An Improved Solving Approach for Interval-Parameter Programming and Application to an Optimal Allocation of Irrigation Water Problem

In this study, an improved single-step method (SSM) is developed based on two-step method (TSM) to solve the interval-parameter linear programming (ILP) model of which the right-hand sides are highly uncertain. Two numerical examples are presented to ascertain appropriate value of λ in SSM. The risk preference degree of λ could be 0.8 for maximum objective function type. To demonstrate the applicability of the developed method, an agricultural water management problem has been provided in the case study section. The results show that SSM is more effective than TSM for complete solutions. There is only partial solution obtained from the first submodel of TSM, because the right-hand side of the wheat output constraint is highly uncertain. Finally, local farmers’ net benefit reaches to [8.949, 12.442] × 108 RMB (the unit of Chinese currency). The priority order of crops that are needed to be irrigated by surface water is maize > wheat > cotton.

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