Upgrading arcs in the covering tour problem

1. Marta Baldomero-Naranjo
2. Andrea Mancuso
3. Adriano Masone
4. Antonio Manuel Rodriguez-Chia
5. Claudio Sterle

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In this study, we present the Covering Tour Problem with Arcs Upgrade (CTPAU). This problem is an extension of the Covering Tour Problem (CTP) that considers the possibility of enhancing the networkby reducing the length of some arcs, i.e., upgrading them. Hence, upgrading an arc means reducing its length, usually within certain limits,at a given cost that is proportional to the extent of the upgrade.The CTPAU is formulated with three different sets of nodes, V, W, and,T that is a subset of V. Two decisions have to be made simultaneously:i) identify the tour of minimum length that passes through a subset ofV, ensuring that all nodes of set T are included in the tour, and thateach node in W is within a given coverage distance from a node on thetour, ii) decide with connections to upgrade.Therefore, the CTPAU seeks to identify the minimum length tour whileintegrating arc upgrading and a budget constraint. In this context, wepresent some MILP formulation and compare them to illustrate the potential and limitations of each one.