Online Optimization of Pickup and Delivery Problem Considering Feasibility

Abstract

A pickup and delivery problem by multiple agents has many applications, such as food delivery service and disaster rescue. In this problem, there are cases where fuels must be considered (e.g., the case of using drones as agents). In addition, there are cases where demand forecasting should be considered (e.g., the case where a large number of orders are carried by a small number of agents). In this paper, we consider an online pickup and delivery problem considering fuel and demand forecasting. First, the pickup and delivery problem with fuel constraints is formulated. The information on demand forecasting is included in the cost function. Based on the orders, the agents’ paths (e.g., the paths from stores to customers) are calculated. We suppose that the target area is given by an undirected graph. Using a given graph, several constraints such as the moves and fuels of the agents are introduced. This problem is reduced to a mixed integer linear programming (MILP) problem. Next, in online optimization, the MILP problem is solved depending on the acceptance of orders. Owing to new orders, the calculated future paths may be changed. Finally, by using a numerical example, we present the effectiveness of the proposed method.