For the simple (uncapacitated) plant location problem for which the coefficient matrix possesses certain properties, we devise a polynomially bounded algorithm by means of which an optimal solution… Expand

Despite the good quality of solutions using heuristics there was no time penalty associated with finding optimal solutions for the problems considered here, suggesting that the major obstacle to their use is making optimal methods accessible to conservation biologists.Expand

Some generalizations of the traveling salesman problem are suggested, leading to problems in which we seek to minimize the summed weight of two or more line-disjoint hamiltonian cycles. A number of… Expand

The 1-median problem on a network asks for a vertex minimizing the sum of the weighted shortest path distances from itself to all other vertices, each associated with a certain positive weight, and an exact algorithm for the resulting ‘pos/neg-weighted’ problem defined on a cactus is devised.Expand

The prime motivation for the present study is a famous problem, allegedly first formulated in 1643 by Fermat, and the so-called Complementary Problem, proposed but incorrectly solved in 1941 by Courant and Robbins, which is extended to cover any combination of positive and negative weights associated with the vertices of a given triangle.Expand

This paper presents a history of a difficult facility layout problem that falls into the category of the Koopmans–Beckmann variant of the quadratic assignment problem (QAP), wherein 30 facilities are… Expand

A highly efficient algorithm (HK) devised by Held and Karp for solving the symmetric traveling-salesman problem was presented at the 7th Mathematical Programming Symposium in 1970 and published in… Expand