Operating room planning with pooling downstream beds among specialties: A stochastic programming approach

TL;DR

It is demonstrated that a full-sharing policy among different specialties in the downstream units enhance the functionality of the system by up to 19.53% and a specialized algorithm that quickly solves the second-stage model for any given first-stage solution for a large number of scenarios is developed.

Abstract

In this paper, we study pooling downstream beds across specialties in a stochastic operating room planning problem. The main sources of uncertainty are stochastic surgical durations and patients' lengths of stay. We developed a two-stage stochastic programming model where in the first stage we decide on 1) the number of non-shared ICU and ward beds to be allocated to each specialty, and 2) the allocation of surgeries to operating rooms during the planning horizon. In the second stage, we decide on 1) the number of shared beds in ICU and wards to be allocated to different specialties on each day during the planning horizon, 2) the surge capacity required to satisfy downstream service to patients, and 3) the overtime incurred in operating rooms. The proposed model aims at minimizing the total cost including the patients' waiting cost, postponement cost, overtime and fixed cost of operating rooms, and the cost of downstream surge capacity. We have implemented the proposed stochastic programming model in a sample average approximation framework. To enhance the efficiency of sample average approximation, we have developed a specialized algorithm that quickly solves the second-stage model for any given first-stage solution for a large number of scenarios. We have carried out extensive computational experiments to evaluate the effectiveness of several pooling policies for downstream beds and also the efficiency of the proposed sample average approximation algorithm. Moreover, we have performed an extensive sensitivity analysis of cost and stochastic parameters. Our results demonstrated that a full-sharing policy among different specialties in the downstream units enhance the functionality of the system by up to 19.53%. Moreover, the results indicated that the solutions obtained by the proposed stochastic model outperform those from the corresponding deterministic problem by 17.43% on average.

Figures (4)

• Figure 1: Optimality gap (%) for different combinations of $|M|$ and $|N|$.
• Figure 2: The RSD of LB for different combinations of $|M|$ and $|N|$.
• Figure 3: Solution times (sec) for different combinations of $|M|$ and $|N|$.
• Figure 4: The RSD and solution time of the upper bound problem (sec) for different values of $|P|$.