A Spoonful of Math Helps the Medicine Go Down: An Illustration of How Healthcare can Benefit from Mathematical Modeling and Analysis

<p>Abstract</p> <p>Objectives</p> <p>A recent joint report from the Institute of Medicine and the National Academy of Engineering, highlights the benefits of--indeed, the need for--mathematical analysis of healthcare delivery. Tools for such analysis have been developed over decades by researchers in Operations Research (OR). An OR perspective typically frames a complex problem in terms of its essential mathematical structure. This article illustrates the use and value of the tools of operations research in healthcare. It reviews one OR tool, queueing theory, and provides an illustration involving a hypothetical drug treatment facility.</p> <p>Method</p> <p>Queueing Theory (QT) is the study of waiting lines. The theory is useful in that it provides solutions to problems of waiting and its relationship to key characteristics of healthcare systems. More generally, it illustrates the strengths of modeling in healthcare and service delivery.</p> <p>Queueing theory offers insights that initially may be hidden. For example, a queueing model allows one to incorporate randomness, which is inherent in the actual system, into the mathematical analysis. As a result of this randomness, these systems often perform much worse than one might have guessed based on deterministic conditions. Poor performance is reflected in longer lines, longer waits, and lower levels of server utilization.</p> <p>As an illustration, we specify a queueing model of a representative drug treatment facility. The analysis of this model provides mathematical expressions for some of the key performance measures, such as average waiting time for admission.</p> <p>Results</p> <p>We calculate average occupancy in the facility and its relationship to system characteristics. For example, when the facility has 28 beds, the average wait for admission is 4 days. We also explore the relationship between arrival rate at the facility, the capacity of the facility, and waiting times.</p> <p>Conclusions</p> <p>One key aspect of the healthcare system is its complexity, and policy makers want to design and reform the system in a way that affects competing goals. OR methodologies, particularly queueing theory, can be very useful in gaining deeper understanding of this complexity and exploring the potential effects of proposed changes on the system without making any actual changes.</p

Capacity management of nursing staff as a vehicle for organizational improvement

<p>Abstract</p> <p>Background</p> <p>Capacity management systems create insight into required resources like staff and equipment. For inpatient hospital care, capacity management requires information on beds and nursing staff capacity, on a daily as well as annual basis. This paper presents a comprehensive capacity model that gives insight into required nursing staff capacity and opportunities to improve capacity utilization on a ward level.</p> <p>Methods</p> <p>A capacity model was developed to calculate required nursing staff capacity. The model used historical bed utilization, nurse-patient ratios, and parameters concerning contract hours to calculate beds and nursing staff needed per shift and the number of nurses needed on an annual basis in a ward. The model was applied to three different capacity management problems on three separate groups of hospital wards. The problems entailed operational, tactical, and strategic management issues: optimizing working processes on pediatric wards, predicting the consequences of reducing length of stay on nursing staff required on a cardiology ward, and calculating the nursing staff consequences of merging two internal medicine wards.</p> <p>Results</p> <p>It was possible to build a model based on easily available data that calculate the nursing staff capacity needed daily and annually and that accommodate organizational improvements. Organizational improvement processes were initiated in three different groups of wards. For two pediatric wards, the most important improvements were found to be improving working processes so that the agreed nurse-patient ratios could be attained. In the second case, for a cardiology ward, what-if analyses with the model showed that workload could be substantially lowered by reducing length of stay. The third case demonstrated the possible savings in capacity that could be achieved by merging two small internal medicine wards.</p> <p>Conclusion</p> <p>A comprehensive capacity model was developed and successfully applied to support capacity decisions on operational, tactical, and strategic levels. It appeared to be a useful tool for supporting discussions between wards and hospital management by giving objective and quantitative insight into staff and bed requirements. Moreover, the model was applied to initiate organizational improvements, which resulted in more efficient capacity utilization.</p

A gradient search and column generation approach for the build-pack planning problem with approved vendor matrices and stochastic demand

10.1080/00207540903049381International Journal of Production Research48195783-5807IJPR