A new model for operating room scheduling with elective patient strategy

Abstract

Hospitals are dealing with the daunting task of scheduling patients in operating rooms under a limited budget, time, and staff. This article finds the optimal schedule of surgeries by minimizing operating rooms' idle times while maximizing the number of scheduled surgeries during the most effective and desirable time windows. Surgeries during ideal time windows are encouraged by assigning bonus weights in the objective function. Stated and implied benefits of this strategy include mitigating financial loss, complications, and death rate due to a reduction in surgery delays. We introduce a binary programming model for scheduling operating rooms and a mixed integer binary program for planning and scheduling both operating and recovery rooms for elected patients under deterministic conditions. We apply an open scheduling strategy for assigning operating rooms to surgeons and a Lagrangian relaxation method for finding promising solutions. We move hard constraints to the objective to reduce the complexity of the proposed NP-hard model. We incorporate a sub-gradient method that selects the best penalty vector. Finally, we benchmark the results to evaluate the efficiency of the proposed solutions.

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

“…The 1990s: The Subgradient-Level Method. The subgradient-level method, first proposed by [34] and subsequently improved by [14], overcomes the unavailability of the knowledge about the optimal value needed to compute Polyak's step-size (7) by adaptively adjusting a "level" estimate based on detection of "sufficient descent" of the function and "oscillation" of solutions.…”

“…Mixed-Integer Linear Programming (MILP) plays an important role across a range of scientific disciplines such as mathematics, operations research, engineering, computer science as well as within a range of areas of strategic importance to society such as manufacturing [1], pharmacy [2][3][4][5], healthcare [6,7], humanitarian applications [8], biology [9,10], power and energy systems [11], and many others. The associated systems are created by interconnecting smaller subsystems, each having its own objective and a set of constraints.…”

“…Within (7) and thereafter unless stated otherwise, the standard Euclidean norm is used. Subgradient directions, however, 1. are generally difficult to obtain computationally when the number of subproblems (5) to be solved is large, 2. change drastically thereby resulting in zigzagging of Lagrangian multipliers and slow convergence, and 3. the lack of the knowledge about the optimal dual value q(λ * ) to set stepsizes.…”

Surrogate "Level-Based" Lagrangian Relaxation for Mixed-Integer Linear Programming

“…Within [17,Figs. 1,2,[5][6][7][8] pp. 537-539], the SAVLR method showed the advantage over the above SLR method to solve GAPs.…”

Decomposition of the Knapsack Problem for Increasing the Capacity of Operating Rooms

“…Furthermore, the authors proposed two modified heuristics, based on the earliest due date and longest processing time rules, to quickly find feasible solutions. In article [9] from 2021, the authors find the optimal schedule of surgeries by minimizing operating rooms' idle times (in our paper we minimizing idle times too) while maximizing the number of scheduled surgeries during the most effective and desirable time windows. Surgeries during ideal time windows are encouraged by assigning bonus weights in the objective function.…”