A lookahead partitioning heuristic for a new assignment and scheduling problem in a distribution system

We introduce a new assignment and scheduling problem in a distribution system, which we refer to as the ASTV problem: Assigning and Scheduling transportation Tasks to Vehicles. In this problem, commodities need to be delivered directly from their origins to their destinations within specified time windows, using a fleet of homogenous capacitated vehicles. A set of routes, each of which performs one or several direct deliveries, need to be constructed such that the operational costs, including vehicle fixed cost, variable traveling and variable waiting costs, are minimized. The problem arises, for example, when delivering food products from several factories, where they are manufactured, to several distribution centers, from which they are delivered to the final customers. We define the problem and describe its relationship to existing problems studied in the literature, in particular pickup and delivery, assignment and scheduling problems. Subsequently we develop a solution method which is based on decomposing (partitioning) the ASTV problem into two interdependent sub-problems. The first consists of Assignment of Tasks to origin-destination full-load Trips (ATT), while the second determines assignment and Scheduling of these Trips to Vehicle routes (STV). We use a bi-criterion objective function in the first problem, whose purpose is to connect the two problems by looking ahead to the rest of the decisions, determined in the second problem. Thus, the solution method is referred to as lookahead partitioning. In this way, decisions of the first problem determine a favorable input for the second problem, which is solved last. An extensive numerical study was conducted to evaluate the performance of the overall heuristic method. The results indicate that our heuristic method is quite efficient.