were considered: makespan, total completion time, and tardiness. These three criteria combined pairs, resulting bi-objective formulations. formulations solved using ε-constraint method to obtain Pareto frontier for each pair. The research is ev...

Order acceptance and scheduling decisions arise when the limited production capacity entails a manufacturer to select among incoming orders. In this paper, we consider an order acceptance and scheduling problem in a single machine environment where the orders are processed without preemption and a sequence dependent setup time is incurred between processing of every consecutive order. The probl...