Determining the Optimal Surgical Case-Mix and Capacity Assignment for Surgical Services in Hospitals Using Simulated Annealing

As a crucial industry,the health system needs both managerial and clinical knowledge to solve its problems. This research studies the strategic planning and capacity allocation in operating rooms considering planning and block scheduling strategies. And then, a combined model for determining the optimal case-mix planning and allocating capacity to surgical services is developed as a stochastic optimal programming to face with the uncertain demand for surgery. The purpose of this model is to minimize undesirable deviations including unsatisfied demand, services overutilization and inactive operating rooms. Because the problem is NP-hard in nature, determining the exact solution for real cases will be difficult exponentially. Therefore, a meta-heuristic simulated annealing algorithm is proposed. The results of the mathematical model using GAMS (COINBONMIN) and simulated annealing method, using MATLAB have been compared. The samples have been extracted from a Canadian hospital with 9 surgical services, 110 surgeries, 16 operating rooms and 220 beds. To decrease the number of variables and solve the mathematic model, only a few services, surgeries and operating rooms have been selected. The number of operating rooms not underutilization as studied by both methods for all samples is zero – the optimal. The difference between the optimal values of the objective function obtained from the stochastic goal programming and the simulated annealing method for the samples lies within the range of [0/05, 0/6]. A stochastic goal programming model has been proposed to determine the number and composition of surgical operations and allocate capacity to surgical services with regard to uncertain demand. The idea of ​​the proposed model is that by changing the number and composition of surgical cases, undesirable deviations can be minimized