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A heuristic solution procedure for set covering is presented that works well for large, relatively dense problems. In addition, a confidence interval is established about the unknown global optimum. Results are presented for 30 large randomly generated problems. INTRODUCTIONThe set covering problem is a combinatorial optimization problem that was shown by Karp [9] to be NP-complete. Since there are many applications of set covering in scheduling, assembly-line balancing, capital investment, switching theory, and information retrieval that involve the solution of large set covering problems, there exists the need for heuristic procedures capable of efficiently obtaining near-optimal solutions to these large problems.In this article we develop a procedure that quickly generates a good solution to large set covering problems, and then we use the interval estimation procedure developed by Golden and Alt [7] on the traveling salesman problem to construct a confidence interval about the unknown global optimum. Finally, we test these procedures on 30 large randomly generated problems. BACKGROUND

In this article, we formally define the GCTP, describe MOD_PRIM in detail, and describe two linearly parallelizable metaheuristics which significantly improve the performance of MOD_PRIM. These metaheuristics are capable of finding near-optimal solutions of very large GCTPs in quadratic time in |V |. We also give empirical results for graphs with up to 25,001 vertices.

In 1984, Bethlehem Steel Corporation installed a new ingot mold stripping facility at its Bethlehem Plant that is capable of handling taller ingots. In order to take maximum advantage of this new facility, we developed a two-phase, computer-based procedure for selecting optimal ingot and internal ingot mold dimensions. Phase I of this procedure generates feasible ingot and internal ingot mold dimensions consistent with both the new stripper's capability and with mill constraints. Phase II then uses a set covering approach to select the optimal ingot and internal ingot mold sizes from among the feasible sizes generated. After analyzing the model, we recommended six new rectangular mold sizes to replace seven existing sizes. To date, implementation of these new ingot and mold sizes is proceeding smoothly and realizing the projected cost reduction benefits.