The pickup delivery location problem on networks

The Pickup Delivery Location Problem (PDLP) is a generalization of the Traveling Salesman Location Problem (TSLP) in which the daily tour involves pickup and delivery provided to customers by a vehicle of a given capacity. Two heuristics are suggested: The first is an extension of a method introduced by Simchi‐Levi and Berman for solving the TSLP. Its worst‐case relative error is shown to be bounded by 1. The second is based on a simple ranking of customers according to their probabilities for positive demand and their weighted average distances from all other locations. in addition, The fully polynomial algorithm of Berman and Simchi‐Levi is extended for solving PDLPs on tree networks. Both heuristics were tested on small‐size general networks and medium‐size tree networks. The average relative error over all test problems in the first class did not exceed 2.5% for the first heuristic and 1% for the second. in most cases, both produced the optimal solution. in about 56% of the tree network problems (with up to 80 nodes), Theoptimal home location of the server was found by at least one of the heuristics, and in about 94% of the problems, Theoptimal or an adjacent node was found by at least one of the heuristics.