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The vector assignment p-median problem (VAPMP) and the ordered p-median problem (OMP) are important extensions of the classic p-median problem. The VAPMP extends the p-median problem by allowing assignment of a demand to multiple facilities, and a wide variety of multi-assignment and backup location problems are special cases of this problem. The OMP optimizes a weighted sum of service distances according to their relative ranks among all demands. The OMP is well known as it represents a generalization of both the p-median and the p-center problems. In this article, a new model is developed which extends both the VAPMP and OMP problems. In addition, beyond median, center, and vector assignment, this new model can resolve problems where the system objective involves maximizing distance. The new model also gives rise to meaningful special-case problems, such as a “reliable p-center” problem. Different integer linear programming (ILP) formulations of the new problem are presented and tested. It is demonstrated that an efficient formulation for a special case of the VAOMP problem can solve medium sized problems optimally in a reasonable amount of time. [ABSTRACT FROM PUBLISHER]

In the classic p-median problem, it is assumed that each point of demand will be served by his or her closest located facility. The p-median problem can be thought of as a ‘‘single-level’’ allocation and location problem, as all demand at a specific location is assigned as a whole unit to the closest facility. In some service protocols, demand assignment has been defined as ‘‘multilevel’’ where each point of demand may be served a certain percentage of the time by the closest facility, a certain percentage of the time by the second closest facility, and so on. This article deals with the case in which there is a need for ‘‘explicit’’ closest assignment (ECA) constraints. The authors review past location modeling work that involves single-level ECA constraints as well as specific constraint constructs that have been proposed to ensure single-level closest assignment. They then show how each of the earlier proposed ECA constructs can be generalized for the ‘‘multilevel’’ case. Finally, the authors provide computational experience using these generalized ECA constructs for a novel multilevel facility interdiction problem introduced in this article. Altogether, this article proposes both a new set of constraint structures that can be used in location models involving multilevel assignment as well as a new facility interdiction model that can be used to optimize worst case levels of facility disruption. [ABSTRACT FROM AUTHOR]