Abstract
This paper studies the unrelated parallel machine scheduling problem with three minimization objectives – makespan, maximum earliness, and maximum tardiness (MET-UPMSP). The last two objectives combined are related to just-in-time (JIT) performance of a solution. Three hybrid algorithms are presented to solve the MET-UPMSP: reactive GRASP with path relinking, dual-archived memetic algorithm (DAMA), and SPEA2. In order to improve the solution quality, min-max matching is included in the decoding scheme for each algorithm. An experiment is conducted to evaluate the performance of the three algorithms, using 100 (jobs) x 3 (machines) and 200 x 5 problem instances with three combinations of two due date factors – tight and range. The numerical results indicate that DAMA performs best and GRASP performs second for most problem instances in three performance metrics: HVR, GD, and Spread. The experimental results also show that incorporating min-max matching into decoding scheme significantly improves the solution quality for the two population-based algorithms. It is worth noting that the solutions produced by DAMA with matching decoding can be used as benchmark to evaluate the performance of other algorithms.
Highlights
INTRODUCTIONManagement concerns are often multi-dimensional. In order to reach an acceptable compromise, one has to measure the quality of a solution on all important criteria
In production scheduling, management concerns are often multi-dimensional
We present three algorithms to solve MET-UPMSP: greedy random adaptive search procedure (GRASP) [1517], dual-archived memetic algorithm (DAMA), and SPEA2 [18]
Summary
Management concerns are often multi-dimensional. In order to reach an acceptable compromise, one has to measure the quality of a solution on all important criteria. Objectives under considerations often include system utilization or makespan, total machining cost or workload, JIT related costs (earliness and tardiness penalties), total weighted flow time, and total weighted tardiness. Parallel machine models are a generalization of single machine scheduling, and a special case of flexible flow shop. Jungwattanakit et al [8] proposed a genetic algorithm (GA) for FFS with unrelated parallel machines and a weighted sum of two objectives – makespan and number of tardy jobs. Cochran et al [13] introduced a two-phase multi-population genetic algorithm to solve multi-objective parallel machine scheduling problems. We consider a multi-objective unrelated parallel machine scheduling problems aiming to simultaneously minimize three objectives – makespan, maximum earliness, and maximum tardiness. This paper is organized as follows: Section 2 describes the problem MET-UPMSP; Section 3 presents the algorithms for MET-UPMSP; Section 4 introduces several performance metrics and analyzes experimental results; Section 5 provides concluding remarks
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