A robust optimization for agricultural crops area planning and industrial production level in the presence of effluent trading

Abstract Suitable cropland use is not only beneficial for satisfying human daily demand, but also for controlling non-point source pollution leaks into adjacent rivers. Optimal industrial production levels are economical, and they also avoid water deterioration. With the promise of being lower than the total allowed emission cap, water use participants have to balance trade-offs between optimal production levels and emission amounts. Effluent trading seems to be a cost-effective method to reduce effluent emission as it allows effluent reallocation among different sectors. Because of changing hydrological information and continuous development of treatment technology, the effluent production ratio is regarded as uncertain and is characterized as polygonal budget sets. This study tries to control the total emission quantity by optimizing cropland use and non-agricultural production levels using effluent trading under uncertain future environments. To illustrate the feasibility of the proposed model, an application is conducted in Indonisian Citarum River. The application finds that the proposed model is able to (1) identify an optimal effluent trading scheme that balances various production plans from multiple water users; (2) balance the trade-off between total emission reduction and total benefit maximization by changing budget levels; and (3) ease the decision makers burden, avoid information losses or distortions, and guide them in adjusting farmland planning, production levels, and effluent trading results under uncertainty. Based on the results, managerial implications are analyzed in terms of (1) the optimal crop area planning in the agricultural sector and the optimal production level in non-agricultural sectors; and (2) the optimal effluent trading pattern that expands economic development without deteriorating water environments. Finally, the comparison analysis with a traditional deterministic model, verify that with the incorporation of robust parameters, flexible solutions are offered to decision makers that have different attitudes toward constraints-violation risks.