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# Telpack Optimization by Implicit Enumeration

IP.com Disclosure Number: IPCOM000075538D
Original Publication Date: 1971-Oct-01
Included in the Prior Art Database: 2005-Feb-24
Document File: 2 page(s) / 26K

IBM

## Related People

Cooper, DW: AUTHOR

## Abstract

The Telpack Problem. The discount on per line cost offered users of telephone Telpacks over the single line cost has a sizable economic impact on all leased telephone networks. Such networks may be designed to utilize the Telpacks in a manner which greatly reduces the network rental cost.

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Telpack Optimization by Implicit Enumeration

The Telpack Problem.

The discount on per line cost offered users of telephone Telpacks over the single line cost has a sizable economic impact on all leased telephone networks. Such networks may be designed to utilize the Telpacks in a manner which greatly reduces the network rental cost. The problem of finding the optimum utilization of Telpacks in a network, which attaches a computer at some city to terminals located at other cities may be expressed as an integer programming problem. However, current integer programming codes have failed when applied. This combinatorial algorithm employs the transportation algorithm and implicit enumeration to reduce the trials necessary for exhaustion. Nomenclature N = Set of coefficients n n epsilon N whose position (pos(n)) references a set of cities in a network (tree structure) of Telpacks whose root is at the computer city; the value (val(n)) of the coefficients is the line capacity for Telpacks. T = Set of coefficients t3t epsilon T whose position references a city with terminals to be connected to the computer city; the value of a coefficient t is the number of single telephone lines required to attach the terminals at city t. Sn = Set of cities in a Telpack network referenced by pos(n). cjk= Cost of a single telephone line (including hookup costs) between cities j and k (for the computer city k = 0). djk= Cost of a Telpack to connect cities j and k (for the computer city k =...