The Traveling Salesman Goes Shopping: The Systematic Deviations of Grocery Paths from TSP Optimality

We examine grocery shopping paths using the traveling salesman problem (TSP) as a normative frame of reference. We define the TSP-path for each shopper as the shortest path that connects all of his purchases. We then decompose the length of each observed path into three components: the length of the TSP-path, the additional distance because of order deviation (i.e., not following the TSP-order of category purchases), and the additional distance because of travel deviation (i.e., not following the shortest point-to-point route). We explore the relationship between these deviations and different aspects of in-store shopping/purchase behavior. Among other things, our results suggest that (1) a large proportion of trip length is because of travel deviation; (2) paths that deviate substantially from the TSP solution are associated with larger shopping baskets; (3) order deviation is strongly associated with purchase behavior, while travel deviation is not; and (4) shoppers with paths closer to the TSP solution tend to buy more from frequently purchased product categories.