# American Institute of Mathematical Sciences

April  2007, 3(2): 313-320. doi: 10.3934/jimo.2007.3.313

## On an optimal control policy for stormwater management in two connected dams

 1 School of Mathematical Sciences, The University of Adelaide, Australia SA 5005, Australia 2 Centre for Industrial and Applied Mathematics, Mawson Lakes Campus, University of South Australia, Mawson Lakes, 5095, Australia, Australia

Received  September 2006 Revised  January 2007 Published  April 2007

We consider the management of water in two connected dams. Stormwater generated by rainfall flows into a large capture dam and is subsequently pumped to a smaller supply dam. We use a discrete state space and assume random supply and daily demand. A simple management policy is to pump as much water as possible each day from the capture dam to the supply dam without allowing the supply dam to overflow. We shall refer to this policy as pump-to-fill. We will show that pump-to-fill minimizes overflow from the system and maximizes the amount of demand met thus providing the optimal pumping policy between a pair of discrete dams in series with a general input and demand process.
Citation: C.E.M. Pearce, J. Piantadosi, P.G. Howlett. On an optimal control policy for stormwater management in two connected dams. Journal of Industrial & Management Optimization, 2007, 3 (2) : 313-320. doi: 10.3934/jimo.2007.3.313
 [1] Phil Howlett, Julia Piantadosi, Paraskevi Thomas. Management of water storage in two connected dams. Journal of Industrial & Management Optimization, 2007, 3 (2) : 279-292. doi: 10.3934/jimo.2007.3.279 [2] Jun Li, Hairong Feng, Kun-Jen Chung. Using the algebraic approach to determine the replenishment optimal policy with defective products, backlog and delay of payments in the supply chain management. Journal of Industrial & Management Optimization, 2012, 8 (1) : 263-269. doi: 10.3934/jimo.2012.8.263 [3] Shuhua Zhang, Xinyu Wang, Hua Li. Modeling and computation of water management by real options. Journal of Industrial & Management Optimization, 2018, 14 (1) : 81-103. doi: 10.3934/jimo.2017038 [4] Andrew J. Whittle, Suzanne Lenhart, Louis J. Gross. Optimal control for management of an invasive plant species. Mathematical Biosciences & Engineering, 2007, 4 (1) : 101-112. doi: 10.3934/mbe.2007.4.101 [5] Térence Bayen, Marc Mazade, Francis Mairet. Analysis of an optimal control problem connected to bioprocesses involving a saturated singular arc. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 39-58. doi: 10.3934/dcdsb.2015.20.39 [6] Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014 [7] Jianbin Li, Ruina Yang, Niu Yu. Optimal capacity reservation policy on innovative product. Journal of Industrial & Management Optimization, 2013, 9 (4) : 799-825. doi: 10.3934/jimo.2013.9.799 [8] Ambros M. Gleixner, Harald Held, Wei Huang, Stefan Vigerske. Towards globally optimal operation of water supply networks. Numerical Algebra, Control & Optimization, 2012, 2 (4) : 695-711. doi: 10.3934/naco.2012.2.695 [9] Zhengyan Wang, Guanghua Xu, Peibiao Zhao, Zudi Lu. The optimal cash holding models for stochastic cash management of continuous time. Journal of Industrial & Management Optimization, 2018, 14 (1) : 1-17. doi: 10.3934/jimo.2017034 [10] Ximin Huang, Na Song, Wai-Ki Ching, Tak-Kuen Siu, Ka-Fai Cedric Yiu. A real option approach to optimal inventory management of retail products. Journal of Industrial & Management Optimization, 2012, 8 (2) : 379-389. doi: 10.3934/jimo.2012.8.379 [11] Qian Zhao, Zhuo Jin, Jiaqin Wei. Optimal investment and dividend payment strategies with debt management and reinsurance. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1323-1348. doi: 10.3934/jimo.2018009 [12] Xiaoming Yan, Ping Cao, Minghui Zhang, Ke Liu. The optimal production and sales policy for a new product with negative word-of-mouth. Journal of Industrial & Management Optimization, 2011, 7 (1) : 117-137. doi: 10.3934/jimo.2011.7.117 [13] Jianxiong Zhang, Zhenyu Bai, Wansheng Tang. Optimal pricing policy for deteriorating items with preservation technology investment. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1261-1277. doi: 10.3934/jimo.2014.10.1261 [14] John Leventides, Iraklis Kollias. Optimal control indicators for the assessment of the influence of government policy to business cycle shocks. Journal of Dynamics & Games, 2014, 1 (1) : 79-104. doi: 10.3934/jdg.2014.1.79 [15] Veena Goswami, Gopinath Panda. Optimal information policy in discrete-time queues with strategic customers. Journal of Industrial & Management Optimization, 2019, 15 (2) : 689-703. doi: 10.3934/jimo.2018065 [16] Guodong Yi, Xiaohong Chen, Chunqiao Tan. Optimal pricing of perishable products with replenishment policy in the presence of strategic consumers. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1579-1597. doi: 10.3934/jimo.2018112 [17] Yiling Chen, Baojun Bian. optimal investment and dividend policy in an insurance company: A varied bound for dividend rates. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 5083-5105. doi: 10.3934/dcdsb.2019044 [18] Yiling Chen, Baojun Bian. Optimal dividend policy in an insurance company with contagious arrivals of claims. Mathematical Control & Related Fields, 2019, 0 (0) : 0-0. doi: 10.3934/mcrf.2020024 [19] Luis F. Gordillo. Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population. Mathematical Biosciences & Engineering, 2014, 11 (3) : 511-521. doi: 10.3934/mbe.2014.11.511 [20] Ruopeng Wang, Jinting Wang, Chang Sun. Optimal pricing and inventory management for a loss averse firm when facing strategic customers. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1521-1544. doi: 10.3934/jimo.2018019

2018 Impact Factor: 1.025