The Slab-Design Problem in the Steel Industry

Planners in the steel industry design a set of steel slabs to satisfy the order book subject to constraints on (1) achieving a total designed weight for each order using multiples of an order-specific production size range, (2) minimum and maximum sizes for each slab, and (3) feasible assignments of multiple orders to the same slab. We developed a heuristic solution based on matchings and bin packing that a large steel plant uses daily in mill operations.

[1]  Francis J. Vasko,et al.  A large-scale application of the partial coverage uncapacitated facility location problem , 2003, J. Oper. Res. Soc..

[2]  Ellis Horowitz,et al.  Fundamentals of Data Structures , 1984 .

[3]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .

[4]  Edward G. Coffman,et al.  Approximation algorithms for bin packing: a survey , 1996 .

[5]  Francis J. Vasko,et al.  Consolidating Product Sizes to Minimize Inventory Levels for a Multi-Stage Production and Distribution System , 1993 .

[6]  R. Gomory,et al.  A Linear Programming Approach to the Cutting-Stock Problem , 1961 .

[7]  Francis J. Vasko,et al.  Assigning slabs to orders: an example of appropriate model formulation , 1994 .

[8]  Francis J. Vasko,et al.  A real-time one-dimensional cutting stock algorithm for balanced cutting patterns , 1993, Oper. Res. Lett..

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

[10]  Francis J. Vasko,et al.  Using a Facility Location Algorithm to Determine Optimum Cast Bloom Lengths , 1996 .

[11]  Katsumi Hirayama,et al.  Application of a Hybrid Genetic Algorithm to Slab Design Problem , 1996 .

[12]  Milind Dawande,et al.  The Surplus Inventory Matching Problem in the Process Industry , 2000, Oper. Res..

[13]  Francis J. Vasko,et al.  A hierarchical approach for one-dimensional cutting stock problems in the steel industry that maximizes yield and minimizes overgrading , 1999, Eur. J. Oper. Res..

[14]  Diwakar Gupta,et al.  Managing Increasing Product Variety at Integrated Steel Mills , 2003 .

[15]  David S. Johnson,et al.  Fast Algorithms for Bin Packing , 1974, J. Comput. Syst. Sci..

[16]  John A. McNamara,et al.  A matching approach for replenishing rectangular stock sizes , 2000, J. Oper. Res. Soc..

[17]  D. K. Friesen,et al.  Variable Sized Bin Packing , 1986, SIAM J. Comput..

[18]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[19]  Paolo Toth,et al.  Knapsack Problems: Algorithms and Computer Implementations , 1990 .

[20]  Ralph E. Gomory,et al.  A Linear Programming Approach to the Cutting Stock Problem---Part II , 1963 .

[21]  Paolo Toth,et al.  A Bound and Bound algorithm for the zero-one multiple knapsack problem , 1981, Discret. Appl. Math..

[22]  Michael Randolph Garey,et al.  Approximation algorithms for bin-packing , 1984 .

[23]  Francis J. Vasko,et al.  A Multiple-criteria Approach to Dynamic Cold-ingot Substitution , 1989 .

[24]  Francis J. Vasko,et al.  A Practical Approach for Determining Rectangular Stock Sizes , 1994 .