Vacating a parking lot under uncertainty

Abstract

First-mile problems have become a major problem for the automobile industry since moving cars from production plants to selling destinations is characterized by using vehicle carriers with limited space. Although supply chain processes have automatized last-mile operations to improve productivity and increase benefits, first-mile analysis has been widely ignored. For example, in the automotive industry, cars are stored in parking lots until they are demanded, which negatively impacts delivery times and increases transportation costs. The previous issues impact the first-mile logistics of the automobile industry to the detriment of copying with delivery times and increasing the operation cost. In this paper, we deal with the previous issues by modeling the movement of cars from the parking lot to the car Carrier as an optimal control problem. Considering that not all cars should leave the parking lot, we search for conditions that guarantee the existence of a unique optimal path when the cars’ requisition is uncertain. Theoretical results provide a closed-form solution that indicates the optimal path to fill the car carrier in a time window. Such solutions allow us to study the impact of exogenous parameters (such as the parking lot size, the starting point, andmarginal costs) on the behavior and features of the optimal path.