Robust Operating Room Scheduling Model with Violation Probability Consideration under Uncertain Surgery Duration
Abstract
:1. Introduction
- ▲
- The first contribution of this paper relates to the novelty of the optimization objective, which is formulated as the sum of the fixed OR opening cost, the patients’ waiting penalty cost, and the OR overtime cost to represent the operational cost of ORs. Thereinto, patients’ waiting times are calculated via the cumulative sum of the accurate patient’s surgery duration. Hence, with this formula, we demonstrate the influence of the uncertain surgery duration on the OR scheduling model.
- ▲
- Based on the developed optimization objective, we formulate the robust OR scheduling model by considering the patient’s uncertain surgery duration. Thereinto, the uncertain surgery duration is represented by a box uncertainty set, and a robustness coefficient is introduced to control the trade-off between the constraint violation probability and optimality. Then, the robust discrete optimization theory and strong dual theory are invoked to transform the robust model equivalently into a Mixed Integer Linear Programming (MILP) model, which is in a tractable analytical form. It is noteworthy that this paper solves the robust optimization problem with uncertain parameters in both the objective function and constraints. Moreover, by invoking the robust discrete theory, we derive the probability bounds of constraint violation for the OR overtime constraints, which is one of the early attempts to study the constraint violation probability based on the theoretical analysis of the OR scheduling model.
- ▲
- Third, we validate the performance of our model by calculating the upper bound of the constraint violation probability and the objective function at different robustness coefficients to investigate the trade-off among robustness, optimality, and reliability. In addition, some insights are provided on the influence of the robustness coefficient on the OR scheduling model. A sensitivity analysis of the uncertain perturbation factor is also performed to obtain variations in hospital cost sensitivity with the constraint violation probability.
2. OR Model and Assumptions
3. Robust OR Scheduling Approach
3.1. Deterministic Model
3.2. Robust Discrete Optimization Model and Transformation
3.2.1. Linearization of the Objective Function
3.2.2. The Overtime Constraints Transformation
3.3. Upper-Bound Constraint Violation Probability
4. Modeling and Analysis
4.1. The Performance Analysis against the Robustness Coefficient
4.2. Sensitivity Analysis
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameters | Descriptions |
---|---|
the set of patients who need to undergo surgery on the next-day. | |
the expected duration of patient i’s surgery. | |
i-th patient’s waiting time weight, we carve out per patient’s waiting cost by the product of and per patient’s actual waiting time. | |
the OR set, in which OR is functionally identical. | |
fixed opening cost of the j-th OR. | |
T | fixed daily opening hours for each OR. |
unit overtime cost. | |
P | constraint violation probability. |
decision variable, variable, if i-th patient is operated in the j-th OR, = 1; otherwise, . | |
decision variable, variable, if j-th OR is open on next-day, . otherwise . | |
decision variable, the overtime of j-th OR, . |
Robust Coefficient | Minimum Total OR Management Cost | Total OR Overtime | Total Patients’ Waiting Time | Constraint Violation Probability |
---|---|---|---|---|
= 0 | 85.95 | 1.99 | 29.84 | 0.59 |
= 0.1 | 88.76 | 2.33 | 29.79 | 0.58 |
= 0.5 | 94.71 | 4.33 | 30.69 | 0.55 |
= 1 | 98.37 | 6.23 | 30.63 | 0.50 |
= 1.5 | 101.37 | 7.86 | 30.52 | 0.46 |
= 2 | 104.97 | 9.66 | 30.50 | 0.41 |
= 2.5 | 107.40 | 10.69 | 31.20 | 0.37 |
= 3 | 109.23 | 10.94 | 32.64 | 0.33 |
= 4 | 109.24 | 11.00 | 32.61 | 0.25 |
= 5 | 109.17 | 11.02 | 32.43 | 0.195 |
= 6 | 109.13 | 11.03 | 32.52 | 0.13 |
109.63 | 11.06 | 32.77 | 0.05 | |
109.87 | 11.09 | 32.89 | 0.02 | |
= 15 | 109.54 | 11.11 | 32.75 | 0.0008 |
= 18 | 109.74 | 11.12 | 32.71 | 0.00002 |
= 20 | 109.35 | 11.13 | 32.65 | 0 1 |
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Ma, Y.; Liu, K.; Li, Z.; Chen, X. Robust Operating Room Scheduling Model with Violation Probability Consideration under Uncertain Surgery Duration. Int. J. Environ. Res. Public Health 2022, 19, 13685. https://doi.org/10.3390/ijerph192013685
Ma Y, Liu K, Li Z, Chen X. Robust Operating Room Scheduling Model with Violation Probability Consideration under Uncertain Surgery Duration. International Journal of Environmental Research and Public Health. 2022; 19(20):13685. https://doi.org/10.3390/ijerph192013685
Chicago/Turabian StyleMa, Yanbo, Kaiyue Liu, Zheng Li, and Xiang Chen. 2022. "Robust Operating Room Scheduling Model with Violation Probability Consideration under Uncertain Surgery Duration" International Journal of Environmental Research and Public Health 19, no. 20: 13685. https://doi.org/10.3390/ijerph192013685