Computational Viability of a Constraint Aggregation Scheme for Integer Linear Programming Problems

Article Abstract:

The results of a computational evaluation of two constraint aggregation approaches for solving integer linear programs is presented. In some applications, particularly set partitioning problems, the schemes can aggregate significantly different number of constraints. The implementation of these approaches using both single and multiple precision arithmetic is discussed. It is shown that in practical implementation and evaluation of an aggregation scheme, the degree of difficulty encountered in solving the equality constrained knapsack problem is crucial. The conclusion is that the aggregation approach has limited value for solving general integer linear programs, but may be useful in developing a heuristic algorithm for the set partitioning problem. A table shows results from solving equality constrained knapsack problems resulting from ILPS.

Algorithms, Algorithm, Sets, Heuristic Methods, NP-Complete Problems

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An Integer Programming Procedure for Assembly System Design Problems

Article Abstract:

Recent advances in robot technology have revolutionized the concept of manufacturing and assembly systems. These advances have created the need for new mathematical models to reflect the capabilities of the new technologies. The system design problem is addressed by defining a workstation selection and task assignment problem for automated assembly systems. This problem is formulated as a zero-one integer program. A procedure for seeking lower and upper bounds to the optimal value of the integer program is described. The upper bound provides a feasible solution to the integer formulation and the lower bound is tighter than the standard linear programming relaxation of the integer forumlation. Computational results indicate that the proposed bounds are extremely tight. An exploded view of an automobile alternator is shown.

Manufacturing, Technology, Robots, Workstations, Production, Industrial Robots, Mathematical Programming, Assembly Line

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Solving 0-1 Integer Programming Problems Arising from Large Scale Planning Models

Article Abstract:

Some large integer programming problems that arose from planning applications were not solvable by standard techniques. Three phases of methods were used to take advantage of the hierarchical structure of the variables: 1) logical methods applied prior to linear programming, 2) constraint generation along with linear programming, and 3) specialized branch and bound. A strong linear programming formulation is very important. The methods for strengthening linear programs and for successful commercial branch and bound code are described. Results of benchmark tests are presented in table form.

Benchmarking, Benchmark, Hierarchical Organization, Programming, Methods, Branch and Bound

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