Overtime Costs Research Articles

Incorporating machine learning and optimization techniques for assigning patients to operating rooms by considering fairness policies

Operating rooms (ORs) are key to a hospital's profitability, and increasing their benefits helps decrease surgical costs, minimize patient waiting times, and boost the number of patients admitted for surgery. This study presents a mixed-integer linear programming (MILP) model to address the issue of treating inpatients in operating rooms waiting for admission to the referral department. Moreover, it proposes a practical algorithm that minimizes overtime costs in operating rooms and increases patient satisfaction. Our model uses an integrated machine learning - tabu search (ML-TS) method. The proposed model uses differential ML and heuristic rules to achieve enhanced performance and scalability in solving complex optimization problems. A fairness policy is implemented, combined with an optimization method, to guide patient prioritization. This approach considers factors like urgency, waiting times, or specific patient needs and helps determine the order in which patients are scheduled for surgery. The outcomes imply that patient adaptability has led to savings ranging from 50% to 65% per surgery. Additionally, the Machine Learning-Tabu Search (ML-TS) algorithm has increased performance by about 35%. These algorithms also let the OR manager define the size of the uncertainty set and regulate overtime costs while accommodating surgeons' preferences as managerial implications insight. It adeptly navigates the solution space, identifies feasible solutions, and accelerates convergence.

STRATEGIC OVERTIME IMPLEMENTATION: ASSESSING CRASH TIME, CRASH COST, AND COST SLOPE IN THE CONSTRUCTION OF KADIRI UNIVERSITY'S 4-STORY BUILDING

The lecture building is an important building which is the center of academic activities where educational activities are carried out. Currently, the construction of a four-story lecture building at Kadiri University is experiencing significant project delays with a deviation of 5.64% from the plan. Crash analysis can be carried out to speed up the duration of the project so that it can be completed on time with additional working hours. This research aims to determine crash time, crash costs, and cost slope for the application of overtime on the 4-story building construction project at Kadiri University. A quantitative and case study approach was used with data collected through observation, interviews, and analysis of project documents. Critical Path Method (CPM) analysis is carried out using Microsoft Project software to identify work that is on the critical path. Crashing is done by calculating crash time, crash cost, and cost slope. The research results show that applying 1 hour of overtime can speed up the project by 12 working days, with an additional cost of IDR 24,488,758. Cost slope analysis shows additional overtime costs of IDR 12,244,379. This research shows that the application of measurable overtime and crashing analysis can effectively overcome project delays in the context of building educational facilities.

Large Scale Customer Points in Genetic Algorithms

Aiming at the path optimization problem of pharmaceutical green logistics distribution, a green logistics path optimization model is designed considering constraints such as time window limitation and vehicle capacity, with the optimization objective of minimizing the sum of vehicle transportation cost, overtime cost and green cost, and the constructed model is solved by using genetic algorithm. The constructed model and designed algorithm are verified by actual distribution data. The example experiments show that the genetic algorithm has better solution quality, higher efficiency and more stable results in solving the vehicle path problem at large-scale customer locations. The research results not only expand the vehicle path problem, but also provide decision-making reference for the distribution optimization of related express logistics enterprises.

Blockchain design for optimal joint production and maintenance over multiple periods for oil-filling production lines

Joint maintenance and production planning result in enhanced system efficiency and a significant reduction in expensive costs. Therefore, this research proposed an integrated blockchain design of two optimization models for the joint scheduling and sequencing of production orders and maintenance jobs over multiple periods with probabilistic and stochastic parameters for the oil-filling process. In the scheduling model, the objective function was to minimize total production and maintenance costs. Further, the sequencing model aimed to minimize the total overtime cost and the sum start times of jobs and orders. The proposed models were implemented on five production lines of five-liter lube oil bottles. Results showed that the developed optimization models effectively achieved concurrent production and maintenance planning at minimal total cost. In practice, this results in effective resource utilization, and saving costly production and maintenance costs. In conclusion, the developed blockchain design is valuable in developing, managing, and controlling optimal joint production and maintenance planning of oil-filling production lines.

Dynamic Home Care Routing and Scheduling with Uncertain Number of Visits per Referral

Despite the rapid growth of the home care industry, research on the scheduling and routing of home care visits in the presence of uncertainty is still limited. This paper investigates a dynamic version of this problem in which the number of referrals and their required number of visits are uncertain. We develop a Markov decision process (MDP) model for the single-nurse problem to minimize the expected weighted sum of the rejection, diversion, overtime, and travel time costs. Because optimally solving the MDP is intractable, we employ an approximate linear program (ALP) to obtain a feasible policy. The typical ALP approach can only solve very small-scale instances of the problem. We derive an intuitively explainable closed-form solution for the optimal ALP parameters in a special case of the problem. Inspired by this form, we provide two heuristic reduction techniques for the ALP model in the general problem to solve large-scale instances in an acceptable time. Numerical results show that the ALP policy outperforms a myopic policy that reflects current practice, and is better than a scenario-based policy in most instances considered. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2018-05225 and RGPIN-2020-210524] and by the Telfer School of Management SMRG Postdoctoral Research Fellowship Support [Grant 2020]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2023.0120 .

Implementasi Metode OMAX Dalam Meningkatkan Produktivitas Kinerja Perusahaan Pada UKM Tas Kulit

Measuring the company level of productivity performance is a very important thing to do to see and evaluate achievements and improvements to productivity levels that are not yet optimal. This case study was taken from the leather bag UKM which is currently experiencing a decline in productivity during the 2020 period. With the increase in working hours, the company must increase workers' overtime costs. In this research, the method used to measure the level of company productivity is the objective matrix or OMAX method and this research refers to the OMAX steps, namely determining productivity criteria on the production line, determining weights, determining levels on the objective matrix, calculating the productivity index, and productivity analysis with a traffic light system. The research results show that the average value of overall productivity in 2020 is 4,388 The highest productivity index was achieved in August amounting to 67,01%. From the traffic light system, it is known that the worst indicator of productivity is the defect factor, so improvements need to be made regarding this.

Literature Review of the Effectiveness of Using Aggregate Planing in the Msme Industry

This research investigates the effectiveness of using Aggregate Planning in the Micro, Small and Medium Enterprises (MSME) industry. Through a literature review using national and international scientific journal articles from 2018-2023, this research identified three main approaches to aggregate planning: Level Strategy, Chase Strategy, and Mixed Strategy. Level Strategy maintains production levels at a constant level, using inventory as a buffer to deal with fluctuations in demand. Chase Strategy adjusts production directly to market demand, minimizing inventory and carrying costs. Mixed Strategy, a combination of Chase Strategy and Level Strategy, combines the flexibility of Chase Strategy with the stability of Level Strategy to optimize production and inventory costs. This research describes how MSMEs in the children's clothing industry implement these three strategies. In Level Strategy, production is kept at a constant level, using inventory as a buffer. In the Chase Strategy, production is matched directly to demand, reducing inventory and carrying costs. In Mixed Strategy, the combination of strategies allows flexible response to demand fluctuations, minimizing inventory costs. The calculation results show that using Mixed Strategy allows companies to optimize production, reduce inventory costs, and respond quickly to variations in market demand. The total costs during this period were the result of production costs, inventory costs, overtime costs, and worker salaries, reaching a total of IDR 124,900,000. This research provides insight into how MSMEs can utilize aggregate planning with various strategies to increase their operational efficiency and flexibility in facing market dynamics.

Wasserstein distributionally robust surgery scheduling with elective and emergency patients

We study a surgery scheduling problem with regard to both elective and emergency patients, where surgery durations are uncertain and emergency patients arrive dynamically. The problem determines, at the beginning of a day, how many operating rooms to open and how to allocate elective and (possibly dummy) emergency patients into them to minimize the operating room opening and expected overtime costs. Incorporating (possibly dummy) emergency patients provides a novel approach for reserving emergency capacity. We propose a robust data-driven model that allows for distributional ambiguity via the Wasserstein metric. We derive its mixed-integer conic reformulation and develop an exact branch-and-cut algorithm. We also uncover our model’s connections to its sample average approximation counterpart. Since emergency patients necessitate adequate and timely treatments, we formalize a rolling horizon scheme to dynamically reschedule and prioritize the emergency patients upon their arrivals. Our scheme handles practical features such as dynamic emergency arrivals and uncertain service duration. We perform simulation studies based on real data and numerical experiments show that our method outperforms the benchmark ones in a variety of performance indicators.

Leveraging machine learning and prescriptive analytics to improve operating room throughput.

Successful days are defined as days when four cases were completed before 3:45pm, and overtime hours are defined as time spent after 3:45pm. Based on these definitions and the 460 unsuccessful days isolated from the dataset, 465 hours, 22 minutes, and 30 seconds total overtime hours were calculated. To reduce the increasing wait lists for hip and knee surgeries, we aim to verify whether it is possible to add a 5th surgery, to the typical 4 arthroplasty surgery per day schedule, without adding extra overtime hours and cost at our clinical institution. To predict 5th cases, 301 successful days were isolated and used to fit linear regression models for each individual day. After using the models' predictions, it was determined that increasing performance to a 77% success rate can lead to approximately 35 extra cases per year, while performing optimally at a 100% success rate can translate to 56 extra cases per year at no extra cost. Overall, this shows the extent of resources wasted by overtime costs, and the potential for their use in reducing long wait times. Future work can explore optimal staffing procedures to account for these extra cases.

Multiple operation theatre scheduling for mitigating the disturbance caused by emergency patients

Scheduling emergency patients is a problem that most hospitals struggle to solve without disturbing elective surgery patients' schedules. The present work undertakes this problem and considers scheduling elective patients surgeries in multiple operation theatres to mitigate the possible disturbance caused by emergency patient arrivals. The resultant problem has been termed as multiple operation theatre problems with total expected disturbance (MOTED). The number of elective surgeries and their corresponding surgery times are known and given in advance. However, emergency patient arrivals are stochastic in nature, which is tackled through scenario-generation techniques. The model assumes that emergency case scenarios can be predicted from historical data, and determines the sequence of elective patients in a multiple operation theatre such that the sum of the total expected disturbance (TED) caused by emergency patients and the total completion time of elective surgeries is minimized. The disturbance minimization increases the satisfaction level of patients, physicians and other medical staff, and indirectly reduces the overtime costs. The work provides an optimal algorithm for the MOTED problem with a single-operation theatre. Three heuristics and two metaheuristics have been proposed to solve the complete MOTED problem. The metaheuristic involves particle swarm optimization (PSO) and ant colony optimization (ACO). An extensive numerical experiment is performed using 48 randomly generated problem instances.

Optimization models for patient and technician scheduling in hemodialysis centers.

Patient and technician scheduling problem in hemodialysis centers presents a unique setting in healthcare operations as (1) unlike other healthcare problems, dialysis appointments have a steady state and the treatment times are determined in advance of the appointments, and (2) once the appointments are set, technicians will have to be assigned to two types of jobs per appointment: putting on and taking off patients (connecting to and disconnecting from dialysis machines). In this study, we design a mixed-integer programming model to minimize technicians' operating costs (regular and overtime costs) at large-scale hemodialysis centers. As this formulation proves to be computationally challenging to solve, we propose a novel reformulation of the problem as a discrete-time assignment model and prove that the two formulations are equivalent under a specific condition. We then simulate instances based on the data from our collaborating hemodialysis center to evaluate the performance of our proposed formulations. We compare our results to the current scheduling policy at the center. In our numerical analysis, we reduced the technician operating costs by 17% on average (up to 49%) compared to the current practice. We further conduct a post-optimality analysis and develop a predictive model that can estimate the number of required technicians based on the center's attributes and patients' input variables. Our predictive model reveals that the optimal number of technicians is strongly related to the time flexibility of patients and their dialysis times. Our findings can help clinic managers at hemodialysis centers to accurately estimate the technician requirements.

Operating room scheduling by emphasising human factors and dynamic decision-making styles: a constraint programming method

ABSTRACT As the most crucial component of a hospital, the operating room (OR) is the primary source of revenue generation and expenditures. The hospital’s overall performance will be enhanced if this ward’s scheduling is accurate. This study investigates a multi-objective mixed-integer programming model for daily OR scheduling of inpatient surgeries. A major consideration is the setup time (e.g. cleaning, sterilising, and preparing the necessary OR equipment) for the OR when commencing additional surgeries in the same OR. The surgical staff’s performance, interaction quality, and compatibility level play a significant role in the surgery’s quality, success, and safety. As individuals’ decision-making styles vary depending on the situation, one of the objectives increases the compatibility of surgical team members by considering their primary and backup decision-making styles. Another objective is to maximise the efficiency of the surgical team. To this end, this paper employs the TOPSIS method to calculate each person’s efficiency level. The final objective is to minimise OR costs (including the opening and overtime cost of OR and wait time cost for each person). To address problem’s computational complexity, this paper develops a constraint programming (CP) method, and also a novel hybrid mixed-integer linear programming-CP method to solve the real-world instances.

Design of Using Activity Based Budgeting Methods for Controlling Employee Overtime Costs

This study aims to design and propose using overtime budgets in companies. This type of research is descriptive exploratory, and the research object is data related to employee overtime in July-December 2021. The financing method used is time-driven activity-based costing (TDABC). This study suggests that companies follow up on departments with over-capacity status to evaluate employee activities during overtime so that it does not affect company performance. The application of the activity-based budgeting method can increase the effectiveness of employee overtime costs because it can prove that there are savings in overtime costs and can increase profits. So that the ABB method can control the overtime budget more efficiently and better. The ABB method can control employee overtime budgets more efficiently. The ABB method can be proposed to companies to control their employees' overtime costs. This research has implications for identifying the need for overtime, purchasing efficient budget allocations, evaluating the impact on financial companies.

An Outer Approximation Method for Scheduling Elective Surgeries with Sequence Dependent Setup Times to Multiple Operating Rooms

In this paper, operating room planning and scheduling problems have been studied. In operating room planning, the allocation of patients to operating rooms and their sequencing are critical in determining the performance of operating rooms. In this paper, three surgery scheduling decisions are considered, including the number of operating rooms to open, the allocation of surgeries to operating rooms, and the sequencing of surgeries in allocated operating rooms. All the surgeries under consideration are elective, and surgery durations are considered deterministic. Further, it is considered that the surgeries have different specialties, and each operating room can accommodate a particular specialty of surgeries, i.e., heterogeneous operating rooms are considered in the current study. Before performing a surgery, setup time is required for operating room turnover and sterilization, and it is considered sequence dependent. A mixed integer nonlinear programming (MINLP) model is developed to minimize the overtime costs of operating rooms for allocation and surgery sequencing with sequence dependent setup times. An outer approximation (OA) method is proposed to solve the problem near optimally. Experiments are conducted to compare the performance of the proposed OA method with the standard mixed integer nonlinear programming model. Computational results show the efficiency of the proposed OA method. Later, a case data from a case hospital is collected and a case study is solved.

Joint patient selection and scheduling under no‐shows: Theory and application in proton therapy

We study how to admit and schedule heterogeneous patients by using simple, interpretable, yet effective policies when capacity is scarce, no‐show behavior is patient‐ and time‐dependent, service duration and reward are deterministic but patient‐dependent, and overtime is costly. Our work is motivated by the aforementioned operational challenges that typically face adopters of new technologies in the healthcare sector. We anchor our study on a partnership with the proton therapy center of Massachusetts General Hospital (MGH), which offers a new radiation technology for cancer patients. We formulate the problem as a nonlinear integer optimization problem. However, as the solution to this formulation lacks both tractability and interpretability, to be relevant to practice, we limit our study to simple and interpretable policies. In particular, we propose a simple index‐based rule and derive analytical performance guarantees for it. We also calibrate our model using empirical data from our partner hospital, and conduct a series of experiments to evaluate the performance of our proposed policy under practical circumstances. The analytical performance guarantees and our numerical experiments demonstrate (a) the strong performance of the proposed policies, and (b) their robustness to various practical considerations (e.g., to potential misspecification of no‐show probabilities). Our results show that our proposed policy, despite being a simple and interpretable index‐based rule, is capable of improving performance by about 20% at an organization such as MGH, and of delivering results that are not far from being optimal across a wide range of parameters that might vary between organizations. This suggests that the proposed policy can be viewed as an effective “one‐fits‐all” capacity allocation rule that can be used in a variety of environments in which operational challenges such as no‐shows and overtime costs need to be navigated using simple and interpretable rules.

PENJADWALAN PERAWAT BERDASARKAN MINIMASI PELANGGARAN PERATURAN DAN MINIMASI BIAYA LEMBUR

The high overtime cost for nurses from Manual Scheduling, in the inpatient unit at ABC Hospital, where the overtime cost was Rp.10,409,910,-, much the difference number working hours between each nurses and many violations of hard constraint. So, it is necessary to make improvements to the scheduling. This study developed the scheduling whose goal is to minimize violations of regulations and minimize overtime costs by Goal Programming (GP). Mathematical formulation for both objectives were solved by LINGO 18.0. The difference in the number of working hours between the highest working hours and the least working hours for nurses who are not on leave, on Manual Scheduling, The Minimizing Regulatory Violations Scheduling and The Minimizing Overtime Costs Scheduling were 53, 0 and 1 hour(s) respectively. The highest number of working hours was 221 hours in Manual Scheduling, while the least number working hours was 175 hours in Minimizing Overtime Scheduling. If the policy in scheduling wanted to minimize violations, using the result of Scheduling for Minimizing Violation of the regulations there were 177 violations and overtime costs was Rp. 3.652.600,- reduced by 64.91%. Meanwhile, if the Hospital wanted to minimize overtime costs, using the result of Scheduling Minimizing Overtime Costs, there were 246 violations and overtime costs was Rp.104,360,- reduced by 99.0%.In the future, the hospital must establish a policy in terms of scheduling, whether the aim is to minimize violations of regulations or minimize overtime costs, so that based on this policy, the mathematical formulation can be determined.

A Proposed eFSR Blockchain System for Optimal Planning of Facility Services with Probabilistic Arrivals and Stochastic Service Durations

This research developed a framework for electronic planning and management of facility services utilizing blockchain technology. In this framework, an electronic Facility Service Record (eFSR) in blockchain form was developed to manage and control service orders received by its main service center from university facilities via an electronic system. Mathematical models were formulated to determine the optimal schedule and sequence of facility services under probabilistic service order arrivals and stochastic service durations. Each task of a facility service is treated as a block. The scheduling model then assigned blocks (service tasks) to skilled technicians on each scheduling period at a minimal total cost of delay, undertime, and overtime costs, while the sequencing model determined the start and finish times of each block during the planning period. The optimal information of blocks was then confirmed and shared through an electronic network among all relevant facilities and the service center. The developed framework was implemented in university facilities to plan and manage 47 service orders for a total of 140 tasks over a period of twelve days. The results showed that the proposed eFSR is effective in managing optimal service tasks and efficient in improving the utilization and performance of the service center resources. In conclusion, the proposed eFSR with the optimal facility service planning provides real-time assistance and decentralized technology to facilities managers when planning service tasks over multiple periods. These advantages will result in the effective management of facilities and a considerable savings in maintenance resources.

BLOCKCHAIN OF OPTIMAL MULTIPLE CONSTRUCTION PROJECTS PLANNING UNDER PROBABILISTIC ARRIVAL AND STOCHASTIC DURATIONS

With the rapid development of projects, firms are facing challenges in planning and controlling complex multiple construction projects. This research, therefore, aims at developing blockchain of optimal scheduling and sequencing of multiple construction projects under probabilistic arrival and stochastic durations. Each project task was considered as a block. Then, a framework for electronic project recording (EPR) system was developed. The EPRs are records for project tasks that make information available directly and securely to authorized users. In this framework, two optimization models were developed for scheduling and sequencing project blocks. The scheduling model aims to assign project tasks to available resources at minimal total cost and maximal the number of assigned project tasks. On the other hand, the sequencing model seeks to determine the start time of block execution while minimizing delay costs and minimizing the sum of task’s start times. The project arrival date and the task’s execution duration were assumed probabilistic and stochastic (normally distributed), respectively. The developed EPR system was implemented on a real case study of five projects with total of 121 tasks. Further, the system was developed when the task’s execution duration follows the Program Evaluation and Review Technique (PERT) model with four replications. The project costs (idle time and overtime costs) at optimal plan were then compared between the task’s execution duration normally distributed and PERT modelled. The results revealed negligible differences between project costs and slight changes in the sequence of project activities. Consequently, both distributions can be used interchangeably to model the task’s execution duration. Furthermore, the project costs were also compared between four solution replications and were found very close, which indicates the robustness of model solutions to random generation of task’s execution duration at both models. In conclusion, the developed EPR framework including the optimization models provided an effective planning and monitoring of construction projects that can be used to make decisions through project progress and efficient sharing of project resources at minimal idle and overtime costs. Future research considers developing a Blockchain of optimal maintenance planning.

Elective surgery scheduling under uncertainty in demand for intensive care unit and inpatient beds during epidemic outbreaks

Amid the epidemic outbreaks such as COVID-19, a large number of patients occupy inpatient and intensive care unit (ICU) beds, thereby making the availability of beds uncertain and scarce. Thus, elective surgery scheduling not only needs to deal with the uncertainty of the surgery duration and length of stay in the ward, but also the uncertainty in demand for ICU and inpatient beds. We model this surgery scheduling problem with uncertainty and propose an effective algorithm that minimizes the operating room overtime cost, bed shortage cost, and patient waiting cost. Our model is developed using fuzzy sets whereas the proposed algorithm is based on the differential evolution algorithm and heuristic rules. We set up experiments based on data and expert experience respectively. A comparison between the fuzzy model and the crisp (non-fuzzy) model proves the usefulness of the fuzzy model when the data is not sufficient or available. We further compare the proposed model and algorithm with several extant models and algorithms, and demonstrate the computational efficacy, robustness, and adaptability of the proposed framework.

A novel and efficient exact technique for integrated staffing, assignment, routing, and scheduling of home care services under uncertainty

We model and solve integrated multi-period staffing, assignment, routing, and scheduling of caregivers for home care services and obtain insights for the case under uncertainty. The goal is to construct a weekly schedule that adheres to related operational considerations and determines optimal staffing of caregivers by minimizing caregivers’ fixed- and overtime costs. For tractability, we incorporate a priori-generated visit pattern—an existing practical approach that deals effectively with hard assignment decisions. First, we propose a novel mixed-integer program (MIP) for the nominal (deterministic) problem. We then incorporate uncertainty in service and travel times and develop a robust counterpart by hybridizing interval and polyhedral uncertainty sets. Second, we show that there is a special mathematical structure within the model that allows us to develop a novel logic-based Benders branching-decomposition algorithm that systematically delays the resolution of difficult routing/ scheduling problems and efficiently solves both the nominal and robust MIP models, i.e., our solution approach for the deterministic case allowed us to solve the robust model. Using a benchmark and newly generated instances from the literature, we show that CPLEX can solve our nominal model with average optimality gap of 56%. On the other hand, our new exact technique can solve our nominal model to an average optimality gap of 5%. Third, we provide practical insights into (i) the price of robustness and (ii) the impacts of nurse flexibility and overtime. The average total cost does not increase beyond 18% than the nominal solution and the cost-savings of nurse flexibility is about 19% on average and higher than overtime’s. We also demonstrate that nurse flexibility impact is high and comparable in both cases, deterministic and stochastic.