Capacity-type cuts for the Multi-Vehicle Covering Tour Problem

The Covered Multi-Vehicle Routing Problem (m-CTP) involves a warehouse and three distinct subsets representing customers, mandatory facilities, and optional facilities. Each client is bound to a specific subset of optional facilities that define their set of coverage. The goal is to determine a set of low-cost routes that satisfy the following constraints: each route starts and ends at the depot; Each must-see facility is visited exactly once on a single route; Each route visits no more than $p$ facilities and has a maximum cost of $q$; For each customer, at least one optional facility of their roofing set must be visited by one of the routes. In this article, we present a new family of capacity-type cutoffs and report several experiments that prove the effectiveness of the algorithm and proposed cutoffs.