An Upperbound Algorithm for the Single and Multiple Terminal Delivery Problem

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Abstract
An upperbound algorithm is presented for solving the multiterminal delivery problem. The method involves determining savings from joining points on routes and making possible assignments as a function of the maximum savings for joining cities on routes. The algorithm permits restrictions to be imposed on the system. If all possibilities are investigated, this approach will lead to an optimal solution using savings as the criterion to be optimized. In practice this may be very time consuming so a limited version is presented where only the most promising nodes are investigated. The methodology developed is applicable to the single terminal problem, since it is a special case of the multiterminal problem. A computer program has been written and a set of problems were solved with the algorithm using an IBM 360/50 computer. The results of a series of single and multi-terminal problems are illustrated in the paper. As is evident from these results the time required to solve a problem increases as a function of the number of demand points and the number of terminals.

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