A tutorial on value function approximation for stochastic and dynamic transportation

This paper provides an introductory tutorial on Value Function Approximation (VFA), a solution class from Approximate Dynamic Programming. VFA describes a heuristic way for solving sequential decision processes like a Markov Decision Process. Real-world problems in supply chain management (and beyond) containing dynamic and stochastic elements might be modeled as such processes, but large-scale instances are intractable to be solved to optimality by enumeration due to the curses of dimensionality. VFA can be a proper method for these cases and this tutorial is designed to ease its use in research, practice, and education. For this, the tutorial describes VFA in the context of stochastic and dynamic transportation and makes three main contributions. First, it gives a concise theoretical overview of VFA's fundamental concepts, outlines a generic VFA algorithm, and briefly discusses advanced topics of VFA. Second, the VFA algorithm is applied to the taxicab problem that describes an easy-to-understand transportation planning task. Detailed step-by-step results are presented for a small-scale instance, allowing readers to gain an intuition about VFA's main principles. Third, larger instances are solved by enhancing the basic VFA algorithm demonstrating its general capability to approach more complex problems. The experiments are done with artificial instances and the respective Python scripts are part of an electronic appendix. Overall, the tutorial provides the necessary knowledge to apply VFA to a wide range of stochastic and dynamic settings and addresses likewise researchers, lecturers, tutors, students, and practitioners.