Approximate dynamic programming for the military inventory routing problem

The United States Army can benefit from effectively utilizing cargo unmanned aerial vehicles (CUAVs) to perform resupply operations in combat environments to reduce the use of manned (ground and aerial) resupply that incurs risk to personnel. We formulate a Markov decision process (MDP) model of an...

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Veröffentlicht in:	Annals of operations research Jg. 288; H. 1; S. 391 - 416
Hauptverfasser:	McKenna, Rebekah S., Robbins, Matthew J., Lunday, Brian J., McCormack, Ian M.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.05.2020 Springer Springer Nature B.V
Schlagworte:	Algorithms Approximation Approximation theory Benchmarks Business and Management Combinatorics Dispersion Dynamic programming Inventory control Iterative methods Management Markov processes Methods Military Military supplies Operations research Operations Research/Decision Theory Original Research Policies Route planning Theory of Computation Unmanned aerial vehicles United States United States > US Approximate dynamic programming Inventory routing problem Least squares temporal differences Markov decision processes Military
ISSN:	0254-5330, 1572-9338
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Abstract	The United States Army can benefit from effectively utilizing cargo unmanned aerial vehicles (CUAVs) to perform resupply operations in combat environments to reduce the use of manned (ground and aerial) resupply that incurs risk to personnel. We formulate a Markov decision process (MDP) model of an inventory routing problem (IRP) with vehicle loss and direct delivery, which we label the military IRP (MILIRP). The objective of the MILIRP is to determine CUAV dispatching and routing policies for the resupply of geographically dispersed units operating in an austere, combat environment. The large size of the problem instance motivating this research renders dynamic programming algorithms inappropriate, so we utilize approximate dynamic programming (ADP) methods to attain improved policies (relative to a benchmark policy) via an approximate policy iteration algorithmic strategy utilizing least squares temporal differencing for policy evaluation. We examine a representative problem instance motivated by resupply operations experienced by the United States Army in Afghanistan both to demonstrate the applicability of our MDP model and to examine the efficacy of our proposed ADP solution methodology. A designed computational experiment enables the examination of selected problem features and algorithmic features vis-à-vis the quality of solutions attained by our ADP policies. Results indicate that a 4-crew, 8-CUAV unit is able to resupply 57% of the demand from an 800-person organization over a 3-month time horizon when using the ADP policy, a notable improvement over the 18% attained using a benchmark policy. Such results inform the development of procedures governing the design, development, and utilization of CUAV assets for the resupply of dispersed ground combat forces.
AbstractList	The United States Army can benefit from effectively utilizing cargo unmanned aerial vehicles (CUAVs) to perform resupply operations in combat environments to reduce the use of manned (ground and aerial) resupply that incurs risk to personnel. We formulate a Markov decision process (MDP) model of an inventory routing problem (IRP) with vehicle loss and direct delivery, which we label the military IRP (MILIRP). The objective of the MILIRP is to determine CUAV dispatching and routing policies for the resupply of geographically dispersed units operating in an austere, combat environment. The large size of the problem instance motivating this research renders dynamic programming algorithms inappropriate, so we utilize approximate dynamic programming (ADP) methods to attain improved policies (relative to a benchmark policy) via an approximate policy iteration algorithmic strategy utilizing least squares temporal differencing for policy evaluation. We examine a representative problem instance motivated by resupply operations experienced by the United States Army in Afghanistan both to demonstrate the applicability of our MDP model and to examine the efficacy of our proposed ADP solution methodology. A designed computational experiment enables the examination of selected problem features and algorithmic features vis-à-vis the quality of solutions attained by our ADP policies. Results indicate that a 4-crew, 8-CUAV unit is able to resupply 57% of the demand from an 800-person organization over a 3-month time horizon when using the ADP policy, a notable improvement over the 18% attained using a benchmark policy. Such results inform the development of procedures governing the design, development, and utilization of CUAV assets for the resupply of dispersed ground combat forces.
Audience	Academic
Author	McCormack, Ian M. Lunday, Brian J. McKenna, Rebekah S. Robbins, Matthew J.
Author_xml	– sequence: 1 givenname: Rebekah S. surname: McKenna fullname: McKenna, Rebekah S. organization: Department of Operational Sciences, Air Force Institute of Technology – sequence: 2 givenname: Matthew J. orcidid: 0000-0002-1718-6839 surname: Robbins fullname: Robbins, Matthew J. email: matthew.robbins@afit.edu organization: Department of Operational Sciences, Air Force Institute of Technology – sequence: 3 givenname: Brian J. orcidid: 0000-0001-5191-4361 surname: Lunday fullname: Lunday, Brian J. organization: Department of Operational Sciences, Air Force Institute of Technology – sequence: 4 givenname: Ian M. surname: McCormack fullname: McCormack, Ian M. organization: Department of Operational Sciences, Air Force Institute of Technology
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CitedBy_id	crossref_primary_10_1007_s10479_025_06738_x crossref_primary_10_1016_j_trc_2024_104892 crossref_primary_10_1016_j_cor_2025_107164 crossref_primary_10_1016_j_ejor_2022_06_031 crossref_primary_10_1007_s10479_024_06158_3 crossref_primary_10_1016_j_cor_2024_106717 crossref_primary_10_1016_j_jtrangeo_2025_104209
Cites_doi	10.1287/trsc.1030.0041 10.1287/ijoc.1090.0351 10.1016/j.ejor.2016.11.023 10.1016/j.ejor.2016.04.017 10.1287/trsc.36.1.94.574 10.1002/9781118029176 10.1057/jors.2010.19 10.1287/trsc.2013.0472 10.1007/s11768-011-1005-3 10.1007/BF02430363 10.1007/BFb0009019 10.1109/CDC.1997.652501
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Copyright	This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply. 2019 COPYRIGHT 2020 Springer This is a U.S. government work and not under copyright protection in the U.S.; foreign copyright protection may apply. 2019.
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Keywords	Approximate dynamic programming Inventory routing problem Least squares temporal differences Markov decision processes Military
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SubjectTerms	Algorithms Approximation Approximation theory Benchmarks Business and Management Combinatorics Dispersion Dynamic programming Inventory control Iterative methods Management Markov processes Methods Military Military supplies Operations research Operations Research/Decision Theory Original Research Policies Route planning Theory of Computation Unmanned aerial vehicles
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Title	Approximate dynamic programming for the military inventory routing problem
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