Scheduling operating room surgical procedures with early and late completion penalty costs

This work explores the impact of a statistical scheduling technique on two classes of idle times in hospital operating suites. Initially, a mathematical model designed to minimize a weighted sum of the two types of idle time was constructed and optimized. However the minimum solution obtained presented large inequalities in the distribution of idle time costs. An example demonstrates the disproportionately high waiting time costs found for one type of waiting cost relative to the other idle time cost. Because the two types of costs were to be absorbed by two different groups, this type of optimal solution was deemed to be unacceptable. For this reason, an ‘equalizing’ solution approach was developed. To provide a realistic basis for the model, over 2000 actual surgical procedure times were used to model the operation of an operating room suite. The operation was then simulated using a two-stage Monte Carlo method to approximate the distribution of times and procedure types. Idle time functions for early and late completion were then statistically fitted to obtain estimates of the expected idle times as a function of the amount of time scheduled by procedure type. Both types of solution, the optimizing and the equalizing, were examined. By using the ratio of the two types of idle time costs, the problem of having to attach specific numerical values to the individual waiting time costs was avoided. Both solutions provided capacity/utilization ranges for effective scheduling to either minimize or equalize the two types of costs. Suggestions for implementation using computer-assisted scheduling methods are discussed.