Household-Level Economies of Scale in Transportation

The efficiency of centralized delivery services over a backbone network in comparison to that of localized or multiple individual trips from the perspective of the overall carbon footprint is a fundamental subject of the analysis of logistical systems. 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 he or she selects 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 centralized delivery services that is necessary, under our model, in order for the overall carbon footprint of the region to decrease.