Improved penalties for fixed cost linear programs using Lagrangean relaxation
Article Abstract:
Branch and bound approaches to integer programming use the Dreibeck-Tomlin penalty most commonly. This penalty has been used successfully to solve fixed cost linear programs by Kennington and Unger, and by Barr, Glover and Klingman. That the Dreibeck-Tomlin penalty can be derived from a Lagrangean relaxation of the integer programming problem is well known, but here it is shown that the Lagrangean relaxation for fixed cost problems yields two penalties in addition to the Dreibeck-Tomlin penalty. These two alternative penalties can sometimes dominate the more popular Dreibeck-Tomlin penalty. The strength of the new penalties is shown by solving a series of text problems and comparing the number of nodes generated on the branch and bound tree and the total computer time needed to solve each problem.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1986
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True interest cost in municipal bond bidding: an integer programming approach
Article Abstract:
Municipal bond underwriters were offered part of the more than $47 billion in tax-exempt debt issues sold to the public in 1982 under a competitive bidding system that uses the criterion of minimum true interest cost, or internal rate of return. The true interest cost (TIC) bidding problem can be represented by a non-linear integer program. A linearization is developed and described that is embedded in a special-purpose, integer-linear branch and bound algorithm. Also presented are the computational results of a number of actual bidding problems.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1986
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Optimization of bank transit check clearing operations
Article Abstract:
As of September 1, 1981, the Federal Reserve system began charging for check clearing and collection, pursuant to the Depository Institutions Deregulation and Monetary Control Act passed in 1980. Consequently, banks must perform check clearing operations more efficiently to compensate for higher processing costs. Optimizing a bank's check clearing and collection processes is modeled using integer programming. The optimization model developed considers process costs associated with transportation and clearing arrangements.
Publication Name: Management Science
Subject: Business, general
ISSN: 0025-1909
Year: 1985
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