Optimization of operating room allocation using linear programming techniques

Optimal Allocation of Chemotherapy Schemes for Metastatic Colon Cancer in Colombia

OBJECTIVES

This study aims to determine the optimal proportion for different chemotherapy schemes in patients with metastatic colorectal cancer who have undergone surgical resection in Colombia.

METHODS

A linear programming model was used to quantify the optimal proportion of the chemotherapy schemes that maximize quality-adjusted life-years (QALYs). The model was evaluated in 6 different scenarios using parametric and dynamic optimization with different budget restriction constraints. The results were compared to the current mixture of schemes used in our country.

RESULTS

The results show that 63%, 37%, and 0.8% of the population should receive the FOLFOXIRI scheme (fluorouracil + leucovorin + oxaliplatin + irinotecan), FOLFIRI (irinotecan + leucovorin + fluorouracil), and FOLFIRI plus cetuximab, respectively. With these proportions, 8734 QALYs and universal coverage of the population are obtained. In an optimistic scenario (high QALYs, low costs, and budget of $40 million), the entire population should receive the FOLFIRI scheme. A pessimistic scenario (low QALYs, high costs, and budget of $15 million) would benefit only 46% of the population with the fluorouracil plus leucovorin scheme. In the other 3 scenarios with higher budget constraints, 52%, 69%, and 86% of the population should receive FOLFIRI, respectively. Dynamic optimization revealed that FOLFIRI and FOLFOX (oxaliplatin + leucovorin + fluorouracil) schemes are more likely to generate higher QALYs with lower costs and a limited budget.

CONCLUSIONS

The current use of chemotherapy schemes is not optimal. An increasing proportion of FOLFIRI, FOLFOX, and FOLFOXIRI should be used more often as schemes to treat metastatic colorectal cancer in Colombia.

Constructing operating theatre schedules using partitioned graph colouring techniques

In hospitals, scheduled operations can often be cancelled in large numbers due to the unavailability of beds for post-operation recovery. Operating theatre scheduling is known to be an N P -hard optimisation problem. Previous studies have shown that the correct scheduling of surgical procedures can have a positive impact on the availability of beds in hospital wards, thereby allowing a reduction in number of elective operation cancellations. This study proposes an exact technique based on the partitioned graph colouring problem for constructing optimal master surgery schedules, with the goal of minimising the number of cancellations. The resultant schedules are then simulated in order to measure how well they cope with the stochastic nature of patient arrivals. Our results show that the utilisation of post-operative beds can be increased, whilst the number of cancellations can be decreased, which may ultimately lead to greater patient throughput and reduced waiting times. A scenario-based model has also been employed to integrate the stochastic-nature associated with the bed requirements into the optimisation process. The results indicate that the proposed model can lead to more robust solutions.

Minimizing Health-Compromising Behaviors via School-Based Programs: An Optimization Approach

School health programs are united by their desire to promote health and health-related outcomes among youth. They are also united by the fact that their expected effects are contingent on successful program implementation, which is often impeded by a multitude of real-world barriers. Techniques used in management science may help optimize school-based programs by accounting for implementation barriers. In this exploratory study, we present a detailed example of the first known application of linear programming (LP), which is an optimization technique, to Positive Action (PA). PA is a social emotional and character development program that includes a six-unit, teacher-delivered, classroom curriculum. We specify how we used LP to calculate the optimal levels of program implementation needed to minimize substance use, subject to known levels of implementation barriers (e.g., disruptive behavior, teacher education, teacher attitudes towards character development, school resources, and school safety). We found that LP is a technique that can be applied to data from a school health program. Specifically, we were able to develop a model that calculated the number of lessons that should be taught to minimize a specific health-compromising behavior, given expected levels of predetermined implementation barriers. Our findings from this exploratory study support the utility of applying LP during the program planning and implementation processes of school health programs.

Multi-phase and Integrated Multi-objective Cyclic Operating Room Scheduling Based on an Improved NSGA-ⅡApproach

The operating room (OR) is an important department in a hospital, and the scheduling of surgeries in ORs is a challenging combinatorial optimization problem. In this paper, we address the problem of multiple resource allocation of ORs and propose a surgery scheduling scheme for OR units. To solve this problem, a multi-phase and integrated multi-objective linear programming model is proposed. The first phase of the proposed model is a resource allocation model, which mainly focuses on the allocation of ORs for each surgical specialty (SS). Based on the results of the first phase, the second phase is the cyclic Master Surgical Schedule model, which aims to schedule the surgeries in each SS. The proposed models are solved by the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which was improved. Finally, two numerical experiments based on practical data are provided to verify the effectiveness of the proposed models as well as to evaluate the performance of the improved NSGA-II. Our final results illustrate that our proposed model can provide hospital managers with a series of “optimal” solutions to effectively allocate relevant resources and ORs for surgeries, and they show that the improved NSGA-II has high computational efficiency and is more suitable in solving larger-scale problems.

Costs and Utilization of Operating Rooms in a Public Hospital in Trinidad, West Indies

CONTEXT

A top-down evaluation of the costs of operating rooms (ORs) is not commonly done because it is relevant mostly in a publicly funded system.

OBJECTIVE

This study was conducted to determine the costs and utilization of ORs in a public hospital in Trinidad, West Indies, for two one-year periods using a top-down model.

DESIGN

Quantitative observational study.Main Outcome Measures: A "cost-block" model suggested for evaluation of intensive care unit costs was adapted to suit ORs. Data were obtained from personal interviews, records, and surveys from the appropriate hospital departments. Adjusted OR utilization times also were recorded for both years.

RESULTS

The total annual costs of 4 ORs for the years 2006 and 2009 were approximately US $2.2 and $3.2 million, respectively. Capital expenditure contributed to 70% of the costs, followed by consumables (15%) and medical staff salary (8%). The daily cost of running the ORs was US $6242 in 2006, which rose to $8873 in 2009. The cost of unutilized OR time was approximately US $298,342 in 2006 and was reduced to $198,315 during 2009.

CONCLUSION

The adapted cost-block model was useful to evaluate the costs of ORs in a public hospital in Trinidad and can be used from the government's expenditure perspective. Because the cost of running the ORs was high, efficiency must be improved to minimize waste.

Case mix planning in hospitals: a review and future agenda

The case mix planning problem deals with choosing the ideal composition and volume of patients in a hospital. With many countries having recently changed to systems where hospitals are reimbursed for patients according to their diagnosis, case mix planning has become an important tool in strategic and tactical hospital planning. Selecting patients in such a payment system can have a significant impact on a hospital's revenue. The contribution of this article is to provide the first literature review focusing on the case mix planning problem. We describe the problem, distinguish it from similar planning problems, and evaluate the existing literature with regard to problem structure and managerial impact. Further, we identify gaps in the literature. We hope to foster research in the field of case mix planning, which only lately has received growing attention despite its fundamental economic impact on hospitals.

The operating room case-mix problem under uncertainty and nurses capacity constraints

Surgery is one of the key functions in hospitals; it generates significant revenue and admissions to hospitals. In this paper we address the decision of choosing a case-mix for a surgery department. The objective of this study is to generate an optimal case-mix plan of surgery patients with uncertain surgery operations, which includes uncertainty in surgery durations, length of stay, surgery demand and the availability of nurses. In order to obtain an optimal case-mix plan, a stochastic optimization model is proposed and the sample average approximation method is applied. The proposed model is used to determine the number of surgery cases to be weekly served, the amount of operating rooms' time dedicated to each specialty and the number of ward beds dedicated to each specialty. The optimal case-mix selection criterion is based upon a weighted score taking into account both the waiting list and the historical demand of each patient category. The score aims to maximizing the service level of the operating rooms by increasing the total number of surgery cases that could be served. A computational experiment is presented to demonstrate the performance of the proposed method. The results show that the stochastic model solution outperforms the expected value problem solution. Additional analysis is conducted to study the effect of varying the number of ORs and nurses capacity on the overall ORs' performance.

Allocating operating room block time using historical caseload variability

Operating room (OR) allocation and planning is one of the most important strategic decisions that OR managers face. The number of ORs that a hospital opens depends on the number of blocks that are allocated to the surgical groups, services, or individual surgeons, combined with the amount of open posting time (i.e., first come, first serve posting) that the hospital wants to provide. By allocating too few ORs, a hospital may turn away surgery demand whereas opening too many ORs could prove to be a costly decision. The traditional method of determining block frequency and size considers the average historical surgery demand for each group. However, given that there are penalties to the system for having too much or too little OR time allocated to a group, demand variability should play a role in determining the real OR requirement. In this paper we present an algorithm that allocates block time based on this demand variability, specifically accounting for both over-utilized time (time used beyond the block) and under-utilized time (time unused within the block). This algorithm provides a solution to the situation in which total caseload demand can be accommodated by the total OR resource set, in other words not in a capacity-constrained situation. We have found this scenario to be common among several regional healthcare providers with large OR suites and excess capacity. This algorithm could be used to adjust existing blocks or to assign new blocks to surgeons that did not previously have a block. We also have studied the effect of turnover time on the number of ORs that needs to be allocated. Numerical experiments based on real data from a large health-care provider indicate the opportunity to achieve over 2,900 hours of OR time savings through improved block allocations.

Nonlinear least-squares data fitting in Excel spreadsheets

We describe an intuitive and rapid procedure for analyzing experimental data by nonlinear least-squares fitting (NLSF) in the most widely used spreadsheet program. Experimental data in x/y form and data calculated from a regression equation are inputted and plotted in a Microsoft Excel worksheet, and the sum of squared residuals is computed and minimized using the Solver add-in to obtain the set of parameter values that best describes the experimental data. The confidence of best-fit values is then visualized and assessed in a generally applicable and easily comprehensible way. Every user familiar with the most basic functions of Excel will be able to implement this protocol, without previous experience in data fitting or programming and without additional costs for specialist software. The application of this tool is exemplified using the well-known Michaelis-Menten equation characterizing simple enzyme kinetics. Only slight modifications are required to adapt the protocol to virtually any other kind of dataset or regression equation. The entire protocol takes approximately 1 h.

A Norm Utilisation for Scarce Hospital Resources: Evidence from Operating Rooms in a Dutch University Hospital

BACKGROUND

Utilisation of operating rooms is high on the agenda of hospital managers and researchers. Many efforts in the area of maximising the utilisation have been focussed on finding the holy grail of 100% utilisation. The utilisation that can be realised, however, depends on the patient mix and the willingness to accept the risk of working in overtime.

MATERIALS AND METHODS

This is a mathematical modelling study that investigates the association between the utilisation and the patient mix that is served and the risk of working in overtime. Prospectively, consecutively, and routinely collected data of an operating room department in a Dutch university hospital are used. Basic statistical principles are used to establish the relation between realistic utilisation rates, patient mixes, and accepted risk of overtime.

RESULTS

Accepting a low risk of overtime combined with a complex patient mix results a low utilisation rate. If the accepted risk of overtime is higher and the patient mix is less complex, the utilisation rate that can be reached is closer to 100%.

CONCLUSION

Because of the inherent variability of healthcare processes, the holy grail of 100% utilisation is unlikely to be found. The method proposed in this paper calculates a realistic benchmark utilisation that incorporates the patient mix characteristics and the willingness to accept risk of overtime.

Scheduling the resident 80-hour work week: an operations research algorithm

OBJECTIVE

The resident 80-hour work week requires that programs now schedule duty hours. Typically, scheduling is performed in an empirical "trial-and-error" fashion. However, this is a classic "scheduling" problem from the field of operations research (OR). It is similar to scheduling issues that airlines must face with pilots and planes routing through various airports at various times. The authors hypothesized that an OR approach using iterative computer algorithms could provide a rational scheduling solution.

METHODS

Institution-specific constraints of the residency problem were formulated. A total of 56 residents are rotating through 4 hospitals. Additional constraints were dictated by the Residency Review Committee (RRC) rules or the specific surgical service. For example, at Hospital 1, during the weekday hours between 6 am and 6 pm, there will be a PGY4 or PGY5 and a PGY2 or PGY3 on-duty to cover Service "A." A series of equations and logic statements was generated to satisfy all constraints and requirements. These were restated in the Optimization Programming Language used by the ILOG software suite for solving mixed integer programming problems.

RESULTS

An integer programming solution was generated to this resource-constrained assignment problem. A total of 30,900 variables and 12,443 constraints were required. A total of man-hours of programming were used; computer run-time was 25.9 hours. A weekly schedule was generated for each resident that satisfied the RRC regulations while fulfilling all stated surgical service requirements. Each required between 64 and 80 weekly resident duty hours.

CONCLUSIONS

The authors conclude that OR is a viable approach to schedule resident work hours. This technique is sufficiently robust to accommodate changes in resident numbers, service requirements, and service and hospital rotations.

Linear Programming to Optimize Performance in a Department of Surgery

BACKGROUND

Linear programming is an analytic method that can be used to develop models for health care that optimize distribution of resources through mathematical means.

STUDY DESIGN

The linear programming model contained objective, decision, and constraint elements. The objective was to optimize financial outcomes for both the hospital and physicians in the Department of Surgery. The decision concerns procedure mix or the number of each type of surgical procedure. Constraints apply to resources that are consumed during the course of the patient's surgical encounter.

RESULTS

The optimal solution produced an increase in professional payments of 3.6% and an increase in hospital total margin of 16.1%. This solution favored surgical procedures that require inpatient care; these patients had greater comorbidity, reflected in a higher case-mix index of 3.74 compared to 2.97. Substantial differences were noted in use of general care and ICU days, and in consumption of preoperative, intraoperative, and recovery room time.

CONCLUSIONS

Aligning quality surgical care with optimal financial performance may be assisted by mathematical models such as linear programming.

Tactical decision making for selective expansion of operating room resources incorporating financial criteria and uncertainty in subspecialties' future workloads

We considered the allocation of operating room (OR) time at facilities where the strategic decision had been made to increase the number of ORs. Allocation occurs in two stages: a long-term tactical stage followed by short-term operational stage. Tactical decisions, approximately 1 yr in advance, determine what specialized equipment and expertise will be needed. Tactical decisions are based on estimates of future OR workload for each subspecialty or surgeon. We show that groups of surgeons can be excluded from consideration at this tactical stage (e.g., surgeons who need intensive care beds or those with below average contribution margins per OR hour). Lower and upper limits are estimated for the future demand of OR time by the remaining surgeons. Thus, initial OR allocations can be accomplished with only partial information on future OR workload. Once the new ORs open, operational decision-making based on OR efficiency is used to fill the OR time and adjust staffing. Surgeons who were not allocated additional time at the tactical stage are provided increased OR time through operational adjustments based on their actual workload. In a case study from a tertiary hospital, future demand estimates were needed for only 15% of surgeons, illustrating the practicality of these methods for use in tactical OR allocation decisions.