Household-Level Economies of Scale in Transportation

One of the fundamental concerns in the analysis of logistical systems is the trade-off between localized, independent provision of goods and services versus provision along a centralized infrastructure such as a backbone network. One phenomenon in which this trade-off has recently been made manifest is the transition of businesses from traditional brick-and-mortar stores to retail sales facilitated via e-commerce, such as grocery delivery services. Conventional wisdom would dictate that such services ought to be more efficient-say from the perspective of the overall carbon footprint-because of the economy of scale achieved by aggregating demand through a delivery van, as opposed to the many separate trips that customers would otherwise take using their own means of transport. In this paper, we quantify the changes in overall efficiency due to such services by looking at household-level economies of scale in transportation: a person might perform many errands in a day (such as going to the bank, grocery store, and post office), and that person has many choices of locations at which to perform these tasks (e.g., a typical metropolitan region has many banks, grocery stores, and post offices). Thus, the total driving distance (and therefore the overall carbon footprint) that that person traverses is the solution to a generalized travelling salesman problem (GTSP) in which they select both the best locations to visit and the sequence in which to visit them. We perform a probabilistic analysis of the GTSP under the assumption that all relevant locations are independently and identically distributed uniformly in a region and then determine the amount of adoption of such services that is necessary, under our model, in order for the overall carbon footprint of the region to decrease.