Priority Preserving Unit Penalties in Network Flow Modeling

Abstract

A general algorithm is presented for determining values for unit cost coefficients that reflect water use priorities for network flow programming models of water resource systems. The overarching principle for setting unit penalties for priority-based operations is that senior unit penalties must exceed the combined junior unit penalties for any feasible competing space-time path through the system for any unit of water potentially available at the senior location. The algorithm accommodates both storage and flow related water uses over multiple periods and accounts for the effects of return flow on flow allocation, which can introduce a complexity that inhibits the use of intuitive or trial-and-error methods for determining cost coefficient values. The approach is formulated initially as a linear program that can be used as a preprocessor to the network flow modeling and is applied to a water-rights model of the Truckee-Carson system. The formulation is generalized for a location connectivity matrix and vector of use priorities.

Drought Water Right Curtailment Analysis for California’s Eel River

“…Appropriative water right priorities can be represented through cost coefficients, with junior lower-priority rights having lower penalties for shortage. Israel and Lund (1999), Ferreira (2007), and Chou and Wu (2014) extend this approach with algorithms for determining cost coefficients accounting for return flows.…”

Determination of cost coefficients of a priority-based water allocation linear programming model – a network flow approach

“…Some examples include CALSIM (Draper et al 2004), OASIS (Hydrologics, Inc., 2009) and WEAP (Stockholm Environment Institute, 2011. Nonetheless, the impacts of non-NFP features on water allocation have not been adequately discussed; only Israel and Lund (1999), Labadie andBaldo (2001), andFerreira (2007) have addressed this topic. Since non-NFP constraints must be strictly satisfied, they could be regarded as a higher level of priorities that would supersede and may disturb the priorities originally defined in the NFP subset as stated by Ferreira (2007).…”

“…These cost coefficients must reflect the flow priorities associated with demand or storage under predefined operating conditions. One straightforward way to achieve this is to assign decreasing unit costs for demand/storage links of higher priority to ensure that the highest priority stakeholder is satisfied first in the cost minimization problem (Israel and Lund, 1999). The costs of internal links other than demand or storage can be kept as zero, thus the allocation will be solely driven by the relative value of costs on the virtual links as shown in Fig.…”

“…The concept of developing a method for establishing cost coefficients of NFP models to adequately represent water allocation priorities was originally proposed by Israel and Lund (1999). 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.…”

Alternative Water Allocation in Kyrgyzstan: Lessons from the Lower Colorado River Basin and New South Wales

“…Modeling platforms have been used to simulate water allocation decisions [9][10][11][12][13][14][15][16][17][18][19][20][21]. The impact of transition from a top-down to a user-based participatory water management approach on water use efficiency and the reallocation of saved water from the first to the second crop was analyzed for the Akbura River basin using a two-stage stochastic linear programming that takes into account the probabilistic water availability.…”