# A tutorial on value function approximation for stochastic and dynamic transportation

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png 4OR Springer Journals

# A tutorial on value function approximation for stochastic and dynamic transportation

, Volume OnlineFirst – Apr 4, 2023
29 pages

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# References (29)

Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023
ISSN
1619-4500
eISSN
1614-2411
DOI
10.1007/s10288-023-00539-3
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

4ORSpringer Journals

Published: Apr 4, 2023

Keywords: Tutorial; Markov decision process; Approximate dynamic programming; Value function approximation; Reinforcement learning; 90-01