Surgery Scheduling Optimization With Consideration Of Time Utilization Of Thesurgical Team

A surgery requires multiple critical medical resources,and thus the hospital's interest is highly dependent on surgery scheduling.In practice,surgery scheduling often ignores uncertainties in surgery durations and time utilization of the surgical team,which results in long waiting time for surgeons and fluctuating workload for the operating room(OR)staff.In this dissertation,we consider several stochastic optimization models that take into account uncertain surgery durations for surgery scheduling problems to improve the time utilization of the surgical team.In order to reduce surgeon waiting times,we consider two problems with the same objective that is to minimize the total cost incurred by surgeon waiting time,OR idling time and overtime.The first problem considers dynamic assignment of surgeries with planned surgeon arrival times.We formulate the problem as a multi-stage stochastic mixed-integer program(SMIP)where each stage corresponds to a surgery completion.To efficiently solve the model,we propose an approximation method based on a two-stage SMIP,combining with several looking ahead strategies for evaluating the recourse cost,such as one period looking ahead(OPLA)heuristic and multi-period looking ahead(MPLA)heuristic.We also propose a lower bound cost model based on the perfect information of surgery durations to evaluate the accuracy of the approximation method.Experimental results show that our methods can efficiently solve large-scale problem instances.It is also shown that dynamic assignment of surgeries significantly outperforms static assignment,especially for cases with a large number of ORs and high variance in surgery durations.Moreover,the MPLA based strategy outperforms the OPLA counterpart and the First-Come-First-Serve(FCFS)assignment rule.The second problem addresses the appointment scheduling of surgeon arrival times by anticipating dynamic assignment of surgeries.We formulate the problem as a simulation optimization(SO)model where surgeries are dynamically allocated according to the FCFS rule.We show that the sample path cost function is Lipchitz-continuous,differentiable and unimodal,and the average cost(objective)function is continuously differentiable.We then exploit a stochastic gradient(SG)algorithm to solve the model.Experimental results show this algorithm fast converges to the global optimum.It is also shown that the value of anticipating dynamic assignment is significant,especially for cases with a large number of ORs,high variance in surgery durations and identical surgeries.When scheduling identical surgeries,the optimal allowances exhibit a zigzag shape in the multi-OR setting,while they exhibit a dome shape in the single-OR setting.Moreover,we consider a joint optimization of appointment sequencing and scheduling surgeon arrival times problem that is solved efficiently by our proposed heuristics.We analyze the properties of the optimal appointment sequencing rule for the multi-OR setting.In order to control fluctuating workload for the OR staff,we consider a chance constrained surgery assignment problem to minimize the OR overtime while making sure that some ORs have reliable completion times.We formulate the problem as a two-stage SMIP as well as a Dantzig-Wolfe decomposition model which is solved by a branch-and-price(B&P)algorithm.We further reformulate the subproblem of the decomposition model using probabilistic cover sets.Experimental results show that both Dantzig-Wolf decomposition and the subproblem reformulation help reduce the complexity of problem,making our algorithm significantly more efficient than the standard B&P and branch-and-cut algorithms.Furthermore,we consider a distributionally robust optimization variant with limited information on surgery durations such as mean and variance.We formulate the chance constraints under the worst-case distribution as a series of linear expressions,and thus we are able to reformulate the whole problem as a mixed-integer program which can be solved by our B&P algorithm.Moreover,we consider a joint optimization of surgery assignment and reassignment with chance constraints.We formulate the problem as a two-stage SMIP with nonanticipative constraints.We show the impacts of reassignment points on the total OR overtime.