A particle swarm optimization algorithm for minimizing makespan of nonidentical parallel batch processing machines

Damodaran, Purushothaman; Diyadawagamage, Don Asanka; Ghrayeb, Omar; Vélez-Gallego, Mario C.

doi:10.1007/s00170-011-3442-z

Cited by 62 publications

(35 citation statements)

References 7 publications

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“…The machines do not fail. 4. Once a machine begins processing a batch, new jobs cannot be added to the batch or removed from the batch.…”

Section: Research Objective and Scopementioning

confidence: 99%

“…The jobs are typically batched when they share the same setup on a machine or when the machine can process multiple jobs simultaneously [1]. The applications of BPM can be found in aeronautical industry [38], hospital sterilization services [2], electronic manufacturing [4] and many more.…”

Section: Chapter 2 Literature Reviewmentioning

confidence: 99%

“…One example of the research is done by Xu and Bean [24] where they presented Random Key Genetic Algorithm (RKGA) in minimizing makespan for non-identical parallel BPM. Following that, Damodaran et al [4] proposed Particle Swarm Optimization (PSO) approach to minimize the makespan for non-identical parallel BPM. They adapted the mathematical formulation from [24] and simplified them with fewer binary variables.…”

Section: Single Batch Processing Machine Environmentmentioning

confidence: 99%

“…Damodaran, et al [4] showed that the problem under study is NP-hard. They proposed a Particle Swarm Optimization (PSO) algorithm.…”

Section: Introductionmentioning

confidence: 99%

“…PSO is a meta-heuristic and does not guarantee an optimal solution. This research proposes a Lagrangian Relaxation (LR) approach for the problem studied in [4] and compares the effectiveness of the approach (in terms of solution quality and computational time) to PSO and other approaches found in the literature. 3 …”

Section: Introductionmentioning

confidence: 99%

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Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Suhaimi

Nguyen

Damodaran

2016

Computers & Industrial Engineering

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Batch Processing Machines (BPMs) are commonly used in electronics manufacturing, semi-conductor manufacturing, and metal-working -to name a few. Scheduling these machines are not an easy task; practical considerations and the exponential number of decision variables involved impede schedulers (or decision makers) from making good decisions. This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. The first decision is to group jobs to form batches such that the machine capacity is not exceeded. The second decision is to sequence the batches formed on the machines such that the makespan is minimized. Both the decisions are intertwined as the processing time of the batch is determined by the composition of the jobs in the batch. The problem under study is shown to be NP-hard. A mathematical model from the literature is adopted to develop a solution approach which would help the decision maker to make meaningful decisions.Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. Using this decomposition approach, the mathematical model is decomposed and a sub-gradient approach was used to update the multipliers. Two sets of constraints were relaxed to consider two Lagrangian Relaxation models. Experiments were conducted with data sets from the literature. The solution quality of the proposed approach was compared with meta-heuristic (i.e. Particle Swarm Optimization (PSO) and Random Key Genetic Algorithm (RKGA)) published in the literature and a commercial solver (i.e. IBM ILOG CPLEX). On smaller instances (i.e. 10 and 20 jobs), the proposed approach outperformed PSO and RKGA. However, the proposed approach and CPLEX report the same results. On larger instances (i.e. 50, 100 and 200 job instances) with two and four-machines, the proposed approach was better than PSO whenever the variability in the processing times were smaller. The proposed approach generally outperformed RKGA and CPLEX on larger problem instances. Out of 200 experiments conducted, the proposed approach helped to find new improved solution on 34 instances and comparable on 105 instances when compared to PSO. The PSO approach was much faster than all other approaches on larger problem instances. The experimental study clearly identifies the problem instances on which the proposed approach can find a better solution. The proposed Lagrangian Relaxation solution approach helps the schedulers to make more informed decisions. Minor modifications can be made to use the proposed solution approach for other practical considerations (e.g. job ready times, tardiness objective, etc.) The main contribution of this research is the proposed solution approach which is effective in solving a class of non-identical batch processing machine problems with better solution quality when compared to existing meta-heuristic. NORTHERN

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“…The machines do not fail. 4. Once a machine begins processing a batch, new jobs cannot be added to the batch or removed from the batch.…”

Section: Research Objective and Scopementioning

confidence: 99%