To address the problem of optimal allocation of water resources in water shortage areas, a reservoir and a pumping station water resource optimal scheduling model under the condition of insufficient irrigation is proposed. The model takes the maximum relative yield of crops as the objective function, the amount of water supplied, water spilled and the water replenished as decision variables, the total amount of water supplied by the system, the water right of the pumping station and the operation criteria as constraints, and uses the dynamic programming method to solve the model. The optimal water supply and water spill process of the irrigation reservoir and the optimal water replenishment process of the pumping station during the entire growth period of dry crops were obtained. Moreover, under the condition of 50 and 75% probability of exceedance, the optimized relative yields of crops increased by 17.1% and 19.6% respectively. The results show that ensuring the optimal operation of joint water source projects can achieve the optimal allocation of limited water resources, and improve the relative yield of crops in irrigation areas, which has important guiding significance for the planning and management of water resources in similar irrigation areas.

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In humid regions with the monsoon climate, seasonal water shortages and water spills occur alternately because of uneven temporal and spatial distributions of water resources. An optimization model for the in-series reservoir (ISR) with replenishment pumping stations was developed to obtain the minimum annual sum of water shortage and systematically considered the reservoir operation rule of water spill and replenishment. This model features multiple dimensions; dynamic programming (DP) may cause a ‘curse of dimensions’, while the decomposition-coordination method has difficulty in judging logic conditions in the reservoir operation rules. So, an improved decomposition and DP aggregation (DDPA) method was proposed. The proposed model and the method were applied to a real case in the humid region of southern China. Compared to a conventional scheduling method, the water supply was increased by 0.8% and replenishment was reduced by 2.5%. Moreover, a comparison between DDPA and six heuristic algorithms was discussed. All heuristic algorithms' objective function values only obtained local optimal solutions, and the water shortage of the system was 0.12–20.5%. The obtained results demonstrated that DDPA was the better choice for highly complex multi-reservoir systems. The proposed optimization algorithm of this study enriched the optimization theory of multi-dimensional and multi-variable complex systems.

Double-reservoir-and-double-pumping-station systems are commonly used for irrigation water supply in hilly regions of southern China. An optimization model for this water supply system is proposed to minimize water shortage. The model features few coupling constraints, including available water in the system and pumping volume limited by regional water rights. Dynamic programming was adopted to solve the subsystem and aggregation models. The results with the model and that with the standard operation policy were compared; the total water shortage was reduced by 87.7%, total water replenishment from outside was reduced by 2.2%, and total water spill was reduced by 60.6% for a system in Nanjing, China. The method may provide a reference for optimal operation of water supply systems comprising reservoirs and pumping stations.

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