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Abstract
Abstract. This paper presents a method to establish the objective function of a network flow programming model for simulating river–reservoir system operations and associated water allocation, with an emphasis on situations when the links other than demand or storage have to be assigned with nonzero cost coefficients. The method preserves the priorities defined by rule curves of reservoir, operational preferences for conveying water, allocation of storage among multiple reservoirs, and transbasin water diversions. Path enumeration analysis transforms these water allocation rules into linear constraints that can be solved to determine link cost coefficients. An approach to prune the original system into a reduced network is proposed to establish the precise constraints of nonzero cost coefficients, which can then be efficiently solved. The cost coefficients for the water allocation in the Feitsui and Shihmen reservoirs' joint operating system of northern Taiwan was adequately assigned by the proposed method. This case study demonstrates how practitioners can correctly utilize network-flow-based models to allocate water supply throughout complex systems that are subject to strict operating rules.
Highlights
The allocation of water in river–reservoir systems usually involves a number of priority-based decisions, which include water rights, reservoir operating rules, commitments and negotiation between stakeholders, preferences for the conveyance of water and other requirements
This portion of water is ineffective to the objective function; the assigned link costs should be able to withstand these impacts to preserve the priorities of water allocation
Future research may extend to derive a comprehensive approach for more generalized linear programming (LP)-based models, accounting for all types of non-network flow programming (NFP) constraints that may be encountered in real-world applications
Summary
The allocation of water in river–reservoir systems usually involves a number of priority-based decisions, which include water rights, reservoir operating rules, commitments and negotiation between stakeholders, preferences for the conveyance of water and other requirements. As a specialization of LP, network flow programming (NFP) only focuses on solving a specific subset of general LP problems that can be formulated in a more restrictive format This loss of generality allows the resources allocation problem to be visually and precisely displayed by the network structure, and gains in return higher computational efficiency and easier comprehension of the priority-based allocation mechanism. Ferreira (2007) further broadened the scope for more general LP problems by demonstrating how different types of side constraints and variables in the LP formulation may affect the priorities defined by the cost coefficients of links in the NFP subset These previous works represented the priority requirement as a set of rules. This pruned procedure functions successfully to efficiently initialize an effective application of water allocation models
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