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Solving Multi-objective Parallel Machines Scheduling Problem by Using Benders Decomposition Method

Ebrahimi Sheikhi, Yones | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56455 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Eshghi, Kourosh
  7. Abstract:
  8. Parallel machine scheduling problems are the decision-making process of allocating limited resources to activities over time. These issues have attracted a lot of attention in the past decades based on their applications in the real world. It can be discussed about the application of parallel machine scheduling problems in computer processing, production lines and multi-stage systems as examples of areas where parallel machine is observed. Most of the research on parallel machine scheduling has focused on the optimization of a single criterion such as total or average task completion time, total completion time with different weights, sum of penalty or tardiness penalty, total number of delayed jobs, number of completed jobs, and total revenue. So far, several methods, including exact and heuristic algorithms, have been proposed to solve different types of parallel machine scheduling problems. This issue is of high importance among researchers and users in this field of multi-objective mathematical programming. In the section of scheduling problems of multi-objective parallel machines, which is considered as a NP-hard problem, different heuristic solution methods are presented, and these algorithms are classified into two different categories. The first group of algorithms that consider two objective functions together and solve the problem of one objective obtained with existing algorithms, the second group of two objective functions with creative and innovative algorithms that can develop single objective methods, or to invent a new method for a specific type of problem, they solve it. On the other hand, cloud computing is becoming a profitable technology as it offers cost-effective IT solutions globally. An efficient algorithm for task scheduling ensures the optimal use of cloud resources and the reduction of execution time dynamically. In this research, the development of unrelated parallel machine scheduling problem for cloud computing problems with assumptions such as that each machine is not available at some times during the planning horizon and tasks are available at a specific time (processing constraints), has been discussed using the mixed integer linear programming model. Also, for each machine, different positions are considered for processing tasks. Two objective functions are considered to minimize the total tardiness and to minimize the total execution cost and communication cost between tasks. Due to the two objective functions and also the difficulty of the problem, Benders method with the sum of weights has been used to solve the problem. The results obtained from solving the problem show that Benders algorithm is more efficient than Ciplex in high dimensions. Also, Benders algorithm spends a lot of time solving in high dimensions
  9. Keywords:
  10. Scheduling ; Cloud Computing ; Resource Optimization ; Multi-Objective Mixed-Integer Programming ; Multi-Objective Benders Decomposition ; Machine Eligibility Constraint ; Unrelated Parallel Machines

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