The multicovering problem

Abstract

The multicovering problem is: Min CX subject to AX ⩾ b, X ϵ {0,}, where A is a matrix whose elements are all zero or one and b is a vector of positive integers: this problem has many applications in scheduling, location and business areas. A variety of industrial, commercial and military contexts give rise to large problems of this kind, frequently at or beyond the limits of current computational tractability. Our research goal is the development of a special-purpose algorithm capable of solving large problems of this kind. Conceptual and computational inputs to the algorithm arise from three sources: from the generalization of computational tools developed for more specific problems (in particular the set covering problem), from the adaptation of general integer programming and combinatorial optimization methods, and from the development within this paper of special techniques designed to take advantage of the structure of the problem studied. Following a description of the algorithm we give some computational results for randomly generated problems.