Optimizing Package Delivery with Quantum Annealers: Addressing Time-Windows and Simultaneous Pickup and Delivery

TL;DR

This paper resorts to the previously published quantum-classical technique for addressing real-world-oriented routing problems, known as Quantum for Real Package Delivery (Q4RPD), and elaborate on solving additional realistic problem instances.

Abstract

Recent research at the intersection of quantum computing and routing problems has been highly prolific. Much of this work focuses on classical problems such as the Traveling Salesman Problem and the Vehicle Routing Problem. The practical applicability of these problems depends on the specific objectives and constraints considered. However, it is undeniable that translating complex real-world requirements into these classical formulations often proves challenging. In this paper, we resort to our previously published quantum-classical technique for addressing real-world-oriented routing problems, known as Quantum for Real Package Delivery (Q4RPD), and elaborate on solving additional realistic problem instances. Accordingly, this paper emphasizes the following characteristics: i) simultaneous pickup and deliveries, ii) time-windows, and iii) mobility restrictions by vehicle type. To illustrate the application of Q4RPD, we have conducted an experimentation comprising seven instances, serving as a demonstration of the newly developed features.

Figures (9)

• Figure 1: General workflow of Q4RPD.
• Figure 2: New workflow of S1. Routing Problem Setup.
• Figure 3: A 12-node PDP instance. A single truck with $W$=$D$=110 can complete the instance. For demonstration purposes, the black () rounded node should be visited last prior to the depot (which is the red node). The green () rounded points indicate orders where the pickup demand is less than the delivery, creating space in the truck. The red () rounded nodes require more pickup than delivery, thus needing space in the truck. Two different executions are shown for demonstrating the impact of considering pickups and deliveries. In route A, pickups are not considered, so $wd_i$=$dd_i$=10 and $wp_i$=$dp_i$=0 in all $i$. In route B, for the red rounded nodes, $wd_i$=$dd_i$=5 and $wp_i$=$dp_i$=15, and for the green rounded nodes, $wd_i$=$dd_i$=15 and $wp_i$=$dp_i$=5. For the remaining orders, $wd_i$=$dd_i$=$wp_i$=$dp_i$=10. Neither time windows nor mobility restrictions are considered.
• Figure 4: A 15-node PDP instance. Two identical trucks with $W = D = 70$ can complete the instance through two routes. The green () and red () rounded points are configured in the same way as explained in the caption of Figure \ref{['fig:pd1']}. Solutions A and B are also calculated using the same procedure as in Fig. \ref{['fig:pd1']}. Neither time windows nor mobility restrictions are considered.
• Figure 5: A 10-node PDP instance. In route A, time windows are not considered. In route B, the time windows [$lt_i,ut_i$] depicted in the lower-left frame are used. A single truck with $W$=$D$=110 can complete the instance at once. For all orders $wd_i$=$dd_i$=$wp_i$=$dp_i$=10. Neither mobility restrictions nor pickups are considered.