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Upper and Lower Bounding Methods for Flowshop and Flexible Flowshop Group Scheduling Problems

Keshavarz, Taha | 2013

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 44523 (01)
  4. University: Shrif University of Technolgy
  5. Department: Industroal Engineering
  6. Advisor(s): Salmasi, Nasser
  7. Abstract:
  8. In this research sequence-dependent flowshop and flexible flowshop group scheduling problems are investigated. Several upper and lower bounding methods are proposed for the research problems. Permutation flowshop sequence-dependent group scheduling problem with minimization of total completion time is considered. Since the problem is shown to be strongly NP-hard, a Memetic algorithm (MA) is proposed. A lower bounding method base on the Branch-and-Price algrithm is also proposed. A statistical comparison shows that both the proposed MA and the proposed lower bounding method have better performance than the other methods from the literature with an average 5.96% percentage gap. Flexible flowshop sequence dependent group scheduling problem with minimization of makespan as the criterion is investigated. A mixed integer linear mathematical model for the research problem is developed. Since the research problem is shown to be NP-hard, a meta-heuristic algorithm based on MA is developed to efficiently solve the problem. A lower bounding technique based on the developed mathematical model is also proposed to evaluate the quality of the proposed MA. The performance of the proposed MA is compared with the existing algorithm in the literature, i.e., tabu search (TS) by solving the available test problems in the literature. A comparison based on paired t-test shows that the average makespan of the proposed MA is 3% lower than the average makespan of the TS. The average percentage gap of MA for small size problems comparing with the optimal solution is 0.8%. The average percentage gap of the proposed MA compared to the proposed lower bound for medium size test problems (problems up to 65 jobs in all groups) is 5%. This research also considers a flexible flowshop sequence-dependent group scheduling problem with minimization of total completion time. A mixed integer linear mathematical model for the research problem is developed. Since the problem is shown to be strongly NP-hard, a MA is proposed. A lower bounding method based on the Branch-and-Price algorithm is also proposed to evaluate the quality of the MA. In order to evaluate the performance of the proposed algorithms, random test problems, ranging in size from small, medium, to large are generated and solved by the MA and the lower bounding method. The results show that the average percentage gap of the MA is 6.03% as compared with the result of the lower bounding method for randomly generated test problems.At last, single machine sequence-dependent group scheduling problem with minimization of total weighted earliness and tardiness, as a strongly NP-hard problem, is investigated in this dissertation. A time-indexed formulation is proposed for the research problem. A branch-and-bound algorithm based on lagrangian relaxation of the proposed model is developed to solve the research problem optimally. The lagrangian relaxation of the proposed time-indexed formulation can be solved as a shortest path problem. In order to evaluate the performance of the proposed branch-and-bound algorithm and to investigate the effect of different parameters on the required CPU time, random test problems are generated and solved by the proposed algorithm
  9. Keywords:
  10. Group Scheduling ; Flexible Flow Shop ; Lower Bound ; Lagrangian Relaxation ; Flow Shop Scheduling ; Sequence Dependent Setup ; Branch and Price Method

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