This paper examines a class of asymmetrical multi-depot vehicle routing problems and location-routing problems, under capacity or maximum cost restrictions. By using an appropriate graph representation, and then a graph extension, the problems are transformed into equivalent constrained assignment problems. Optimal solutions are then found by means of a branch and bound tree. Problems involving up to 80 nodes can be solved without difficulty.
This paper describes an integer linear programming algorithm for vehicle routing problems involving capacity and distance constraints. The method uses constraint relaxation and a new class of subtour elimination constraints. Two versions of the algorithm are presented, depending upon the nature of the distance matrix. Exact solutions are obtained for problems involving up to sixty cities.
The aim of this article is to develop an exact algorithm for the asymmetrical capacitated vehicle routing problem, i.e., the multiple traveling salesman problem subject to capacity restrictions. The problem is solved by means of a branch and bound tree in which subproblems are modified assignment problems subject to some restrictions. Two branching rules and three partitioning rules are examined. Computational results for problems involving up to 260 nodes (cities) are reported.
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