The fleet size and mix problem for capacitated arc routing

There have been several attempts to solve the capacitated arc routing problem with m vehicles starting their tours from a central node. The objective has been to minimize the total distance travelled. In the problem treated here we also have the fixed costs of the vehicles included in the objective function. A set of vehicle capacities with their respective costs are used. Thus the objective function becomes a combination of fixed and variable costs. The solution procedure consists of four phases. In the first phase, a Chinese or rural postman problem is solved depending on whether all or some of the arcs in the network demand service with the objective of minimizing the total distance travelled. It results in a tour called the giant tour. In the second phase, the giant tour is partitioned into single vehicle subtours feasible with respect to the constraints. A new network is constructed with the node set corresponding to the arcs of the giant tour and with the arc set consisting of the subtours of the giant tour. The arc costs include both the fixed and variable costs of the subtours. The third phase consists of solving the shortest path problem on this new network to result in the least cost set of subtours represented on the new network. In the last phase a postprocessor is applied to the solution to improve it. The procedure is repeated for different giant tours to improve the final solution. The problem is extended to the case where there can be upper bounds on the number of vehicles with given capacities using a branch and bound method. Extension to directed networks is given. Some computational results are reported.