Makespan minimisation on parallel batch processing machines with non-identical job sizes and release dates

Öztürk, Onur; Espinouse, Marie‐Laure; Mascolo, Maria Di; Gouin, Alexia

doi:10.1080/00207543.2011.641358

Cited by 48 publications

(11 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Common scheduling objective studied for non-identical BPM scenario is minimizing the total completion time or makespan [2]. 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.…”

Section: Single Batch Processing Machine Environmentmentioning

confidence: 99%

“…Majority of the literature considers the case of non-identical jobs and identical machines [20]. Earlier study on this objective may have been done by [2] where non-identical job size is considered. The methods used to minimize the makespan objective vary from exact approaches like B&B and Dynamic Programming (DP) to meta-heuristic approaches such as SA and PSO.…”

Section: Minimize Makespan In Batch Processing Machinesmentioning

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%

“…The formation resulted in a batch where the size of the batch is the sum of all the size of the jobs in the batch. In any circumstances, the batch size should not exceed the capacity of the machine that processes it [2]. In this research, literature on parallel BPM is divided into two categories: identical and non-identical parallel BPM.…”

Section: Single Batch Processing Machine Environmentmentioning

confidence: 99%

“…Constraint (2) ensures that each job is assigned to exactly one batch on one machine. Constraint (3) ensures that the total size of all the jobs assigned to the batch does not exceed the machine capacity.…”

Section: Mixed Integer Linear Programming (P)mentioning

confidence: 99%

See 4 more Smart Citations

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

Suhaimi

Nguyen

Damodaran

2016

Computers & Industrial Engineering

View full text Add to dashboard Cite

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

show abstract

Section: Single Batch Processing Machine Environmentmentioning

confidence: 99%

Section: Minimize Makespan In Batch Processing Machinesmentioning

confidence: 99%