A fuzzy robust stochastic mathematical programming approach for multi-objective scheduling of the surgical cases

In this paper, the problem of elective surgery scheduling is studied, and resources like surgeons, nurses and operating rooms (ORs) are considered. The problem is to assign surgeries to operating rooms in order to meet three goals: (1) maximizing the number of surgeries that can be done using given fixed resources, (2) minimizing the total fixed costs and overtime costs of the ORs, and (3) minimizing the maximum of completion time of operating rooms. We take into account the uncertainty with the stochastic parameter for the regular operating time of OR in model and fuzzy constraint for resources and overtime. A multi-objective model is proposed to choose the operations to be scheduled on the selected day, and to assign the elective surgeries to OR sessions. In the first phase, we formulated a fuzzy robust optimization model and in the second phase, the sensitivity of the model to different values for penalties in the objective function, is analyzed. The efficiency of the proposed solution is validated by numerical results of applying the model to the case of a public hospital in Iran.