A multi-stage monte carlo sampling based stochastic programming model for the dynamic vehicle allocation problem

Optimization under uncertainty has seen many applications in the industrial world. The objective of this paper is to study the stochastic dynamic vehicle allocation problem (SDVAP), which is faced by many trucking companies, container companies, rental car agencies and railroads. To maximize profits and to manage fleets of vehicles in both time and space, this paper has formulated a multistage stochastic programming based model for SDVAP. A Monte Carlo Sampling Based Algorithm has been proposed to solve SDVAP. A probabilistic statement regarding the quality of the solution is also identified by introducing lower and upper bounds of the optimal solution. A five-stage experimental network was introduced for demonstration of this algorithm. The computational results indicate a high quality SDVAP solution, strongly suggesting that the algorithm can be used for real world decision making under uncertainty.