The capacitated vehicle routing problem (CVRP) is the problem of finding a routing schedule to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. For operational purposes, in many practical applications a long term routing schedule is made, often based on average demand. When demand substantially differs from the average, constructing a new schedule is beneficial. The vehicle rescheduling problem (VRSP) is the problem of finding a new schedule that not only minimizes the total traveling costs but also minimizes the costs of deviating from the original schedule. In this paper a mathematical programming formulation of the rescheduling problem is presented as well as a heuristic solution method referred to as the two-phase heuristic. We provide sufficiency conditions for which it produces the optimal solution. Finally, we perform computational experiments to study the performance of the two-phase heuristic.