A Progressive Hedging Approach for Surgery Planning Under Uncertainty

Abstract

We propose a multistage stochastic mixed-integer programming formulation for the assignment of surgeries to operating rooms over a finite planning horizon. We consider the demand for and the duration of surgery to be random variables. The objective is to minimize three competing criteria: expected cost of surgery cancellations, patient waiting time, and operating room overtime. We discuss properties of the model and an implementation of the progressive hedging algorithm to find near-optimal surgery schedules. We conduct numerical experiments using data from a large hospital to identify managerial insights related to surgery planning and the avoidance of surgery cancellations. We compare the progressive hedging algorithm to an easy-to-implement heuristic for practical problem instances to estimate the value of the stochastic solution. Finally, we discuss an implementation of the progressive hedging algorithm within a rolling horizon framework for extended planning periods.

Robust capacity planning for accident and emergency services

“…Mohiuddin et al [41] identify and review 19 studies related to simulation modelling for emergency departments in the UK. Another comprehensive review of simulation modelling studies in emergency departments for normal and disaster conditions can be found in Gul et al [27]. Among 106 reviewed papers, only few studies consider an optimization approach [1,18,22,51,59].…”

Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface

“…The steel-maker requires the maximum productivity with the preservation of quality, and thus the relevant parameters of the casting process need to be determined. In terms of the above defined quantities and derived relationships, the deterministic model aims to maximize v z subject to (8), (9), (10), (11), (12), (13).…”

“…The vector function g of inequality constraints includes inequality conditions (e. g. Eqs. (12), (13), (17)) while the vector function h of equality constraints incorporates the heat transfer model (Eqs. (8) and 9) and other equality conditions (e. g. Eqs.…”

“…Since there is almost no heat withdrawal from the strand in the second loop, the casting speed has to be reduced to 1.8366 m/min in order to fulfil the temperature constraints and the range of the metallurgical length given by Eqs. (12) and (13), respectively.…”

“…The CPLEX solver without parallel computing was used for the solution of scenario-related sub-problems in sequential order. Gul et al [12] built a stochastic multi-stage mixed-integer model for the surgery planning problem under uncertainty. The authors applied the PHA, they compared it to a heuristic method and evaluated the value of the stochastic solution.…”