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Phase-type Distribution in the Sequencing and Scheduling Problem and its Application in Operating Room Problem

Varmazyar, Mohsen | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51700 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Salmasi, Nasser; Modarres, Mohammad
  7. Abstract:
  8. Operating rooms (ORs) are considered as the most valuable resource in hospital, which are the largest revenue generator and, at the same time, the largest cost center of hospitals. Hospital managers have been interested in improving the efficiency and effectiveness of ORs by developing modern planning and scheduling tools. This research studies the stochastic operating room (OR) scheduling problem integrated by Post-Anesthesia Care Unit (PACU), named the operating theater room (OTR) problem. Due to the inherent uncertainty in surgery duration and its consecutive PACU time, the completion time of the operation of a patient should be modeled as the sum of a number of random variables. Several researchers have proposed the use of normal distribution for its well-known additive property, but there are questions regarding its fitting adequacy to real OTR data, which tends to be asymmetric with a long tail. We propose to estimate the surgery and PACU times with the family of continuous phase-type (CPH) distributions, which provides both fitting adequacy and additive property. Phase-type (PH) distributions are a family of discrete and continuous probability distributions constructed by mixtures of geometric or exponential phases. Special properties and characteristics of PH distributions make them attractive for approximating a variety of random variables and modeling real-world stochastic arrival or service times. In order to estimate the service time parameters in OTR problem, we use an expectation-maximization (EM) algorithm. We illustrate the efficiency of the proposed algorithm by comparing its results to that of two existing algorithms in the literature. Solving the OTR problem with considering CPH distribution, we develop a search algorithm embedding constructive heuristic and meta-heuristic algorithms as a sequence generator engine for the patients and apply the CPH distribution as a chance constraint to eventually find the schedule of each sequence in OTR problems. We use the additive property of CPH distribution to compute the completion time of surgery for each patient. The results of experiments for the search algorithm with 12 constructive heuristics show that two of them outperform other constructive heuristics. We propose four meta-heuristic algorithms based on simulated annealing (SA) and tabu search (TS) algorithm to consider as a sequence generator engine for the search algorithm. The best algorithm among several tested constructive heuristic algorithms is used as the neighborhood structure of meta-heuristic algorithms. The results of experiments demonstrate that the TS algorithm considering the best constructive heuristicas a neighborhood search provides better performance than the other proposed meta-heuristic algorithms. We also compare this algorithm with the only existing algorithm similar to our research problem that we could find in the literature. We show that our best algorithm has a better performance compared to the existing algorithm in the literature. We also show the performance of our proposed search algorithm by comparing the CPH and common methods used in hospitals such as average surgery time (AST) to determine the schedule of patients. We conclude that the AST method renders an infeasible schedule because of disregarding the inherent variability of the surgery durations and violating the completion time threshold in most of the cases, whereas the CPH method produces feasible schedules that meet the completion time threshold with the designated probability
  9. Keywords:
  10. Operating Room Scheduling ; Expectation Maximazation Algorithm ; Heuristic Algorithm ; Makespan ; Sequencing ; Meta Heuristic Algorithm ; Continuous Phase-Type Distribution ; Operating Room Scheduling by Post-Anesthesia Care Unit (PACU) ; Discrete Phase-Type Distribution

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