The Multiperiod Capacitated Minimal Spanning Tree With Node Outage Costs problem consists of scheduling the installation of links in a network so as to connect a set of terminal nodes S = [2,3…N] to a central node (node 1) with minimal present value of costs. The cost of the network is the sum of link layout cost and node outage costs. Node outage cost associated with each terminal node is the economic cost incurred by the network user whenever the terminal node is disabled due to failure of a link. In the network, some of the terminal nodes are active at the beginning of the planning horizon while others are activated over time. The link capacities limit the number of terminal nodes sharing a link. This problem is formulated as an integer-programming problem. A branch exchange heuristic procedure is used for solving the problem, and a Lagrangian relaxation method is used to find a lower bound for the optimal objective function value.
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