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Time-indexed Mathematical Models for Order Acceptance and Scheduling Problems

Fallah, Samira | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49701 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Kianfar, Farhad
  7. Abstract:
  8. Scheduling has been an active area of research for decades. A substantial amount of work has been done to define, classify, and solve scheduling problems. Most of these problems are computationally difficult to solve, and incorporating other decisions into them increases the complexity of these problems. This thesis focuses on order acceptance and scheduling (OAS) problems, and proposes time-indexed mixed integer and linear programming (MILP) models for the first time. An OAS problem can be defined with parameters of processing time, release date, due date, and deadline for each order. There are also a maximum revenue that will be brought by each order and an importance weight of each order. Furthermore, there could be a setup time between orders if they are processed consecutively. In the thesis, both the general OAS problem (OAS2) that will be defined with all above parameters, and a special case (OAS1) that will exclude the release dates and setup times are considered. After developing a time-indexed MILP for both OAS1 and OAS2, their efficiency and effectiveness were tested computationally. To enhance both the efficiency and the effectiveness of OAS1, three dominance properties were suggested, and it was observed that while the optimality gap was decreased, the computational time was also reduced considerably so that large instances can be solved. We also introduce a tabu search algorithm in this context. The results of a computational experiment shows that the execution time of our algorithm is considerably smaller than those of the literature. Since OAS2 is more challenging than OAS1, the time-indexed MILP developed could not solve problem instances to optimality in a reasonable time. Hence, different methods were proposed to find near optimal lower bounds and upper bounds for the problem. To obtain good upper bounds, a linear programming (LP) relaxation method with three new valid inequalities were proposed, and it is shown that LP relaxation with valid inequalities improves almost all upper bounds for all sizes of instances.
  9. Keywords:
  10. Order Acceptance ; Scheduling ; Tabu Search Algorithm ; Valid Inequalities ; Dominance Properties

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