Multi-Objective Decision Support Model for Operating Theatre Resource Allocation: A Post-Pandemic Perspective

Abstract

Background: Healthcare systems are increasingly strained by limited operating room resources and rising demand, a situation intensified by the COVID-19 pandemic. These pressures have resulted in overcrowded surgical departments, prolonged waiting times for elective procedures, worsened patient health outcomes, and increased hospital expenditure costs. Methods: To address these challenges, this study proposes a multi-objective mathematical optimization model as the analytical core of a decision support approach for OR resource allocation. The model considers multiple constrained resources, including OR time, intensive care units, medium care units, and nursing staff, and aims to minimize both elective patients’ waiting times and total incurred costs over a one-week planning horizon. Developed using real hospital data from a large facility in Thailand, the model was implemented in LINGO version 16.0, and a sensitivity analysis was conducted to assess the impact of surgical department priorities and overtime allowances. Results: Compared to current practices, the optimized OR schedule reduced average waiting times by approximately 7% and total costs by 5%, while balancing resource utilization. Conclusions: This study provides a data-driven tool to support hospital resource planning, improve OR efficiency, and respond effectively to future healthcare crises.

1. Introduction

Over the last few decades, healthcare organizations have been striving to reduce healthcare costs while improving the quality of their services and resource utilization. The growing demand for timely, affordable, and high-quality healthcare services has pressured hospitals to effectively manage their resources and processes. Studies estimate that approximately 60% to 70% of all patients admitted to the hospital require some form of surgical intervention [1]. Hence, the operating room (OR) department is one of the most important facilities and a central hub in the hospital. In general, ORs generate over 40% of a hospital’s total revenue and incur a tablesimilar proportion of its expenses. An OR is connected to various downstream resources, such as the intensive care unit (ICU), medium care unit (MCU), nursing staff, radiology department, rehabilitation, physical therapy department, etc. [2]. Most of these downstream resources are scarce and highly expensive to operate. They are often influenced by surgical programs [3]. The unavailability of one of these resources can result in inefficient use of resources, affect surgical outcomes, or lead to delays in the transfer of care to downstream postoperative care [4]. A study by Negash et al. [5] revealed that the most common cause of cancellation was lack of OR time (workday ending before scheduled cases are finished). This was followed by issues related to perioperative patient preparation. Others were institutional factors, of which the lack of an ICU bed was the most common.

In the context of healthcare emergencies—such as resource shortages, the COVID-19 pandemic, budget constraints, supply chain disruptions, and equipment failures—healthcare organizations face significant challenges. Therefore, providing timely and appropriate treatment to patients becomes a crucial aspect of quality care and plays an important role in maintaining a sustainable healthcare system. [6]. For instance, during the COVID-19 pandemic, the regular function of the OR department was disrupted, and critical downstream recovery resources, such as ICU, MCU, and healthcare personnel, were dedicated to COVID-19 patients. In the US, the cancellation of elective surgeries helped decrease ICU overcapacity from 327 to 237% (lower bound) or from 525 to 329% (upper bound) [7]. This resulted in a substantial backlog in surgical services and extended waiting times for surgery patients [8]. The consequences of prolonged delays in surgical intervention not only impact patients’ health conditions and contribute to reduced patient satisfaction but also result in increased healthcare expenditure. This expenditure includes additional hospital visits, medication costs, consultations with general practitioners and physiotherapists, and potentially prolonged recovery periods [9]. These challenges underscore the necessity for the optimal allocation of OR time across surgical departments, especially when resources are scarce.

Resource allocation involves determining how to assign available resources to specific tasks in order of priority. In disaster scenarios, where multiple stakeholders are responsible for carrying out predefined roles, the allocation process should be guided by three key principles, as outlined by Beamon and Balcik [10]. These include ensuring timely assistance to those in need (effectiveness), making the best possible use of available resources (efficiency), and distributing aid fairly among all affected parties (equity) [11]. The main goals of healthcare organizations are to clear the backlog of patients and provide prompt access to surgical care for patients who have been waiting for their scheduled procedures, as well as to restore normal functioning of the OR department. Strategies employed by OR managers to address surgical backlogs include increasing installed capacity, managing demand, and improving efficiency [12]. Improvement of resource synchronization in surgical departments is, therefore, becoming a priority to reduce both bottlenecks and backlog. Since downstream resources are directly influenced by the surgical program, the optimal OR time allocation to different surgical departments and optimal daily surgery caseload from different surgical departments can be beneficial in optimizing OR efficiency and improving utilization of downstream resources [13]. For these reasons, OR time allocation management problems have become popular in the healthcare literature over the last two decades [14].

This study presents a multi-objective mathematical optimization model that serves as the analytical core of a decision support approach for resource allocation in the OR department. The model determines optimal OR block assignments to surgical departments under resource constraints, including ICU/MCU bed availability and staffing limitations. By incorporating real-world hospital data, departmental prioritization rules, and uncertain resource capacities, the model aims to minimize elective patients’ waiting times and the total operational costs incurred within a one-week planning horizon. Although it is implemented using the commercial solver LINGO, the model is designed for future integration into comprehensive decision support systems applicable in hospital environments.

2. Literature Review

2.1. Operating Room Resource Management

OR resource management is recognized as a crucial task in hospital organization. It is a highly complex process driven by the need to balance the demands of multiple surgical departments with limited available capacity and resources. This complexity arises from the interplay between various factors, including healthcare personnel, equipment, facilities, and the diverse needs of surgical departments. The resources required for each patient can be uncertain and vary significantly across different departments. The involvement of various stakeholders in OR planning and scheduling often leads to conflicting objectives, as they aim to improve quality and satisfaction while simultaneously reducing costs and managing resources effectively.

OR planning and scheduling problems can be classified into three decision levels: strategic, tactical, and operational. The strategic level addresses the allocation of surgical resources among different departments on a long-term basis, known as case mix planning (CMP). The tactical level involves the development of a master surgery schedule (MSS) for one or several months. The operational level concerns the assignment of surgeries to specific ORs on specific dates (advanced scheduling) [14]. Since downstream resources are highly influenced by the allocation of OR time to different surgical departments [13], OR time is studied under three strategies: block strategy, open strategy, and modified block strategy [15]. The block strategy involves pre-allocating OR blocks to different surgeons or departments at specific times (e.g., 8 h per block from 8:00 to 16:00). The open strategy offers greater flexibility, where no OR sessions are pre-allocated, allowing all departments to schedule cases into any available and suitable OR. The modified block scheduling strategy combines both approaches, providing flexibility and convenience for management [16]. Surgery patients are classified into two groups based on urgency: elective and emergency patients. Elective surgery patients can have their procedures delayed and well-planned, whereas emergency patients require urgent, unexpected surgeries. Up to 75% of surgeries are elective [13,14]. To minimize disruptions and maximize resource efficiency, emergency surgeries are often handled in dedicated units [15,16,17,18].

The objective of resource allocation in healthcare is to reduce total costs and patient waiting times while maximizing resource efficiency. Various studies have incorporated hospital-related costs into OR planning and scheduling. Fügener et al. [19] identified four cost components: fixed costs, overcapacity costs, staffing costs, and additional weekend staffing costs. This contributes significantly to hospital expenses. Zhang et al. [20] considered patient-related and hospital costs, focusing on expenses incurred by opening and overusing surgical blocks and exceeding regular ICU capacity.

For instance, Denton et al. [21] studied optimization models for planning and scheduling multiple ORs under uncertainty, aiming to balance the fixed cost of opening ORs and the total cost of overtime. Lin and Li [22] focused on minimizing operating costs while maximizing OR utilization. Fügener et al. [23] addressed the tactical MSS problem, aiming to minimize downstream costs by leveling bed demand and reducing weekend bed requests. Shafaei and Mozdgir [24] developed a mathematical model to construct an MSS, minimizing OR spare time while considering the initial OR block allocation at the strategic level. Similarly, Lu et al. [25] developed a multiphase OR scheduling approach that addressed two different decision levels. The first phase mainly focused on an allocation of the number of OR blocks for each SS, with the objectives of maximizing profit and minimizing overtime costs. In the second phase, the MSS model was constructed to schedule surgeries in each SS to maximize the number of scheduled patients in all ORs in a certain specialty, minimize underutilization and overtime costs, and balance ORs according to a standard of OR working time, simultaneously. A multi-objective linear programming (MOLP) model was used to handle the problem. To reduce the complexity of the model, downstream resources (ICUs and wards) and uncertainty in surgery duration were ignored. Patrão et al. [26] proposed two stages of OR planning and scheduling. They introduced an integer linear programming model (ILP) that is based on patient volume in CMP at a strategic level to assign the number of OR blocks to each SS, and at the tactical level, the model aimed to determine the MSS.

The literature indicates a widespread focus on combining strategic and tactical levels in OR planning and scheduling, using optimization methods [27]. However, there is less emphasis on approaches that simultaneously reduce total costs and patient waiting times and maximize resource efficiency. Moreover, many studies predominantly consider hospital-related costs, often neglecting patient-related costs, which are crucial in the planning and scheduling process. Prolonged waiting times for surgery incur significant patient-related costs, including additional healthcare expenditures and a decline in the quality of life [9]. Our study incorporates multiple cost components, including patient-related costs (waiting times) and hospital-related costs (overtime and overcapacity penalties). Integrating these costs in OR planning is essential, as they conflict with each other in terms of reducing patient waiting time versus adding more overtime resources. Therefore, our study aims to minimize total incurred costs, reduce patient waiting times, and optimize resource utilization efficiency.

As summarized in

Table 1. Summary of related works.

Study	Decision Level	Cost Consideration	Objective Function
Fugener [19]	Tactical level	Fixed cost and downstream costs	Minimize downstream cost
Zhang et al. [20]	Operational level	Cost incurred by performing and delaying procedures, fixed OR cost and overtime cost	Minimizes the total cost
Denton et al. [21]	Operational level	Fixed cost and overtime cost	Minimize weight sum of the total cost Minimize total overtime cost
Lin and Li [22]	Tactical level	Waste cost and overtime cost	Minimize operating costs Maximize resource utilization
Fugener [23]	Integrated strategic and tactical	Downstream costs	Maximize hospital revenue
Shafaei and Mozdgir [24]	Tactical MSS	None	Minimize OR spare time
Lu et al. [25]	Two stages, strategic and tactical	Overtime costs	Maximize profit Minimize overtime costs
Patrão et al. [26]	Integrated strategic and tactical	Cost of misplacing patients	Maximize benefit of assigning OR to specialty
This Study	Integrated strategic and tactical	Waiting cost and overtime cost	Minimize patient waiting time Minimize total incurred costs

, this study addresses key gaps in the existing literature by adopting an integrated approach to OR resource management at the strategic and tactical levels. Unlike previous studies that often isolate either cost objectives or planning horizons, our model jointly considers patient-related costs (e.g., waiting time) and hospital-related costs (e.g., overtime), aiming to minimize total incurred costs, reduce patient waiting times, and enhance resource utilization efficiency.

Strategic inputs—such as surgical case mix, patient backlog volumes, number of available OR blocks, ICU/MCU capacity, and staff availability—are defined in advance, reflecting institutional resource settings and planning policies. The primary tactical decision involves the weekly allocation of OR blocks to surgical departments. This mid-range planning horizon allows for a more flexible, responsive strategy to gradually clear surgical backlogs and optimize resource deployment in the face of demand variability. By integrating strategic parameters with tactical planning decisions, the model supports higher-level hospital decision-making beyond day-to-day operations, with the aim of improving long-term system performance and resilience.

2.2. Patient Waiting List Management

Patient waiting list management is a critical component of healthcare delivery, especially in the context of surgical services where demand for services significantly exceeds supply. Ineffective and inefficient resource management in the OR department can consequently affect elective surgery waiting lists, leading to prolonged waiting times, negatively impacting patient health and satisfaction, and sometimes resulting in patients leaving before receiving treatment. Reducing patient waiting times is a critical performance indicator in healthcare systems and is crucial for patient satisfaction and loyalty to healthcare centers [28]. Therefore, various strategies have been employed by hospital managers to address elective patient surgical backlogs, such as increasing installed capacity, improving efficiency, managing demand [12], and integrating different levels of patient importance (priority) to increase patients’ satisfaction levels and reduce the poor quality of service [29].

For instance, VanBerkel and Blake [30] addressed waiting list problems by considering increasing installed capacity, aiming to optimize resources, and decreasing patient wait times in OR planning and scheduling procedures. They utilized discrete-event simulation to analyze the impact of changing bed capacity and OR time on throughput and waiting times. However, the option to increase capacity is limited by constraints such as budget, space, and human resources and is infeasible for some hospitals in some areas.

Comparatively, the option to improve the effectiveness and efficiency of OR management is generally more meaningful and feasible for hospitals [31]. A study by Spratt and Kozan [32] considered improving efficiency by constructing a mixed-integer nonlinear programming (MINLP) approach to formulate the problem of generating an MSS for managing the waiting list, adhering to staff and equipment restrictions, and ensuring timely treatment of patients.

Other than the above-mentioned approaches, demand-side management is critical when there is nothing much to do with the supply side. Bowers [33] developed a model simulation of waiting list management that incorporated patient priority to explore the impact of seasonal variations in demand and supply on waiting times for elective surgical procedures in different specialties. The simulation estimated the number of patients who would be treated within the specified target waiting time. Powers et al. [34], on the other hand, proposed a dynamic priority scoring (DPS) system to rank elective surgery patients more equitably, based on a combination of waiting time and clinical factors.

As summarized in

Table 2. Summary of strategies for managing the waiting list.

Study	Strategies	Methodology	Key Findings
VanBerkel and Blake [30]	Increasing Capacity	Discrete-event simulation	Increasing bed capacity and OR time can significantly impact throughput and reduce waiting times using discrete-event simulation
Spratt and Kozan [32]	Improving Efficiency	Mixed-integer nonlinear programming (MINLP)	Ensured timely treatment of patients while managing resources
Bowers [33]	Demand-Side Management	Model simulation	Estimated number of patients treated within target waiting time
Powers et al. [34]	Demand-Side Management	Dynamic priority scoring (DPS)	Focused on equitable ranking of patients
This study	Considering All Three Strategies	Mathematical modeling (MINLP)	Allocate optimal resources, provide fair access time to surgical service across department, minimize total cost

, existing studies on patient waiting list management typically focus on isolated strategies—such as increasing capacity [30], improving operational efficiency [32], or applying demand-side management techniques like dynamic prioritization [34,35]. While each approach contributes to reducing waiting times or improving fairness, they address the problem in a fragmented manner and often ignore critical system-level constraints such as limited ICU/MCU resources or interdepartmental equity.

In contrast, this study proposes an integrated optimization framework that simultaneously considers all three strategic dimensions: capacity, efficiency, and demand-side prioritization. By employing a mathematical programming approach, our model allocates OR blocks across departments, prioritizes patients based on clinical urgency and fairness, and minimizes total system costs—encompassing both hospital-related (e.g., overtime) and patient-related (e.g., prolonged waiting) consequences. This integrative perspective not only supports more holistic and sustainable surgical backlog management but also advances existing research by embedding real-world constraints into both strategic and tactical decision-making processes.

Recently, waiting list management has received increased attention, particularly since the suspension of elective surgery due to the COVID-19 pandemic. The extension of OR time has been used to reduce waiting lists by taking advantage of empty ORs and existing surgical teams [12]. Unfortunately, during the peak of the pandemic, downstream resources such as ICU and MCU were redirected for use by COVID-19 patients, resulting in unavailability to handle the patient flow from the OR. As a result, this led to a dramatically increased surgery backlog, and the volume of the surgery backlog accumulated from the cancellation of elective surgery remains unknown. Some studies integrated waiting list estimation and backlog clearance time projections using the simulation method, as shown in

Table 3. Summary of integration of waiting list management and resource management.

Study	Objectives	Methodology	Key Findings
Wang et al. [35]	Estimate surgery backlog size and clearance time resulting from COVID-19	Forecasting and queuing models	Provided estimates for backlog size and project time for clearance, aiding in recovery planning
Oussedik et al. [36]	Model orthopedic pathway to estimate elective surgery waiting lists and suggest recovery strategies	Pathway modeling	Proposed strategies for managing orthopedic surgery waiting list and optimizing resources
Joshi et al. [37]	Use machine learning for predictive analysis to estimate backlog clearance time and associated costs	Machine learning algorithm	Offered real-time estimations on clearance time and costs, facilitating resource optimization
This study	Formulate mathematical model for managing resources and waiting list	Math modeling technique (MINLP)	Optimal resource allocation results in minimum average waiting time and costs

. For instance, Wang et al. [35] estimated the backlog size in Ontario due to COVID-19 disruption and the time needed for backlog clearance utilizing forecasting and queuing models. Oussedik et al. [36] modeled the orthopedic pathway to estimate elective waiting list numbers and suggest recovery strategies. Furthermore, Joshi et al. [37] used machine learning for predictive analytics and offered real-time estimations on backlog clearance time and associated costs based on resource optimization. However, due to the ongoing pandemic, the exact size of elective surgery waiting lists remains unknown. Abdullah et al. [7] developed a two-stage discrete event simulation framework to evaluate elective surgery cancellation and resumption strategies, considering the trade-offs between overutilization, extended wait times, and operational outcomes.

Efficient OR planning is critical for addressing the surgical waiting list [38]. As the pandemic transitions into an endemic phase, there is widespread recognition of the importance of effectively managing waiting lists and reallocating resources in OR planning. However, as summarized, a notable gap exists in the literature concerning the integration of elective surgery waiting list management with the allocation of OR resources. This study seeks to address this gap by examining three strategies in OR resource reallocation: increasing capacity, prioritizing surgical departments, and optimizing resource utilization within the OR system to enhance efficiency in order to minimize patient waiting time and total incurred costs.

3. Methodology

This section describes the overall processes of the proposed mathematical model for OR resource allocation, as shown in Figure 1. First, parameters and decision variables are described. Then, the multi-objective optimization model is formulated and explained. We provide an overview of the mathematical model, including the objective functions, constraints, and datasets from a large hospital for verifying the model and validating the model with sensitivity analysis.

3.1. Indices, Parameters, and Decision Variables

Table 4. Description of parameters and decision variables.

Sets	Descriptions
T	Set of days in weekly planning horizon
r	Set of resources including operating room (or), intensive care unit (icu), medium care unit (mcu), and nursing hours (nh)
Indices
t	Index of days, t = 1, 2, …, T
s	Index of number of surgical departments, s = 1, 2, …, S
Parameters
${\mathit{O}}_{\mathit{s}}$	The average operation duration of surgical specialty s
${\mathit{P}}_{\mathit{s}}$	Relative important weight of specialty s
${\mathit{\mu }}_{\mathit{s}}$	Average number of patients per OR block for specialty s
${\mathit{l}}_{\mathit{s},\mathit{u}\mathit{p}}$	Average LOS of surgical specialty s patients in MCU before surgery
${\mathit{l}}_{\mathit{s},\mathit{d}\mathit{o}\mathit{w}\mathit{n}}$	Average LOS of surgical specialty s patients in MCU after surgery and ICU
${\mathit{l}}_{\mathit{s},\mathit{i}\mathit{c}\mathit{u}}$	Average LOS of surgical specialty s patients in ICU after surgery
${\mathit{n}\mathit{w}}_{\mathit{s}}$	Average nursing workload (in hours) required for specialty s patients in ICU
${\mathit{C}}_{\mathit{r},\mathit{t}}$	Available capacity of resource r on day t, rÎR = {or, icu, mcu, nh}
${\mathit{\phi }}_{\mathit{r}}$	Maximum overtime of resources allowed for resources r over T
${\mathit{U}}_{\mathit{r},\mathit{T}}$	Target utilization of resources rÎR = {or} in planning horizon T
${\mathit{D}\mathit{e}\mathit{m}}_{\mathit{s}}$	Weekly demand for surgical specialty s
${\mathit{W}\mathit{L}}_{\mathit{s}}$	Total patients waiting in each surgical department s
${\mathit{R}\mathit{e}\mathit{q}}_{\mathit{s},\mathit{T}}^{\mathit{m}\mathit{a}\mathit{x}}$	Maximum requirement number of OR blocks of specialty over T
${\mathit{R}\mathit{e}\mathit{q}}_{\mathit{s},\mathit{T}}^{\mathit{m}\mathit{i}\mathit{n}}$	Minimum requirement number of OR blocks of specialty over T
${\mathit{R}\mathit{e}\mathit{q}}_{\mathit{r},\mathit{T}}^{\mathit{u}\mathit{t}\mathit{i}}$	Resource utilization requirement of resource r over T
${\mathit{W}\mathit{C}\mathit{o}\mathit{s}\mathit{t}}_{\mathit{s}}$	Cost of waiting for surgery for patients from specialty s
${\mathit{O}\mathit{C}\mathit{o}\mathit{s}\mathit{t}}_{\mathit{r}}$	Cost of overcapacity resources r
${\mathit{w}}_{\mathit{W}}$	Relative weight of patient waiting time
${\mathit{w}}_{\mathit{O}}$	Relative weight of overtime cost
Decision variables
${\mathit{x}}_{\mathit{s}\mathit{T}}$	Number of OR blocks assigned to surgical department s in planning horizon T
${\mathit{T}}_{\mathit{W}\mathit{L},\mathit{s}}$	Number of weeks required to clear patient waiting list of surgical department s
${\partial }_{\mathit{T}\mathit{C}}$	Average number of weeks required to clear patient waiting list in hospital
${\mathit{o}}_{\mathit{r},\mathit{T}}$	Overcapacity of resources r needed over T and T + 2
${\mathit{U}}_{\mathit{r},\mathit{T}}$	Utilizations of resource r over T and T + 2

describes indices, parameters, and decision variables that are used to develop the mixed integer non-linear programming (MINLP) model for the deterministic OR allocation problem, aiming to minimize the patient waiting time and the total incurred cost associated with OR block allocation.

3.2. Deterministic OR Resource Allocation (DORA) Model

3.2.1. Objective Function

The proposed model consists of two objectives, namely minimizing patient waiting times in Equation (1) and minimizing total incurred costs in Equation (2). In Equation (1), the objective involves calculating the cumulative waiting cost that needs to be minimized for all surgical departments. This is achieved by multiplying the weekly waiting cost for each surgical discipline and the number of patients on each surgical department’s waiting list by the decision variable, number of weeks required to clear the patient waiting list. The model solution aims to minimize the average patient waiting time of each surgical department, denoted as $T_{WL,s}.$

$$Minimize Z_w=\sum _s^S\left(T_{WL,s}·{WCost}_s · {WL}_s\right)$$

(1)

$$Minimize Z_O=\sum _r^R\sum _s^S\left(o_{r,T} ·P_s·{OCost}_r{·\partial }_{TC}\right)$$

(2)

In Equation (2), the formulation comprises four cost components, which are costs associated with the overcapacity of OR, ICU, MCU, and nursing workload. It computes the overall overcapacity cost of all resources by multiplying unit values of overcapacity for these resources by the unit cost and then multiplying the result by the average waiting list clearance time. These two distinct formulas can then be converted into a unified objective function, as shown in Equation (3) below. The objective function (3) is referred to as the “total incurred cost”.

$$MIN Z= w_w·Z_w+w_o·Z_o$$

(3)

The weighting of each objective function $w_w \mathrm{a}\mathrm{n}\mathrm{d} w_o$ can be interpreted as a reflection of the hospital’s preferences toward the performance indicators. In general, different hospitals may have different priorities in weighting different performance indicators due to various factors. For instance, Tanantong et al. [39] used five sets of weight settings for the weight of cost objectives, namely 0.8, 0.2, 0.6, 0.4, and 0.5, and the weight of satisfaction objectives, namely 0.2, 0.8, 0.4, 0.6, and 0.5.

3.2.2. Constraints

This section outlines constraints considered in our model.

$$\sum _{t=1}^{T-2}{x}_{sT} \le \sum _{t=1}^{T-2}{C}_{r,t}+o_{r,t} \forall r\in \left\{or \right\}, \forall s\in S$$

(4)

$$\sum _{s=1}^S\left(x_{sT} · {\mu }_{s }· l_{s,icu}\right) \le \sum _{t=1}^T{C}_{r,t}+o_{r,t} \forall r\in \left\{ icu \right\}, \forall t\in T$$

(5)

$$\sum _{s=1}^S\left\{x_{sT} · {\mu }_{s }· \left(l_{s,up}+l_{s,down} \right)\right\} \le \sum _{t=1}^T{C}_{r,t}+o_{r,T} \forall r\in \left\{ mcu \right\}, \forall t\in T$$

(6)

$$\sum _{s=1}^S\left(x_{sT} · {\mu }_{s }· {nw}_s\right) \le \sum _{t=1}^T{C}_{r,t}+o_{r,T} \forall r\in \left\{ nh \right\}, \forall t\in T$$

(7)

Constraint (4) ensures that the number of allocated OR blocks does not exceed available OR blocks in a one-week planning horizon. Constraint (5) ensures that required ICU time for all patients in planning horizons does not exceed available ICU time. Constraint (6) determines the total amount of time needed for both preoperative and postoperative stays. This constraint ensures that the number of patients admitted to the MCU following surgery and prior to surgery does not exceed available MCU beds in a one-week planning horizon. Constraint (7) ensures that the total amount of nursing time does not exceed available time.

$$o_{r,t} \le {\phi }_{r }·\sum _{t=1}^{T-2}{C}_{r,t} \forall r\in \left\{ or \right\}, \forall t\in T$$

(8)

$$o_{r,t} \le {\phi }_{r }·\sum _{t=1}^{T-2}{C}_{r,t} \forall r\in \left\{ icu,mcu,nh \right\}, \forall t\in T-2$$

(9)

Constraint (8) and Constraint (9) are crucial for imposing constraints on the maximum allowable overtime for all resources over a one-week planning horizon. They ensure that the variables denoting overcapacity for OR blocks, ICU time, MCU, and nursing time do not exceed the maximum permissible threshold of resource facilities. This threshold is calculated as the total supply capacity for each resource multiplied by the corresponding percentage allowance, which is derived from the hospital perspective.

To optimize the utilization of resources, including OR, ICU, MCU, and ICU nursing workload, it is essential to establish constraints that ensure that these resources are used effectively. Constraint (10) is formulated to set the minimum requirements for the utilization of these resources.

$$U_{r,T} \ge {Req}_{r,T}^{uti} \forall r \in \left\{ or, icu,mcu,nh \right\}$$

(10)

Constraints (11) and (12) play a significant role in defining boundaries for the allocation of OR blocks to each specialty over the planning period. These constraints determine both the lower and upper limits for the number of OR blocks that should be allocated to each department. This perspective reflects the minimum and maximum service level provided to patients from less profitable surgical departments.

$$\sum _s^S\sum _{t=1}^{T-2} x_{sT} \ge {Req}_{s,T}^{min} \forall r \in \left\{or\right\}$$

(11)

$$\sum _s^S\sum _{t=1}^{T-2} x_{sT} \le {Req}_{s,T}^{max} \forall r \in \left\{or\right\}$$

(12)

Constraint (13) guarantees that the allocation of OR blocks must be adequate to clear the weekly demand of each specialty over the planning period.

$$\sum _{t=1}^{T-2}{x}_{sT} · {\mu }_{s } \ge {Dem}_s \forall s\in S$$

(13)

Constraint (14) ensures that the total number of blocks assigned to all specialties collectively must be sufficient to handle total patient throughput weekly. In other words, the resource allocation should be capable of accommodating the combined needs of all patients across various surgical departments within a given week.

$$\sum _t^T\sum _s^S\left({\mu }_{s }·{x_{sT} · \partial }_{TC}\right) \ge \sum _s^S{WL}_s$$

(14)

Finally, Constraint (15) restricts all decision variables to be positive integer values, and Constraint (16) is the non-negativity of resource utilization, overcapacity of resources r, number of weeks required to clear patient waiting list of surgical department s, and average number of weeks required to clear patient waiting list in the hospital.

$$x_{sT}\in \mathbb{N},\hspace{1em}\hspace{1em}s\in S, t=1, 2, \dots , T+2$$

(15)

$$U_{r,T} \ge 0, o_{r,T}\ge 0, T_{WL,s}\ge 0, { \partial }_{TC}\ge 0,\hspace{1em}\hspace{1em}r\in R, t=1\dots . T+2$$

(16)

3.3. Numerical Case Study: Overview of Hospital Dataset

The datasets for numerical analysis were collected from a large hospital with more than 5000 surgical interventions per year. In the hospital, there are 8 different surgical groups: ear, nose, and throat (ENT), obstetrics and gynecology (OBG), orthopedic surgeries (ORT), neurosurgery (NEU), general surgeries (GEN), vascular surgeries (VAS), cardiac surgeries (CAR), and urology surgeries (URO). There are eight operating rooms, one of which is dedicated to emergency patients. The hospital operates these ORs on 8 h surgical blocks during regular time from Monday to Friday. There are 20 ICU rooms and 35 MCU beds, which operate continuously, 24 h day, seven days a week. Additionally, there are 60 nurses available in the ICU. Mean surgery duration, mean LOS in the ICU and MCU (preoperative and postoperative stay), and mean ICU nursing hours needed are adopted from historical data and statistics obtained from Jittamai & Kangwansura [40]. Resources required by each surgical patient and overall resource availability are measured in hours. We assume that any patient can access any available ICU or MCU beds and that MCU beds are used for both preoperative and postoperative care in the planning horizon.

Before the pandemic, OR blocks were allocated based on the number of patients in each surgical department and the limited availability of downstream facilities. As detailed in

Table 5. Current OR block assignment.

Specialty	No. Blocks Assigned	Number of Patients on Waiting List	Expected Waiting Time (Weeks)
ENT	5	1092	36.4
OBG	3	468	31.2
URO	3	416	34.67
GEN	5	1144	31.77
VAS	3	416	52
OTH	5	1196	42.71
NEU	3	260	43.33
CAR	1	104	52

, the number of patients in each surgical department was assessed, and the number of OR blocks assigned. Over a one-week planning horizon, the current setting resulted in an average of 90% of resources being used and the average waiting time of the patient in each department being 41.32 weeks.

4. Experimental Results and Discussion

In this section, we present the numerical experiment conducted for the deterministic operating room resource allocation (DORA) problem, along with a detailed discussion of the results obtained. The DORA model was solved using LINGO version 16, utilizing datasets obtained from the aforementioned hospital. The solution can be obtained within a few seconds, providing insights into optimal resource allocation and its impact on various metrics.

4.1. Comparative Analysis: Model Solution Versus Current Hospital Setting

Figure 2 illustrates the number of OR blocks reallocated based on our model solution compared to the current allocation in the hospital. Notably, significant changes in OR block allocations have occurred across different surgical departments.

For instance, the ENT and GEN departments experienced increases from 5 to 8 blocks and from 8 to 10 blocks, respectively, while the OBG and URO departments experienced reductions from 3 to 2 blocks and from 8 to 7 blocks per week, respectively. The increase in OR blocks allocated to departments such as ENT, GEN, and OTH directly addresses the patient waiting list demand for the surgical services within these specialties. By providing additional OR blocks, more surgeries can be accommodated, thereby reducing the backlog of cases and dramatically reducing average patient waiting time. Conversely, the reduction in OR blocks allocated to departments such as OBG and URO reflects a more efficient use of resources. By reallocating OR blocks from these two departments, the model solution can better match capacity with demand, thereby reducing underutilization of downstream resources and minimizing idle time in OR.

The outcomes presented in Figure 3 show that our model substantially reduces the time required to clear the waiting list compared to the current setting. Departments such as ENT, GEN, OTH, and CAR demonstrated a remarkable decrease in waiting list clearance times, transitioning from 43.68 to 27.3 weeks, 57.2 to 28.6 weeks, 59.8 to 42.71 weeks, and 52 to 26 weeks, respectively. However, the OBG, URO, VAS, and NEU departments showed an increase in waiting list clearance times, increasing from 31.2 to 46.8 weeks, 34.6 to 52 weeks, 28.88 to 43.33 weeks, respectively. The variation in waiting list clearance times across departments is a direct consequence of the model’s resource-aware optimization strategy. The model seeks to improve overall system efficiency by reallocating OR blocks in a way that aligns with both the urgency of patient backlogs and the availability of downstream resources, such as ICU, MCU, and nursing staff.

Each surgical department has distinct resource consumption patterns—some require longer postoperative stays or higher-intensity care, leading to more pressure on constrained resources. Allocating a large number of OR blocks to these resource-intensive departments without accounting for downstream availability would lead to bottlenecks, underutilization in other areas, and prolonged system-wide delays. Therefore, the model redistributes OR blocks to balance the clinical urgency of patients with the efficient use of institutional capacity. As a result, departments with high urgency but manageable resource intensity (e.g., ENT, GEN, CAR) see a significant reduction in waiting times, while others with lower urgency or higher downstream demands (e.g., OBG, URO, VAS) may experience increased delays. This trade-off is intentional and reflects the model’s multi-objective approach to minimizing total cost—including both patient- and hospital-related components—while maximizing overall resource utilization.

In addition, resource utilization across different facilities was compared between the current setting and our proposed model, as shown in Figure 4. The OR is 100% utilized based on our model solution, while the current setting uses 80% of available capacity with downstream ICU and MCU utilization rates of 98.28% and 99.59%, compared to the current setting resource utilization of 94% and 89.79%, respectively. And nursing time is relatively unchanged.

Table 6. Objective values of current setting vs. our model.

	Current Setting	Proposed Model	% Decrease (Proposed Model: Current Setting)
Objective value (unit cost)	4,725,300	4,089,871	13.45%
Mean waiting time (weeks)	41.32	37.67	8.81%
Sd waiting time (weeks)	13.87	9.86	28.87%
Mean utilization (%)	90.60	99.25	8.7%
Sd utilization (%)	7.95	0.74	90%
Patient throughput	140	148	5.71%

shows a comparative statistical analysis between the model solution and current setting. There is a notable decrease in both the objective value and average patient waiting time, as well as improved resource utilization. Specifically, the mean and standard deviation of patient waiting time decreased by approximately 8.81% and 28.87% respectively, while the objective value decreased by about 13.45%.

The mean resource utilization of resources is 99.25%, and the standard deviation is 0.74%; for the current hospital setting, the average is 90.6%, and standard deviation is 7.94%. The significant reduction in standard deviation implied that our model demonstrated better and more balanced resource utilization across different resource facilities upstream and downstream.

The results highlight the effectiveness of our proposed model in optimizing OR block allocation within surgical departments. By reallocating OR blocks, the model solution achieved significant reductions in average patient waiting time and total incurred cost while also improving resource utilization across different resource facilities. These findings highlight the potential of modeling approaches for enhancing OR resource management and operational efficiency, ultimately leading to improved patient wait time. Although the model’s solution offers improved OR resource allocation by reducing objective value, resource utilization deviation, and shortening patient waiting times across various surgical departments compared to current practices, unfortunately, the model is generated based on constrained resources and neglects the surgical department priority.

Given the significant global burden of surgical backlog and the constraints posed by limited and costly overtime resources, it is vital for OR managers to consider prioritization techniques and allow overtime resource aid to address the surgical backlog. In scenarios where overtime is not possible due to hospital conditions, setting priorities among surgical departments becomes crucial. This determines the order in which departments are granted access to OR blocks, impacting patient wait times and resource distribution. For instance, during crises such as pandemics or emergencies where resources are limited, decisions must be made wisely to allocate resources where they are most needed. Despite expensive overtime costs, from a crisis perspective, it is necessary to utilize overtime resources to help reduce the burden of the surgical backlog and patient waiting times. To better understand the trade-off between overtime resource allowance and additional costs incurred, the study conducts a cost–benefit analysis to assess the financial implications of such increases and strike a balance between reducing patient waiting times and considering financial aspects.

Through this analysis, hospital administrators can gain insights into the trade-offs between total additional overtime costs and average patient waiting time on the waiting list. This information provides valuable support for decision-making within hospitals regarding long-term and short-term investments in resource facilities and ensures efficient resource allocation.

For these reasons, sensitivity analysis of surgical department priority and overtime allowances will be carried out. In the next subsection, we will continue performing sensitivity analysis with the aim of further improving the allocation of OR resources.

4.2. Sensitivity Analysis

In this section, a comprehensive sensitivity analysis is performed on two key critical parameters: surgical department priority and overtime resources allowance. OR managers should set these parameters through their strategies, while other parameters such as surgery duration and patient length of stay in ICU and MCU are not under the control of managers. For generalization purposes, this study offers valuable insights to support better decision-making and alignment with hospital goals by proposing four different scenarios of prioritization setting: 1. priority based on clinical need: prioritizing departments based on their severeness; 2. equal access: providing each department with equal right to access to resources in order to ensure fairness; 3. tackling long waiting lists: prioritizing departments with long patient waiting lists; 4. prioritizing cases based on resource requirements (low and high): aiming to optimize resource efficiency and utilization. To assess the impact of overtime allowance on patient waiting time, four variations in overtime allowance are considered, ranging from 10% to 25% compared to the baseline, no overtime. The scenarios examined are as follows: Scenario 1, overtime allowance increased by 10%; Scenario 2, 15%; Scenario 3, 20%; and Scenario 4, 25%. These variations allow us to explore the impact of incremental changes in overtime allowances on patient waiting list clearance time as well as total overtime costs.

As shown in Figure 5, there is no significant difference in patient waiting time in varying prioritization settings across different scenarios.

Figure 6 shows significant differences in total patient throughput across various priority settings. In the base case scenario, 148 patients can be treated per week, while Scenario 2 increases throughput to 151 patients per week. This highlights the trade-off between equity access and equality access. Scenario 3 addresses long backlogs and results in a throughput of 150 patients per week. In Scenarios 4 and 5, prioritizing cases based on resource requirements leads to varying throughputs, with high-resource-intensity departments focusing on treating 153 patients and low-resource-intensity departments focusing on treating 141 patients per week.

Additionally, there is considerable variation in resource utilization among facilities across different scenarios. Equality access, backlog concern, and low-resource intensity scenarios exhibit high variation in utilization rates. In contrast, the equity access and high-resource intensity scenarios show minimal variation in resource utilization across facilities, as shown in Figure 7. These scenarios provide OR managers with valuable insights for informed decision-making. By characterizing each priority scheme into different scenarios, administrators can better understand the implications of various approaches for priority-setting within surgical departments. These insights help align priority-setting practices with institutional objectives and healthcare delivery models. They offer a deeper understanding of the trade-offs and considerations involved in allocating limited OR resources effectively while striving to meet the needs of a diverse patient population and optimize resource efficiency.

In Figure 8, a notable observation arises regarding the impact of different overtime allowances on average waiting times. With a 10% increase in the overtime allowance for resources, the average waiting time shows a significant decrease of approximately 9%, decreasing from 37.7 to 34.5 weeks. Further increases to 15% and 20% in the overtime resource allowance result in smaller decreases from the base case, approximately 13.5% and 17.5%, respectively. Interestingly, when the overtime allowance is increased to 25%, there is no change in average waiting time compared to the 20% overtime allowance; it remains at approximately 1%. This plateau effect occurs because the model balances overtime and waiting costs to minimize total system cost. As the overtime allowance increases, the model initially leverages the additional capacity to reduce patient backlogs more quickly. However, beyond a certain threshold—around the 20% mark—the marginal cost of additional overtime outweighs the marginal benefit of further reducing patient waiting time. At this point, the model has already achieved a near-optimal allocation of resources where waiting time costs are minimized. Increasing overtime further becomes economically inefficient, and thus, the model does not utilize the extra capacity even if it is available. This result highlights a key insight for hospital decision-makers: more overtime does not always lead to better system performance and should be carefully calibrated based on cost trade-offs and capacity constraints.

Table 7. Scenario comparison.

	No. OT	Scenario 1	Scenario 2	Scenario 3	Scenario 4
Average WL clearance time (weeks)	37.7	34.5	32.6	31.1	30.7
% decrease from base case (%)	-	8.55%	13.38%	17.45%	18.50%
% increase in overtime costs from 10%	-	-	136.2%	267.6%	304.4%

presents the relationship between overtime allowances, waiting times, and incurred costs, emphasizing the importance of balancing resource allocation for efficient waiting list management with optimal overtime allowances. Hospital administrators can refer to this guideline to determine whether increasing operations overtime is necessary to reduce average patient waiting times. By carefully considering the trade-offs between resource utilization, waiting times, and incurred costs, administrators can make informed decisions to optimize patient care delivery while ensuring the efficient use of resources.

5. Conclusions

This study proposed a multi-objective optimization-based decision-support framework (DORA) to enhance hospital resource management and support surgical backlog recovery in constrained healthcare environments. The model integrates two decision levels—strategic OR block allocation and tactical patient prioritization—while accounting for resource limitations across ICU/MCU beds, nursing hours, and overtime availability. By aligning hospital and patient-centered objectives, the framework enables efficient resource use and equitable patient access under post-pandemic pressures.

From a managerial perspective, the DORA model offers a practical tool for hospital administrators seeking to optimize OR scheduling under resource constraints. It enables scenario analysis that accounts for ICU/MCU availability, overtime policies, and departmental priorities. This allows decision-makers to proactively reallocate blocks and test various policy options in advance, ensuring preparedness in uncertain or disrupted conditions. Insights from the model—such as the diminishing impact of increased overtime—can guide cost-effective staffing and planning decisions.

In addition to its operational utility, the model’s built-in prioritization mechanism provides flexibility for institutions to tailor decision rules to organizational goals, whether emphasizing urgency, fairness, or cost containment. These features strengthen its applicability as a strategic planning tool for medium-term capacity expansion and sustainable backlog management.

Nevertheless, the model has several limitations. It assumes deterministic demand and fixed surgical durations and does not explicitly model emergency surgeries or real-time disruptions in patient flow. The current solution approach—based on exact optimization—may also face computational limits as the problem scales. These assumptions restrict the model’s responsiveness to real-world uncertainty.

Future work could address these gaps by incorporating stochastic programming, simulation-based modeling, or robust/resilient optimization approaches. Exploring metaheuristic methods may also improve scalability and enable real-time decision support. Expanding the model’s adaptability to different healthcare systems beyond the current context would further enhance its generalizability and policy relevance.