The zone hopping problem

In the zone hopping problem, n packages are to be moved by common carrier from location A to their final destinations, where the final destination of each of the packages is located in the common carrier's billing zone B. A savings may result if some of these packages are moved by a vehicle to a location D closer to the final destinations of the packages (but in the same common carrier's billing zone) by a vehicle and then delivered to their final destinations by the common carrier. The problem is to determine how many packages should be moved from A to D in order to maximize the savings. This problem is formulated as a special case of a knapsack problem and two algorithms are developed for solving this problem. Computational experience shows that these algorithms almost always find a solution within 1% of the optimal solution and are extremely efficient computationally.