On the capacity inequalities for the heterogeneous vehicle routing problem

Fractional and Rounded capacity inequalities are two important families of valid inequalities known for the homogeneous Capacitated Vehicle Routing Problem (CVRP). Such inequalities impose the minimum number of vehicles required to service each and every subset of customers, be it a fractional or an integer value. In case of the Heterogeneous version of the routing problem (HCVRP), the minimum number of vehicles required for a subset of customers is not defined uniquely: it depends on the vehicle types and fleet composition that was engaged in serving the customers. This paper revises existing literature on the capacity-based valid inequalities for the HCVRP and presents new routines to separate them exactly using mixed integer linear programming (MILP). In addition, this paper proposes a new family of capacity-based valid inequalities for the HCVRP together with an exact routine to separate them. A computational study demonstrates applicability of considered inequalities in solving HCVRP instances using a standard MILP solver.