Mathematical optimization to improve cows' artificial insemination services.

Engineering tools and mathematical optimization are applied in this study to plan the work of the agents of the cow artificial insemination service (inseminator) in Israel. Time is crucial in insemination as the chances of conception decline with increasing delay between the start of estrus and insemination. About 1,090 artificial inseminations of cows are performed daily in Israel. They involve 412 farms in 283 villages, and are performed by 29 inseminators; the work plan should balance the work load among the inseminators. To this end, the working time of an inseminator in each village is required. Thus, a model to predict the working time in a village was developed. Subsequently, a mathematical optimization model was designed and solved, which aims to allocate customers to trips and to determine the itinerary of each trip to minimize total distance/time. The main benefits included a 21.4% reduction in total traveling time and a 55% reduction in the difference between the lengths of the longest and shortest working days. Moreover, the longest delay in reaching an estrous cow is reduced from 7.6 to 5.9 h (i.e., by 1.7 h), which may increase the conception ratio by some 7%. In addition, the trade-off between work balance and total traveling time was studied.

Incorporating patient travel times in decisions about size and location of dialysis facilities.

This report demonstrates the power and usefulness of mathematical optimization as a decision support tool in the medical services industry by presenting an application to dialysis service planning. Models to predict the number of dialysis beds in a given region are usually population-based. Dialysis planners and providers have found a need to accommodate sparsely populated regions by making some allowance for patient travel times. A formal approach to incorporating travel times into dialysis planning, based on the formulation and solution of a mixed-integer programming model, is presented. The development of a method for dialysis planning serves as a platform to demonstrate the use of integer programming to support decision making. Major modeling principles are presented; output interpretation and sensitivity analysis are illustrated by examples; and computational requirements are discussed.