Computation of a generalized set covering problem

Abstract

This paper is concerned with an algorithm for the Generalized Covering Problem. This paper shows a procedure to yield a Generalized Covering Problem form a General 0-1 integer program and shows that a Generalized Covering Problem can be transformed to a Pure Set Covering Problem. This transformation allows us to use a Set Covering Problem algorithm for the computation of a Generalized Covering Problem. The special structure of a Generalized Covering Problem permits us a rather efficient, yet simple solution procedure that is basically a Branch and Bound type algorithm coupled with linear programming and a suboptimization technique. The algorithm``s originality stems from an efficient suboptimization procedure which heuristically constructs integer solutions from the solutions to the relaxed Linear Programming problem. Also, this algorithm uses Dual Simplex Algorithm to solve the nested sequence of Linear Programming problems. Finally, this paper shows that our algorithm could be used to solve the nested sequence of Generalized Set Covering Problems so as to solve a general 0-1 integer program.