Stochastic decision models for last mile distribution using approximate dynamic programming
After localized disasters, donations are sometimes collected at the same facility as they are distributed, and the damaged infrastructure is overwhelmed by the congestion. However, separating the donation facilities from the points of distribution requires a vehicle to bring items between locations. We investigate dispatching policies for vehicles in such a scenario. We initially consider the case with one collection facility called a Staging Area (SA) and one Point of Distribution (POD). Among other things, we prove that if we have two or more vehicles, it is optimal to continuously dispatch the vehicles under most circumstances. Furthermore, we define two common-sense practical decision policies - Continuous Dispatching (CD) and Full Truckload Dispatching (FTD) - and demonstrate that CD performs well for one vehicle, at least as well as FTD across the board. This begs the question, can CD work on larger, more realistic networks? To answer this, we expand our network to two SAs and two vehicles to best compare to our prior work. First, we evaluate two Value Function Approximation methods and find that Rollout Algorithms can serve as a proxy for the optimal solution. Against this as a benchmark, CD performs well when the amount of items donated greatly exceeds the demand, and also when demand exceeds supply, but struggles when the two are equivalent. Next, we expand our network and consider general numbers of SAs and vehicles. Before we can begin, we must redefine CD for the expanded network. We describe several variations of CD for general networks, requiring different information to implement. So, by comparing them, we evaluate the value of the different pieces of information that a practitioner may have in the field. We find that visiting each SA equally on a rotating basis is a powerful strategy, although a better approach can be found by combining information about inventory levels, the locations of the vehicles, and the expected accumulation at each SA. Given the chaotic nature of humanitarian logistics, it is unlikely that this information may be obtained accurately, and so we recommend the rotating strategy.