A Dynamic Spatial Price Equilibrium Model of Integrated Urban Production-Transportation Operations Considering Freight Delivery Tours

Abstract

This paper introduces a dynamic spatial price equilibrium model that estimates urban freight-related flows for integrated producer-carrier operations that compete in a market where a generic commodity is traded. The model is applicable to cases where suppliers compete in a market by producing a commodity that is delivered to customers by means of delivery tours. The model obtains the patterns of commodity flows, production levels, and delivery tours that maximize economic welfare. The model is then reinterpreted as a Nash equilibrium model, where a set of suppliers deploys strategies involving production and delivery decisions to maximize profits, that is then solved with a heuristic approach that decomposes the interrelated decisions into how much to produce, how best to deliver to customers, and how much to charge for the cargo. Once the suppliers make these decisions, a market-clearing mechanism determines the amount of supplies that the various consumer nodes purchase from the suppliers. At this stage, the suppliers readjust their market strategies in anticipation of the next time period. The process ends when equilibrium is reached. Three different dynamics of the suppliers’ decisions on production levels are tested to gain insight into how efficiently each helps to reach the equilibrium solutions. By developing a model that explicitly considers delivery tours, the paper makes a significant contribution to the fields of spatial price equilibrium and freight demand modeling.