On finding a cyclic tour and a vehicle loading plan yielding maximum profit ?
We consider a problem in which it is required to find a cyclic tour and a vehicle loading plan maximizing the total profit realized from purchasing and selling commodities loaded at vertices of the tour. It is shown that the problem reduces to the metric traveling salesman problem. We present polynomial-time approximation algorithms with proven performance guarantees for solving some variants of the problem corresponding to different loading schemes. We also identify special cases where our algorithms find either optimal or asymptotically optimal solutions.
traveling salesman problem approximation algorithms