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

Abstract

We examine grocery shopping paths through the lens of the We examine grocery shopping paths through the lens of the Traveling Salesman Problem (TSP), a classic paradigm from the field of operations research. We define the path for each shopper as the shortest path that connects all of his purchases, and we study the systematic deviations seen in his actual behavior. We decompose the length of each observed path into three components: the length of the TSP-optimal path, the additional distance due to order deviation (i.e., not following the TSP-optimal order of category purchases), and the additional distance due to travel deviation (i.e., not following the shortest point-to-point paths). We then explore the relationship between these deviations and purchase behavior. Among other things, our results show a strong relationship between order deviation and basket size, but no association between travel deviation and basket size. Finally, we look at the implications of relaxing three of the rigid assumptions of the TSP by allowing for: (1) varying degrees of forward-lookingness across shoppers based on their observed order of purchases, (2) the possibility of unplanned purchases, and (3) the possibility of planned category visits but no resulting purchases.