Optimal minimal-contact customer routing through grocery stores

Grocery shopping has remained an essential activity even during the peak of the COVID-19 pandemic. In this context, we present an optimization framework for identifying routes through a grocery store that eliminate or minimize contacts between customers at grocery stock points while also minimizing the time spent within the store. We develop a discrete-event simulation of the customer arrival process, and simulate the arrival of customers with varying shopping list sizes and movement patterns. We then present two optimization formulations for generating optimal shopping routes on a real-time basis for each customer arriving to the store given the route information of other customers already present in the store. The first formulation eliminates contacts between customers whereas the second minimizes contacts between customers. Both formulations are mixed-integer problems based on extensions to the Miller-Tucker-Zemlin formulation of the traveling salesman problem. We also explore an alternate scenario for the deployment of these formulations wherein the customers and the store can plan visits ahead of time. This framework can be applied to more general contexts wherein minimizing contacts between randomly arriving agents needing to visit a subset of nodes in a connected network is required.