A set covering approach to metallurgical grade assignment

Abstract Early in 1986 Bethlehem Steel Corporation installed two continuous slab caster machines to modernize the steelmaking facilities at two of its major plants. The installation of this equipment, at a total cost of about half a billion dollars, required accompanying production planning and control systems (PPC) in order to function efficiently. The PPC module responsible for assigning metallurgical grades to customer orders uses a minimum cardinality set covering approach which not only minimizes the number of metallurgical grades required to satisfy a given collection of customer orders, but also is able to ‘show preference’ to priority orders. The algorithm, Optsol is used in a two-pass mode to quickly generate very good solutions to these large scale (up to 1000 zero-one variables and 2500 constraints) problems. When compared to the traditional method of grade assignment, this approach has the potential to significantly improve caster productivity and to reduce semi-finished inventory.

[1]  B. M. Khumawala.  An Efficient Branch and Bound Algorithm for the Warehouse Location Problem , 1972 .

[2]  G. Nemhauser,et al.  Exceptional Paper—Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms , 1977 .

[3]  Donald Erlenkotter,et al.  A Dual-Based Procedure for Uncapacitated Facility Location , 1978, Oper. Res..

[4]  S. Lin,et al.  Heuristic Programming as an Aid to Network Design , 1975, Networks.

[5]  R. E. Marsten.  An Algorithm for Large Set Partitioning Problems , 1974 .

[6]  Kurt Spielberg,et al.  Set Covering by Single-Branch Enumeration with Linear-Programming Subproblems , 1971, Oper. Res..

[7]  George L. Nemhauser,et al.  Note--On "Location of Bank Accounts to Optimize Float: An Analytic Study of Exact and Approximate Algorithms" , 1979 .

[8]  Lazaros P. Mavrides.  An Indirect Method for the Generalized k-Median Problem Applied to Lock-Box Location , 1979 .

[9]  F. J. Vasko,et al.  Hybrid heuristics for minimum cardinality set covering problems , 1986 .

[10]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[11]  L. Schrage.  Implicit representation of variable upper bounds in linear programming , 1975 .

[12]  Andrew C. Ho,et al.  Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study , 1980 .

[13]  Robert E. Markland,et al.  Theory and Application of an Optimizing Procedure for Lock Box Location Analysis , 1981 .

[14]  Javier Etcheberry,et al.  The Set-Covering Problem: A New Implicit Enumeration Algorithm , 1977, Oper. Res..

[15]  Francis J. Vasko,et al.  Using a facility location algorithm to solve large set covering problems , 1984 .

[16]  Francis J. Vasko,et al.  A Dynamic Programming Model for Determining Continuous-Caster Configurations , 1982 .

[17]  Harvey M. Salkin,et al.  Set Covering by an All Integer Algorithm: Computational Experience , 1973, JACM.

[18]  Francis J. Vasko,et al.  Optimal Selection of Ingot Sizes Via Set Covering , 1987, Oper. Res..

[19]  Roy E. Marsten,et al.  Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications , 1981, Networks.

[20]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[21]  R. Nauss,et al.  Optimization of Bank Transit Check Clearing Operations , 1985 .

[22]  Edward K. Baker,et al.  Efficient heuristic algorithms for the weighted set covering problem , 1981, Comput. Oper. Res..