A Matheuristic for a Real-world Variant of the Multiple Traveling Salesman Problem

Significant long-term cost savings can be achieved when labor-intensive daily operations are executed at minimal cost. We consider here a real-world planning problem that was reported to us by a real estate valuation company. The planning problem consists of scheduling on-site visits such that the total operating costs are minimized. We show that this problem represents a new variant of the multiple traveling salesman problem to which existing approaches cannot be applied directly. We formulate the problem as a mixed-binary linear program and develop a matheuristic for large-scale instances. The matheuristic employs a new strategy to construct subproblems effectively and techniques to exclude variables that are unlikely to be non-zero in an optimal solution. Our computational analysis demonstrates that the mixed-binary linear program is able to devise optimal or near-optimal solutions for instances with up to 200 visits in short running times. The matheuristic performs equally well on small-and medium-sized instances and proves to be highly scalable.