Market Approach to Length Constrained Min-Max Multiple Depot Multiple Traveling Salesman Problem

We consider a routing problem that arises in Persistent Intelligence Surveillance Reconnaissance missions, and pose it as a multiple depot traveling salesman problem, with an objective to minimize the maximum tour length, and an additional set of constraints on the revisit period of every node. We aim to satisfy the revisit period constraints by enforcing equivalent tour length constraints. We present a Mixed Integer Liner Programming (MILP) formulation for this proposed problem which is solved in a branch and cut framework. We also present a market-based solution, an iterative procedure, where each salesman is assigned prices in each iteration and the node assignments are updated accordingly. The quality of the solutions and computation time of the market-based solution are compared to a MILP solution using several numerical simulations. The MILP formulation does not scale well for larger instances with more than hundred nodes, however, the market based approach is able to produce quality solutions to these instances with only a few seconds of computation time.