The assessment of the sustainability of agricultural systems is multidimensional in nature and requires holistic measures using indicators with different measurements and units reflecting social, economic, and environmental aspects. To simplify the assessment process, various indicators have different units, and measurements are grouped under broad indicator heads, and normalization and/or transformation processes are carried out in order to aggregate them. In this study, a total of 50 indicators from agricultural sustainability categories of productivity, stability, efficiency, durability, compatibility, and equity are employed to investigate which normalization technique is the most suitable for further mathematical analysis for developing a final composite indicator. To understand the consistency and quality of normalization measurement techniques and compare the benefits and drawbacks of the various selected normalization processes, the indicators of agricultural sustainability are considered. Each of the different techniques for normalization has advantages and drawbacks. This study shows that the proportionate normalization and hybrid aggregation rules of the arithmetic mean and the geometric mean are appropriate for the selected data set, and that this technique has a wider applicability for developing composite indicators for agricultural sustainability assessment.

A new method is proposed for long-term reservoir operation planning with stochastic inflows. In particular, the problem is formulated as a two-stage stochastic linear program with simple recourse. The stochastic inflows are approximated by multiple inflow scenarios, leading to a very large deterministic model which is hard to solve using conventional optimization methods. This paper presents an efficient interior-point optimization algorithm for solving the resulting deterministic problem. It is also shown how exploiting the problem structure enhances the performance of the algorithm. Application to regulation of the Great Lakes system shows that the proposed approach can handle the stochasticity of the inflows as well as the nonlinearity of the operating conditions in a real-world reservoir system.