No abstract

Most optimization-based decision support systems are used repeatedly with only modest changes to input data from scenario to scenario. Unfortunately, optimization (mathematical programming) has a well-deserved reputation for amplifying small input changes into drastically different solutions. A previously optimal solution, or a slight variation of one, may still be nearly optimal in a new scenario and managerially preferable to a dramatically different solution that is mathematically optimal. Mathematical programming models can be stated and solved so that they exhibit varying degrees of persistence with respect to previous values of variables, constraints, or even exogenous considerations. We use case studies to highlight how modeling with persistence has improved managerial acceptance and describe how to incorporate persistence as an intrinsic feature of any optimization model.

The search theory open literature has paid little, if any, attention to the multiple‐searcher, moving‐target search problem. We develop an optimal branch‐and‐bound procedure and six heuristics for solving constrained‐path problems with multiple searchers. Our optimal procedure outperforms existing approaches when used with only a single searcher. For more than one searcher, the time needed to guarantee an optimal solution is prohibitive. Our heuristics represent a wide variety of approaches: One solves partial problems optimally, two use paths based on maximizing the expected number of detections, two are genetic algorithm implementations, and one is local search with random restarts. A heuristic based on the expected number of detections obtains solutions within 2% of the best known for each one‐, two‐, and three‐searcher test problem considered. For one‐ and two‐searcher problems, the same heuristic's solution time is less than that of other heuristics. For three‐searcher problems, a genetic algorithm implementation obtains the best‐known solution in as little as 20% of other heuristic solution times. © 1996 John Wiley & Sons, Inc.

The Chilean Ministry of Education oversees preschool, primary, and secondary education in both urban and rural areas. Many parts of Chile are sparsely populated and there are currently over 4,000 rural schools (almost 38% of all schools in Chile) educating 9.5% of the students in the country. Many of the rural schools are small with only one teacher responsible for instruction of all local students (multigrade schools). The geographical distribution of the rural schools has not been coordinated and this has resulted in unequal utilization of existing schools and some unreasonably long travel distances by students. Good management of the rural schools is fundamental to meeting Chile's goal of providing quality education to its citizens. Seeking to improve the situation, the Ministry of Education ordered a study of the optimal location and size of rural schools with the general goals of reducing the number of lesser quality multigrade schools and reducing student travel distances while maintaining reasonable costs. This paper presents results of this study obtained using an integer linear program that has been embedded in a geographical information system. We present computational results for the entire country. Recommendations include where to open new rural schools as well as where to expand, reduce, close, or leave unchanged existing schools. We show how recommendations are sensitive to key parameters such as the cost of transportation.

Planning United States military procurement commits a significant portion of our nation's wealth and determines our ability to defend ourselves, our allies, and our principles over the long term. Our military pioneered and has long used mathematical optimization to unravel the distinguishing complexities of military capital planning. The succession of mathematical optimization models we present exhibits increasingly detailed features; such embellishments are always needed for real-world, long-term procurement decision models. Two case studies illustrate practical modeling tricks that are useful in helping decision makers decide how to spend about a trillion dollars.