A minimax assignment problem on a linear communication network

A system of n communication centres is considered. The communication centres are to be located at a set of n prespecified positions lying in sequence on a linear network. Each communication centre transmits messages to every other centre at a rate of messages per unit of time . The messages that centre transmits to centre are sensed by all intermediate centres. A branch-and-bound method is introduced dealing with the following minimax assignment problem: minimise where A represents the set of all possible assignments of positions to centres The term represents the traffic at i which is defined as the number of messages compiled by the centre (at i) per unit of time, all inward and outward messages (at i) included. Based on numerical experience, a comparative analysis of the minimax assignment problem and the classical minisum Quadratic Assignment Problem (QAP) is performed.