{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T15:52:22Z","timestamp":1782229942112,"version":"3.54.5"},"reference-count":70,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T00:00:00Z","timestamp":1742774400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T00:00:00Z","timestamp":1742774400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100014013","name":"UK Research and Innovation","doi-asserted-by":"publisher","award":["EP\/S021612\/1"],"award-info":[{"award-number":["EP\/S021612\/1"]}],"id":[{"id":"10.13039\/100014013","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012317","name":"UCLH Biomedical Research Centre","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012317","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Value iteration can find the optimal replenishment policy for a perishable inventory problem, but is computationally demanding due to the large state spaces that are required to represent the age profile of stock. The parallel processing capabilities of modern graphics processing units (GPUs) can reduce the wall time required to run value iteration by updating many states simultaneously. The adoption of GPU-accelerated approaches has been limited in operational research relative to other fields like machine learning, in which new software frameworks have made GPU programming widely accessible. We used the Python library JAX to implement value iteration and simulators of the underlying Markov decision processes in a high-level interface, and relied on this library\u2019s function transformations and compiler to efficiently utilize GPU hardware. Our method can extend use of value iteration to settings that were previously considered infeasible or impractical. We demonstrate this on example scenarios from three recent studies which include problems with over 16 million states and additional problem features, such as substitution between products, that increase computational complexity. We compare the performance of the optimal replenishment policies to heuristic policies, fitted using simulation optimization in JAX which allowed the parallel evaluation of multiple candidate policy parameters on thousands of simulated years. The heuristic policies gave a maximum optimality gap of 2.49%. Our general approach may be applicable to a wide range of problems in operational research that would benefit from large-scale parallel computation on consumer-grade GPU hardware.<\/jats:p>","DOI":"10.1007\/s10479-025-06551-6","type":"journal-article","created":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T13:52:47Z","timestamp":1742824367000},"page":"1609-1638","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Going faster to see further: graphics processing unit-accelerated value iteration and simulation for perishable inventory control using JAX"],"prefix":"10.1007","volume":"349","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4156-3419","authenticated-orcid":false,"given":"Joseph","family":"Farrington","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wai Keong","family":"Wong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kezhi","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Utley","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,3,24]]},"reference":[{"key":"6551_CR1","doi-asserted-by":"crossref","unstructured":"Aamer, A., Eka Yani, L., & Alan Priyatna, I. (2020). Data analytics in the supply chain management: Review of machine learning applications in demand forecasting. Operations and Supply Chain Management An International Journal, 14(1), 1\u201313. https:\/\/doi.org\/10.31387\/oscm0440281","DOI":"10.31387\/oscm0440281"},{"key":"6551_CR2","doi-asserted-by":"publisher","unstructured":"Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., Kudlur, M., Levenberg, J., Monga, R., Moore, S., Murray, D.\u00a0G., Steiner, B., Tucker, P., Vasudevan, V., Warden, P., Wicke, M., Yu, Y., & Zheng, X. (2016). TensorFlow: a system for large-scale machine learning. In Proceedings of the 12th USENIX conference on operating systems design and implementation (OSDI \u201816) (pp. 265\u2013283). https:\/\/doi.org\/10.48550\/arXiv.1603.04467","DOI":"10.48550\/arXiv.1603.04467"},{"key":"6551_CR3","doi-asserted-by":"publisher","unstructured":"Abouee-Mehrizi, H., Mirjalili, M., & Sarhangian, V. (2023). Platelet inventory management with approximate dynamic programming. https:\/\/doi.org\/10.48550\/arXiv.2307.09395","DOI":"10.48550\/arXiv.2307.09395"},{"key":"6551_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2022.105968","volume":"147","author":"E Ahmadi","year":"2022","unstructured":"Ahmadi, E., Mosadegh, H., Maihami, R., Ghalehkhondabi, I., Sun, M., & S\u00fcer, G. A. (2022). Intelligent inventory management approaches for perishable pharmaceutical products in a healthcare supply chain. Computers & Operations Research, 147, Article 105968. https:\/\/doi.org\/10.1016\/j.cor.2022.105968","journal-title":"Computers & Operations Research"},{"key":"6551_CR5","doi-asserted-by":"publisher","unstructured":"Akiba, T., Sano, S., Yanase, T., Ohta, T., & Koyama, M. (2019). Optuna: A next-generation hyperparameter optimization framework. In Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining (KDD \u201819) (pp. 2623\u20132631). https:\/\/doi.org\/10.1145\/3292500.3330701","DOI":"10.1145\/3292500.3330701"},{"issue":"3","key":"6551_CR6","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1016\/j.jedc.2010.10.001","volume":"35","author":"EM Aldrich","year":"2011","unstructured":"Aldrich, E. M., Fern\u00e1ndez-Villaverde, J., Ronald Gallant, A., & Rubio-Ram\u00edrez, J. F. (2011). Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors. Journal of Economic Dynamics and Control, 35(3), 386\u2013393. https:\/\/doi.org\/10.1016\/j.jedc.2010.10.001","journal-title":"Journal of Economic Dynamics and Control"},{"issue":"1","key":"6551_CR7","doi-asserted-by":"publisher","first-page":"351","DOI":"10.1007\/s10479-015-2019-x","volume":"240","author":"S Amaran","year":"2016","unstructured":"Amaran, S., Sahinidis, N. V., Sharda, B., & Bury, S. J. (2016). Simulation optimization: A review of algorithms and applications. Annals of Operations Research, 240(1), 351\u2013380. https:\/\/doi.org\/10.1007\/s10479-015-2019-x","journal-title":"Annals of Operations Research"},{"key":"6551_CR8","volume-title":"Dynamic programming","author":"R Bellman","year":"1957","unstructured":"Bellman, R. (1957). Dynamic programming. Princeton University Press."},{"key":"6551_CR9","unstructured":"Blake, J.\u00a0T., Thompson, S., Smith, S., Anderson, D., Arellana, R., & Bernard, D. (2003). Optimizing the platelet supply chain in Nova Scotia. In Proceedings of the 29th meeting of the EURO working group on operational research applied to health services (ORAHS 2003) (pp. 47\u201366). http:\/\/orahs.di.unito.it\/docs\/2003-ORAHS-proceedings.pdf#page=47. Retrieved from April 1, 2020"},{"key":"6551_CR10","doi-asserted-by":"publisher","unstructured":"Bonnet, C., Luo, D., Byrne, D., Surana, S., Abramowitz, S., Duckworth, P., Coyette, V., Midgley, L.\u00a0I., Tegegn, E., Kalloniatis, T., Mahjoub, O., Macfarlane, M., Smit, A.\u00a0P., Grinsztajn, N., Boige, R., Waters, C.\u00a0N., Mimouni, M.\u00a0A., Sob, U. A.\u00a0M., de\u00a0Kock, R., Singh, S., Furelos-Blanco, D., Le, V., Pretorius, A., & Laterre, A. (2024). Jumanji: A diverse suite of scalable reinforcement learning environments in JAX. https:\/\/doi.org\/10.48550\/arXiv.2306.09884","DOI":"10.48550\/arXiv.2306.09884"},{"issue":"2","key":"6551_CR11","doi-asserted-by":"publisher","first-page":"456","DOI":"10.1016\/j.ejor.2016.09.050","volume":"258","author":"MA Boschetti","year":"2017","unstructured":"Boschetti, M. A., Maniezzo, V., & Strappaveccia, F. (2017). Route relaxations on GPU for vehicle routing problems. European Journal of Operational Research, 258(2), 456\u2013466. https:\/\/doi.org\/10.1016\/j.ejor.2016.09.050","journal-title":"European Journal of Operational Research"},{"key":"6551_CR12","unstructured":"Bradbury, J., Frostig, R., Hawkins, P., Johnson, M.\u00a0J., Leary, C., Maclaurin, D., Necula, G., Paszke, A., VanderPlas, J., Wanderman-Milne, S., & Zhang, Q. (2022). JAX: Composable transformations of Python+NumPy programs. http:\/\/github.com\/google\/jax. Retrieved from December 7, 2022"},{"key":"6551_CR13","doi-asserted-by":"publisher","unstructured":"B\u00e4umelt, Z., Dvo\u0159\u00e1k, J., & \u0160$${\\rm \\mathring{u}}$$cha, P., & Hanz\u00e1lek, Z. (2016). A novel approach for nurse rerostering based on a parallel algorithm. European Journal of Operational Research,251(2), 624\u2013639. https:\/\/doi.org\/10.1016\/j.ejor.2015.11.022","DOI":"10.1016\/j.ejor.2015.11.022"},{"issue":"3","key":"6551_CR14","doi-asserted-by":"publisher","first-page":"306","DOI":"10.1108\/JAMR-09-2017-0091","volume":"15","author":"V Chaudhary","year":"2018","unstructured":"Chaudhary, V., Kulshrestha, R., & Routroy, S. (2018). State-of-the-art literature review on inventory models for perishable products. Journal of Advances in Management Research, 15(3), 306\u2013346. https:\/\/doi.org\/10.1108\/JAMR-09-2017-0091","journal-title":"Journal of Advances in Management Research"},{"key":"6551_CR15","doi-asserted-by":"publisher","unstructured":"Chen, P. & Lu, L. (2013). Markov decision process parallel value iteration algorithm on GPU. In Proceedings of 2013 international conference on information science and computer applications (pp. 299\u2013304). https:\/\/doi.org\/10.2991\/isca-13.2013.51","DOI":"10.2991\/isca-13.2013.51"},{"key":"6551_CR16","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/j.jpdc.2019.11.009","volume":"137","author":"D-A Constantinescu","year":"2020","unstructured":"Constantinescu, D.-A., Navarro, A., Fern\u00e1ndez-Madrigal, J.-A., & Asenjo, R. (2020). Performance evaluation of decision making under uncertainty for low power heterogeneous platforms. Journal of Parallel and Distributed Computing, 137, 119\u2013133. https:\/\/doi.org\/10.1016\/j.jpdc.2019.11.009","journal-title":"Journal of Parallel and Distributed Computing"},{"issue":"3","key":"6551_CR17","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1080\/17477778.2018.1497461","volume":"13","author":"D Dalalah","year":"2019","unstructured":"Dalalah, D., Bataineh, O., & Alkhaledi, K. A. (2019). Platelets inventory management: A rolling horizon sim-opt approach for an age-differentiated demand. Journal of Simulation, 13(3), 209\u2013225. https:\/\/doi.org\/10.1080\/17477778.2018.1497461","journal-title":"Journal of Simulation"},{"issue":"2","key":"6551_CR18","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1016\/j.ejor.2021.10.045","volume":"301","author":"BJ De Moor","year":"2022","unstructured":"De Moor, B. J., Gijsbrechts, J., & Boute, R. N. (2022). Reward shaping to improve the performance of deep reinforcement learning in perishable inventory management. European Journal of Operational Research, 301(2), 535\u2013545. https:\/\/doi.org\/10.1016\/j.ejor.2021.10.045","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"6551_CR19","doi-asserted-by":"publisher","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182\u2013197. https:\/\/doi.org\/10.1109\/4235.996017","journal-title":"IEEE Transactions on Evolutionary Computation"},{"key":"6551_CR20","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.ijpe.2017.02.006","volume":"187","author":"M Dillon","year":"2017","unstructured":"Dillon, M., Oliveira, F., & Abbasi, B. (2017). A two-stage stochastic programming model for inventory management in the blood supply chain. International Journal of Production Economics, 187, 27\u201341. https:\/\/doi.org\/10.1016\/j.ijpe.2017.02.006","journal-title":"International Journal of Production Economics"},{"issue":"2","key":"6551_CR21","doi-asserted-by":"publisher","first-page":"658","DOI":"10.1016\/j.ijpe.2013.05.020","volume":"145","author":"Q Duan","year":"2013","unstructured":"Duan, Q., & Liao, T. W. (2013). A new age-based replenishment policy for supply chain inventory optimization of highly perishable products. International Journal of Production Economics, 145(2), 658\u2013671. https:\/\/doi.org\/10.1016\/j.ijpe.2013.05.020","journal-title":"International Journal of Production Economics"},{"key":"6551_CR22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2019.103796","volume":"111","author":"V Duarte","year":"2020","unstructured":"Duarte, V., Duarte, D., Fonseca, J., & Montecinos, A. (2020). Benchmarking machine-learning software and hardware for quantitative economics. Journal of Economic Dynamics and Control, 111, Article 103796. https:\/\/doi.org\/10.1016\/j.jedc.2019.103796","journal-title":"Journal of Economic Dynamics and Control"},{"key":"6551_CR23","unstructured":"Ebuyer (2024). NVIDIA GeForce RTX 3060 Graphics Card. https:\/\/www.ebuyer.com\/store\/Components\/cat\/Graphics-Cards-Nvidia\/subcat\/GeForce-RTX-3060?q=nvidia+3060. Retrieved from December 11, 2024."},{"issue":"1","key":"6551_CR24","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.tmrv.2019.08.006","volume":"34","author":"AW Flint","year":"2020","unstructured":"Flint, A. W., McQuilten, Z. K., Irwin, G., Rushford, K., Haysom, H. E., & Wood, E. M. (2020). Is platelet expiring out of date? A systematic review. Transfusion Medicine Reviews, 34(1), 42\u201350. https:\/\/doi.org\/10.1016\/j.tmrv.2019.08.006","journal-title":"A systematic review. Transfusion Medicine Reviews"},{"key":"6551_CR25","doi-asserted-by":"publisher","unstructured":"Freeman, C.\u00a0D., Frey, E., Raichuk, A., Girgin, S., Mordatch, I., & Bachem, O. (2021). Brax\u2014A differentiable physics engine for large scale rigid body simulation. https:\/\/doi.org\/10.48550\/arXiv.2106.13281","DOI":"10.48550\/arXiv.2106.13281"},{"issue":"1","key":"6551_CR26","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1287\/opre.23.1.46","volume":"23","author":"BE Fries","year":"1975","unstructured":"Fries, B. E. (1975). Optimal ordering policy for a perishable commodity with fixed lifetime. Operations Research, 23(1), 46\u201361. https:\/\/doi.org\/10.1287\/opre.23.1.46","journal-title":"Operations Research"},{"key":"6551_CR27","doi-asserted-by":"publisher","first-page":"3696","DOI":"10.1109\/WSC.2014.7020198","volume":"2014","author":"MC Fu","year":"2014","unstructured":"Fu, M. C., Bayraksan, G., Henderson, S. G., Nelson, B. L., Powell, W. B., Ryzhov, I. O., & Thengvall, B. (2014). Simulation optimization: A panel on the state of the art in research and practice. Proceedings of the Winter Simulation Conference, 2014, 3696\u20133706. https:\/\/doi.org\/10.1109\/WSC.2014.7020198","journal-title":"Proceedings of the Winter Simulation Conference"},{"key":"6551_CR28","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/j.cor.2014.08.017","volume":"54","author":"S Gunpinar","year":"2015","unstructured":"Gunpinar, S., & Centeno, G. (2015). Stochastic integer programming models for reducing wastages and shortages of blood products at hospitals. Computers and Operations Research, 54, 129\u2013141. https:\/\/doi.org\/10.1016\/j.cor.2014.08.017","journal-title":"Computers and Operations Research"},{"key":"6551_CR29","doi-asserted-by":"publisher","unstructured":"Haijema, R. & Minner, S. (2019). Improved ordering of perishables: The value of stock-age information. International Journal of Production Economics, 209(C), 316\u2013324. https:\/\/doi.org\/10.1016\/j.ijpe.2018.03.008","DOI":"10.1016\/j.ijpe.2018.03.008"},{"issue":"3","key":"6551_CR30","doi-asserted-by":"publisher","first-page":"760","DOI":"10.1016\/j.cor.2005.03.023","volume":"34","author":"R Haijema","year":"2007","unstructured":"Haijema, R., van der Wal, J., & van Dijk, N. M. (2007). Blood platelet production: Optimization by dynamic programming and simulation. Computers & Operations Research, 34(3), 760\u2013779. https:\/\/doi.org\/10.1016\/j.cor.2005.03.023","journal-title":"Computers & Operations Research"},{"issue":"4","key":"6551_CR31","doi-asserted-by":"publisher","DOI":"10.1002\/cmm4.1027","volume":"1","author":"EM Hendrix","year":"2019","unstructured":"Hendrix, E. M., Ortega, G., Haijema, R., Buisman, M. E., & Garc\u00eda, I. (2019). On computing optimal policies in perishable inventory control using value iteration. Computational and Mathematical Methods, 1(4), Article e1027. https:\/\/doi.org\/10.1002\/cmm4.1027","journal-title":"Computational and Mathematical Methods"},{"issue":"2","key":"6551_CR32","doi-asserted-by":"publisher","first-page":"813","DOI":"10.1007\/s10479-021-03982-9","volume":"315","author":"M Heydar","year":"2022","unstructured":"Heydar, M., O\u2019Reilly, M. M., Trainer, E., Fackrell, M., Taylor, P. G., & Tirdad, A. (2022). A stochastic model for the patient-bed assignment problem with random arrivals and departures. Annals of Operations Research, 315(2), 813\u2013845. https:\/\/doi.org\/10.1007\/s10479-021-03982-9","journal-title":"Annals of Operations Research"},{"key":"6551_CR33","doi-asserted-by":"publisher","DOI":"10.1145\/3570638","author":"P Hijma","year":"2022","unstructured":"Hijma, P., Heldens, S., Sclocco, A., van Werkhoven, B., & Bal, H. E. (2022). Optimization techniques for GPU programming. ACM Computing Surveys. https:\/\/doi.org\/10.1145\/3570638","journal-title":"ACM Computing Surveys"},{"key":"6551_CR34","unstructured":"Inamoto, T., Matsumoto, T., Ohta, C., Tamaki, H., & Murao, H. (2011). An implementation of dynamic programming for many-core computers. In Proceedings of the SICE Annual Conference 2011 (pp. 961\u2013966). https:\/\/ieeexplore.ieee.org\/abstract\/document\/6060648. Retrieved February 15, 2023"},{"key":"6551_CR35","doi-asserted-by":"publisher","unstructured":"Jeon, W., Ko, G., Lee, J., Lee, H., Ha, D., & Ro, W.\u00a0W. (2021). Chapter six\u2014deep learning with GPUs. In Advances in computers, volume 122 of hardware accelerator systems for artificial intelligence and machine learning (pp. 167\u2013215). Elsevier. https:\/\/doi.org\/10.1016\/bs.adcom.2020.11.003","DOI":"10.1016\/bs.adcom.2020.11.003"},{"key":"6551_CR36","unstructured":"J\u00f3hannsson, A.\u00a0P. (2009). GPU-based Markov decision process solver. Reykjav\u00edk University. https:\/\/en.ru.is\/media\/skjol-td\/MSThesis_ArsaellThorJohannsson.pdf. Retrieved February 15, 2023"},{"key":"6551_CR37","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.eswa.2017.08.046","volume":"91","author":"A Kara","year":"2018","unstructured":"Kara, A., & Dogan, I. (2018). Reinforcement learning approaches for specifying ordering policies of perishable inventory systems. Expert Systems with Applications, 91, 150\u2013158. https:\/\/doi.org\/10.1016\/j.eswa.2017.08.046","journal-title":"Expert Systems with Applications"},{"issue":"1","key":"6551_CR38","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10614-015-9544-1","volume":"49","author":"R Kirkby","year":"2017","unstructured":"Kirkby, R. (2017). A toolkit for value function iteration. Computational Economics, 49(1), 1\u201315. https:\/\/doi.org\/10.1007\/s10614-015-9544-1","journal-title":"Computational Economics"},{"key":"6551_CR39","doi-asserted-by":"publisher","DOI":"10.1007\/s10614-022-10234-w","author":"R Kirkby","year":"2022","unstructured":"Kirkby, R. (2022). Quantitative macroeconomics: Lessons learned from fourteen replications. Computational Economics. https:\/\/doi.org\/10.1007\/s10614-022-10234-w","journal-title":"Computational Economics"},{"key":"6551_CR40","doi-asserted-by":"publisher","unstructured":"Lam, S.\u00a0K., Pitrou, A., & Seibert, S. (2015). Numba: a LLVM-based Python JIT compiler. In Proceedings of the second workshop on the LLVM compiler infrastructure in HPC, LLVM \u201915 (pp. 1\u20136). https:\/\/doi.org\/10.1145\/2833157.2833162","DOI":"10.1145\/2833157.2833162"},{"key":"6551_CR41","doi-asserted-by":"publisher","unstructured":"Lange, R.\u00a0T. (2022a). evosax: JAX-based evolution strategies. https:\/\/doi.org\/10.48550\/arXiv.2212.04180","DOI":"10.48550\/arXiv.2212.04180"},{"key":"6551_CR42","unstructured":"Lange, R.\u00a0T. (2022b). gymnax: A JAX-based reinforcement learning environment library. http:\/\/github.com\/RobertTLange\/gymnax Retrieved January 18, 2023"},{"key":"6551_CR43","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.compchemeng.2016.01.001","volume":"87","author":"MC Lau","year":"2016","unstructured":"Lau, M. C., & Srinivasan, R. (2016). A hybrid CPU-graphics processing unit (GPU) approach for computationally efficient simulation-optimization. Computers & Chemical Engineering, 87, 49\u201362. https:\/\/doi.org\/10.1016\/j.compchemeng.2016.01.001","journal-title":"Computers & Chemical Engineering"},{"issue":"3","key":"6551_CR44","doi-asserted-by":"publisher","first-page":"896","DOI":"10.1016\/j.ejor.2021.11.029","volume":"301","author":"B Liu","year":"2022","unstructured":"Liu, B., & Papier, F. (2022). Remanufacturing of multi-component systems with product substitution. European Journal of Operational Research, 301(3), 896\u2013911. https:\/\/doi.org\/10.1016\/j.ejor.2021.11.029","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"6551_CR45","doi-asserted-by":"publisher","first-page":"561","DOI":"10.1016\/j.ejor.2018.08.029","volume":"273","author":"X Liu","year":"2019","unstructured":"Liu, X., Yang, T., Pei, J., Liao, H., & Pohl, E. A. (2019). Replacement and inventory control for a multi-customer product service system with decreasing replacement costs. European Journal of Operational Research, 273(2), 561\u2013574. https:\/\/doi.org\/10.1016\/j.ejor.2018.08.029","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"6551_CR46","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/s10479-017-2635-8","volume":"283","author":"EJ Lodree","year":"2019","unstructured":"Lodree, E. J., Altay, N., & Cook, R. A. (2019). Staff assignment policies for a mass casualty event queuing network. Annals of Operations Research, 283(1), 411\u2013442. https:\/\/doi.org\/10.1007\/s10479-017-2635-8","journal-title":"Annals of Operations Research"},{"key":"6551_CR47","doi-asserted-by":"publisher","unstructured":"Makoviychuk, V., Wawrzyniak, L., Guo, Y., Lu, M., Storey, K., Macklin, M., Hoeller, D., Rudin, N., Allshire, A., Handa, A., & State, G. (2021). Isaac gym: High performance GPU-based physics simulation for robot learning. https:\/\/doi.org\/10.48550\/arXiv.2108.10470. arXiv:2108.10470 [cs]","DOI":"10.48550\/arXiv.2108.10470"},{"key":"6551_CR48","unstructured":"Mirjalili, M. (2022). Data-driven modelling and control of hospital blood inventory. University of Toronto. https:\/\/tspace.library.utoronto.ca\/bitstream\/1807\/124976\/1\/Mirjalili_Mahdi_202211_PhD_thesis.pdf. Retrieved November 15, 2022"},{"issue":"10","key":"6551_CR49","doi-asserted-by":"publisher","first-page":"2048","DOI":"10.1111\/trf.17080","volume":"62","author":"M Mirjalili","year":"2022","unstructured":"Mirjalili, M., Abouee-Mehrizi, H., Barty, R., Heddle, N. M., & Sarhangian, V. (2022). A data-driven approach to determine daily platelet order quantities at hospitals. Transfusion, 62(10), 2048\u20132056. https:\/\/doi.org\/10.1111\/trf.17080","journal-title":"Transfusion"},{"issue":"2","key":"6551_CR50","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1080\/03155986.1975.11731604","volume":"13","author":"S Nahmias","year":"1975","unstructured":"Nahmias, S. (1975). A comparison of alternative approximations for ordering perishable inventory. INFOR, 13(2), 175\u2013184. https:\/\/doi.org\/10.1080\/03155986.1975.11731604","journal-title":"INFOR"},{"issue":"4","key":"6551_CR51","doi-asserted-by":"publisher","first-page":"735","DOI":"10.1287\/opre.23.4.735","volume":"23","author":"S Nahmias","year":"1975","unstructured":"Nahmias, S. (1975). Optimal ordering policies for perishable inventory-II. Operations Research, 23(4), 735\u2013749. https:\/\/doi.org\/10.1287\/opre.23.4.735","journal-title":"Operations Research"},{"issue":"4","key":"6551_CR52","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1287\/opre.30.4.680","volume":"30","author":"S Nahmias","year":"1982","unstructured":"Nahmias, S. (1982). Perishable inventory theory: A review. Operations Research, 30(4), 680\u2013708. https:\/\/doi.org\/10.1287\/opre.30.4.680","journal-title":"Operations Research"},{"key":"6551_CR53","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-7999-5","author":"S Nahmias","year":"2011","unstructured":"Nahmias, S. (2011). Perishable inventory systems. In International series in operations research & management science. Springer. https:\/\/doi.org\/10.1007\/978-1-4419-7999-5","journal-title":"In International series in operations research & management science. Springer."},{"issue":"3","key":"6551_CR54","doi-asserted-by":"publisher","first-page":"1580","DOI":"10.1007\/s11227-018-2692-z","volume":"75","author":"G Ortega","year":"2019","unstructured":"Ortega, G., Hendrix, E. M., & Garc\u00eda, I. (2019). A CUDA approach to compute perishable inventory control policies using value iteration. The Journal of Supercomputing, 75(3), 1580\u20131593. https:\/\/doi.org\/10.1007\/s11227-018-2692-z","journal-title":"The Journal of Supercomputing"},{"key":"6551_CR55","unstructured":"Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Kopf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., & Chintala, S. (2019). PyTorch: An imperative style, high-performance deep learning library. In Advances in neural information processing systems: Proceedings of the 33rd conference on neural information processing systems (NeurIPS 2019). https:\/\/papers.nips.cc\/paper\/2019\/hash\/bdbca288fee7f92f2bfa9f7012727740-Abstract.html. Retrieved from January 13, 2023."},{"key":"6551_CR56","doi-asserted-by":"publisher","DOI":"10.1016\/j.jedc.2020.103894","volume":"114","author":"A Peri","year":"2020","unstructured":"Peri, A. (2020). A hardware approach to value function iteration. Journal of Economic Dynamics and Control, 114, Article 103894. https:\/\/doi.org\/10.1016\/j.jedc.2020.103894","journal-title":"Journal of Economic Dynamics and Control"},{"key":"6551_CR57","doi-asserted-by":"publisher","unstructured":"Perumalla, K. & Alam, M. (2021). Design considerations for GPU-based mixed integer programming on parallel computing platforms. In Proceedings of the 50th international conference on parallel processing workshop (ICPP Workshops \u201821). https:\/\/doi.org\/10.1145\/3458744.3473366","DOI":"10.1145\/3458744.3473366"},{"key":"6551_CR58","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/j.cie.2017.05.021","volume":"110","author":"S Rajendran","year":"2017","unstructured":"Rajendran, S., & Ravindran, A. R. (2017). Platelet ordering policies at hospitals using stochastic integer programming model and heuristic approaches to reduce wastage. Computers & Industrial Engineering, 110, 151\u2013164. https:\/\/doi.org\/10.1016\/j.cie.2017.05.021","journal-title":"Computers & Industrial Engineering"},{"key":"6551_CR59","doi-asserted-by":"publisher","unstructured":"Ruiz, S., & Hern\u00e1ndez, B. (2015). A parallel solver for Markov decision process in crowd simulations. Proceedings of the Fourteenth Mexican International Conference on Artificial Intelligence (MICAI) (pp. 107\u2013116). https:\/\/doi.org\/10.1109\/MICAI.2015.23","DOI":"10.1109\/MICAI.2015.23"},{"key":"6551_CR60","unstructured":"Sargent, T.\u00a0J. & Stachurski, J. (2022). Dynamic programming on the GPU via JAX - QuantEcon Notes. https:\/\/notes.quantecon.org\/submission\/622ed4daf57192000f918c61\/comments. Retrieved January 24, 2023."},{"key":"6551_CR61","unstructured":"Sargent, T.\u00a0J. & Stachurski, J. (2024). Quantitative Economics with Python using JAX\u2014optimal savings II: Alternative algorithms. https:\/\/jax.quantecon.org\/opt savings 2.html. Retrieved from December 11, 2024."},{"key":"6551_CR62","unstructured":"Shen, M. (2024). How much is an Nvidia A100? https:\/\/modal.com\/blog\/nvidia-a100-price-article. Retrieved from December 11, 2024"},{"key":"6551_CR63","doi-asserted-by":"publisher","DOI":"10.1002\/9781119584445","volume-title":"Fundamentals of Supply Chain Theory","author":"LV Snyder","year":"2019","unstructured":"Snyder, L. V., & Shen, Z.-J. (2019). Fundamentals of Supply Chain Theory (2nd ed.). Wiley.","edition":"2"},{"key":"6551_CR64","doi-asserted-by":"publisher","unstructured":"Srimool, G., Uthayopas, P., & Pichitlamkhen, J. (2011). Speeding up a large logistics optimization problems using GPU technology. In Proceedings of the 8th electrical engineering\/electronics, computer, telecommunications and information technology (ECTI) association of Thailand\u2014Conference 2011 (pp. 450\u2013454). https:\/\/doi.org\/10.1109\/ECTICON.2011.5947872","DOI":"10.1109\/ECTICON.2011.5947872"},{"issue":"2","key":"6551_CR65","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1287\/opre.20.2.318","volume":"20","author":"SY Su","year":"1972","unstructured":"Su, S. Y., & Deininger, R. A. (1972). Generalization of White\u2019s method of successive approximations to periodic Markovian decision processes. Operations Research, 20(2), 318\u2013326. https:\/\/doi.org\/10.1287\/opre.20.2.318","journal-title":"Operations Research"},{"key":"6551_CR66","doi-asserted-by":"publisher","unstructured":"Sun, R., Sun, P., Li, J., & Zhao, G. (2019). Inventory cost control model for fresh product retailers based on DQN. In Proceedings of the 2019 IEEE international conference on big data (big data) (pp. 5321\u20135325). https:\/\/doi.org\/10.1109\/BigData47090.2019.9006424","DOI":"10.1109\/BigData47090.2019.9006424"},{"key":"6551_CR67","volume-title":"Reinforcement Learning: An Introduction (2nd edn)","author":"RS Sutton","year":"2018","unstructured":"Sutton, R. S., & Barto, A. G. (2018). Reinforcement Learning: An Introduction (2nd edn). The MIT Press."},{"key":"6551_CR68","unstructured":"United Nations (2022). The sustainable development goals report 2022. https:\/\/unstats.un.org\/sdgs\/report\/2022\/The-Sustainable-Development-Goals-Report-2022.pdf. Retrieved February 19, 2023"},{"issue":"2","key":"6551_CR69","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1016\/j.ejor.2019.08.035","volume":"281","author":"MA Voelkel","year":"2020","unstructured":"Voelkel, M. A., Sachs, A.-L., & Thonemann, U. W. (2020). An aggregation-based approximate dynamic programming approach for the periodic review model with random yield. European Journal of Operational Research, 281(2), 286\u2013298. https:\/\/doi.org\/10.1016\/j.ejor.2019.08.035","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"6551_CR70","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1016\/j.ejor.2017.06.068","volume":"265","author":"PC Yianni","year":"2018","unstructured":"Yianni, P. C., Neves, L. C., Rama, D., & Andrews, J. D. (2018). Accelerating Petri-Net simulations using NVIDIA graphics processing units. European Journal of Operational Research, 265(1), 361\u2013371. https:\/\/doi.org\/10.1016\/j.ejor.2017.06.068","journal-title":"European Journal of Operational Research"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-025-06551-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-025-06551-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-025-06551-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T08:18:11Z","timestamp":1757146691000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-025-06551-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,24]]},"references-count":70,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["6551"],"URL":"https:\/\/doi.org\/10.1007\/s10479-025-06551-6","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,24]]},"assertion":[{"value":"25 October 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no relevant financial or non-financial interests to declare.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}