Two-compartment stochastic single vehicle routing problems with simultaneous pickups and deliveries from N ordered customers

Abstract

ABSTRACT We consider a vehicle with two compartments that starts its route from a depot and visits N ordered customers in order to deliver new (or fresh or useful) products and to collect old (or expired or useless) products. The new products are placed in Compartment 1 and the old products are placed in Compartment 2. The quantity of new products that each customer demands and the quantity of old products that each customer returns are random variables with known joint distribution. The vehicle is allowed during its route to return to the depot in order to replenish Compartment 1 with new products and to unload the old products from Compartment 2. Under a suitable cost structure, it is possible to find the optimal restocking strategy by implementing a suitable dynamic programming algorithm. We also find the optimal restocking strategy for the corresponding infinite-time horizon problem. We further consider the same problem without the assumption that the customers are ordered. Numerical experiments indicate that the optimal restocking strategy can be computed for values of N up to 9.