Academic Journal
Lagrangian approach to minimize makespan of non-identical parallel batch processing machines
| Title: | Lagrangian approach to minimize makespan of non-identical parallel batch processing machines |
|---|---|
| Authors: | Suhaimi, Nurul Mubinah Binti |
| Contributors: | Damodaran, Purushothaman, Department of Industrial and Systems Engineering |
| Publisher Information: | Northern Illinois University |
| Publication Year: | 2014 |
| Collection: | Northern Illinois University (NIU): Huskie Commons Repository |
| Subject Terms: | Electronic data processing--Batch processing, Production scheduling--Data processing, Lagrangian functions, Operations research |
| Description: | Advisors: Purushothaman Damodaran. ; Committee members: Omar Ghrayeb; Murali Krishnamurthi; Christine Nguyen. ; 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-heuristics (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 ... |
| Document Type: | text |
| File Description: | 82 pages; application/pdf |
| Language: | English |
| Relation: | http://commons.lib.niu.edu/handle/10843/17756 |
| Availability: | http://commons.lib.niu.edu/handle/10843/17756 |
| Rights: | NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors. |
| Accession Number: | edsbas.F981940A |
| Database: | BASE |
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