An efficient computational method for large scale surgery scheduling problems with chance constraints

• Published in: Computational optimization and applications Vol. 69; no. 2; pp. 535 - 561
• Main Authors: Noorizadegan, Mahdi, Seifi, Abbas
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2018; Springer Nature B.V
• Subjects: Columnar structure; Computer simulation; Convex and Discrete Geometry; Decomposition; Formulations; Job shops; Management Science; Mathematics; Mathematics and Statistics; Operations Research; Operations Research/Decision Theory; Optimization; Production scheduling; Scheduling; Search algorithms; Sensitivity analysis; Shortest-path problems; Statistics; Surgeons; Surgery; Integer programming; Integer chance constrained programming; Set-partitioning formulation; Surgery planning and scheduling
• ISSN: 0926-6003; 1573-2894
• DOI: 10.1007/s10589-017-9947-0

We propose an efficient solution method based on a decomposition of set-partitioning formulation of an integrated surgery planning and scheduling problem with chance constraints. The studied problem is characterized by a set of identical operating rooms (ORs), a set of surgeries with uncertain durations, a set of surgeons, and surgery dependent turnover times. The decision variables include the number of ORs to open, assignments of surgeries and surgeons to ORs in admissible periods, and the sequence of surgeries to be performed in a period. The objective is to minimize the cost of opening ORs and the penalties associated with turnover times.In the proposed formulation, the column generation subproblem is decomposed over ORs and time periods. The structure of the subproblem is further exploited and transformed to a shortest path problem. A search algorithm has been devised to efficiently solve the resulting subproblem, subject to some optimality and feasibility conditions. The proposed computational method outperforms the standard chance constrained model and reduces the solution time significantly. Furthermore, extensive simulation experiments have been carried out to compare the performance of three variants of the underlying formulations and evaluate the sensitivity of the decisions to the probability of exceeding a session length.