The Minimum‐Covering/Shortest‐Path Problem*

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Abstract
Due to the inherent multiobjective nature of many network design and routing problems, there has been a tremendous increase in multiobjective network modeling in recent years. In this article we introduce one such model, the minimum‐covering/shortest‐path (MinCSP) problem, and formulate several variations of the problem. The MinCSP problem is a two‐objective path problem: minimization of the total population negatively impacted by the path and minimization of the total path length. A population is considered to be negatively impacted by the path if the path comes within some predetermined distance of the population. Consequently, the MinCSP problem extends the concept of coverage from facility location modeling to network design. Additionally, several existing solution methods for the problem are briefly discussed and potential applications presented.

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