Optimal distribution of financial incentives to foster off-hour deliveries in urban areas

The main objective of this paper is to develop mathematical formulations to gain insight into the best way to distribute financial incentives to receivers of urban deliveries to maximize participation in off-hour deliveries. The paper considers two different types of incentive budgets: exogenous, and endogenous. The exogenous case represents the condition in which an external decision maker determines the incentive budget that is to be distributed among potential participants in off-hour deliveries. In the case of an endogenous incentive budget, the entity distributing the incentives must raise the necessary funds using revenue generation mechanisms such as tolls and fines. The optimal incentives are obtained from the Karush–Kuhn–Tucker conditions of a mathematical program that maximizes the number of truck trips shifted to the off-hours as a function of the incentives. The mathematical models developed in this paper provide guidelines about how to optimally distribute financial incentives to foster off-hour deliveries.