Managing inventory in a one warehouse multiretailer distribution system with travelling salesman tour vehicle routing costs

We investigate the one warehouse multi-retailer distribution problem with travelling salesman tour vehicle costs. We model the system in the framework of the more general production/distribution network with arbitrary non-negative monotone joint order costs. Our goal is to develop heuristics whose costs are probably close to the cost of an optimal policy for these systems. To this end, we first show that the travelling salesman tour lengths through the central warehouse and the retailers ordering are close to submodular. We also show that although they are close, this closeness is dependent on the graph. We give four heuristics that quickly compute submodular functions which are close to the length of the travelling salesman tour lengths.;In addition we propose a dynamic program that computes optimal power of two policies for the one warehouse multiretailer system, assuming only that the order costs are non-negative monotone.;Finally, we perform computational tests that show that our submodular estimates of travelling salesman tour lengths, and our power of two policies for one warehouse multi-retailer distribution systems have less error than our theoretic worst case analysis would lead us to believe.;We also show that if we are given a submodular function which is close to the true order cost in a general production/distribution system, then we can find a power of two policy whose cost is close to the cost of an optimal policy.