Retail on Autonomous Wheels: A Time-Sensitive Traveling Salesman Problem

Abstract

The rapid advancement in self-driving technology has brought mobile retail into the spotlight. Motivated by its tremendous potential, we present a model, theory, and insights into the operations of the business model, where a wheeled store traverses across a service region, selectively seeks locations in which to perch, and fulfills local customer demand. The goal of the retailer is to balance between perching and migrating to maximize the total revenue during a service time window. To dispatch such a store, the retailer needs to consider the following time-sensitive factors: (i) How busy the service is, (ii) how soon customers come to the store, and (iii) how fast the product freshness decays. We propose and analyze a model that incorporates these factors into the classical traveling salesman problem (TSP), which we call the "time-sensitive TSP" (TSTSP). Using the continuous approximation approach, we derive the order of the optimal revenue, as well as the upper and lower bounds in the asymptotic regime as demands increase to infinity. The tightness of bounds is validated. Our analytical and numerical analysis demonstrates that store mobility creates value by bringing proximity to customers and by taking advantage of flexible repositioning to reach high-profit areas. In particular, the store opts to migrate more frequently during the initial period of the business hours than later on. The store also shifts more time to perching if customer response time becomes longer. These findings demonstrate the potential of mobile retail to emerge as a competitive new retail form.

Keywords: continuous approximation, TSP, time-sensitive TSP, mobile retail