Research Article: A linear bi-level multi-objective program for optimal allocation of water resources

Date Published: February 14, 2018

Publisher: Public Library of Science

Author(s): Ijaz Ahmad, Fan Zhang, Junguo Liu, Muhammad Naveed Anjum, Muhammad Zaman, Muhammad Tayyab, Muhammad Waseem, Hafiz Umar Farid, Yong Deng.


This paper presents a simple bi-level multi-objective linear program (BLMOLP) with a hierarchical structure consisting of reservoir managers and several water use sectors under a multi-objective framework for the optimal allocation of limited water resources. Being the upper level decision makers (i.e., leader) in the hierarchy, the reservoir managers control the water allocation system and tend to create a balance among the competing water users thereby maximizing the total benefits to the society. On the other hand, the competing water use sectors, being the lower level decision makers (i.e., followers) in the hierarchy, aim only to maximize individual sectoral benefits. This multi-objective bi-level optimization problem can be solved using the simultaneous compromise constraint (SICCON) technique which creates a compromise between upper and lower level decision makers (DMs), and transforms the multi-objective function into a single decision-making problem. The bi-level model developed in this study has been applied to the Swat River basin in Pakistan for the optimal allocation of water resources among competing water demand sectors and different scenarios have been developed. The application of the model in this study shows that the SICCON is a simple, applicable and feasible approach to solve the BLMOLP problem. Finally, the comparisons of the model results show that the optimization model is practical and efficient when it is applied to different conditions with priorities assigned to various water users.

Partial Text

The ever-increasing population growth and industrialization are putting constant pressure on water resources and it is more likely that the available water resources may not be able to meet the future water demands. The shortage of water resources has become more severe due to the uneven distribution of available water resources among various water demand sectors and is a major constraint to economic development in many countries around the world [1]. Conflicts among various water demand sectors often arise when these sectors compete for limited water resources. As a solution to these conflicts, earlier studies have developed optimization models for water allocation to achieve sustainable development, such as dynamic programming [2,3], genetic algorithms [4,5], and game theory approach [6]. However, these models are difficult to apply to practical water allocation issues because of their complex programming requirements to deal with discontinuous, multi-dimensional, non-differentiable, stochastic, uncertainty and non-convexity problems in solving multi-objective functions [7,8].

Bi-level programming issues are frequently found in the allocation of water resources among various water users [30]. The proposed model offers an insight into the economic, water supply and hydrologic interaction for water allocation to distinctive water users. In the present study, there are not only conflicts among the different water users but also between the water users and reservoir managers. Consequently, BLMOLP was evolved to optimally allocate the water resources among competing water users for sustainable economic development. The developed BLMOLP model is applied to a single reservoir by aggregating the releases from the reservoir for water allocation. However, the model structure may be improved by way of integrating parallel stems and can be applied to complex water resource networks or the model can be run separately for each reservoir in the network. The reservoir is fulfilling the irrigation water demands of the areas located right away downstream, however, the water shortages occur in the further downstream areas in the course of the dry seasons.

In this study, a bi-level multi-objective model has been developed for the optimal water allocation under the heirachical structure. The model consists of a ROM and a BLMOLP. The ROM estimates the AW for allocation in a dry seasoan, which is used as an input to the BLMOLP. The BLMOLP model allocates the AW based on the decisions made by the upper level DMs (i.e. leaders) and the lower level DMs (i.e. followers). The model has been applied to the Swat River basin of Pakistan for an optimal allocation of AW among competing water use sectors, i.e. irrigation, industry, domestic and environment. Different techniques have been used to estimate the NEB to water use in irrigation, domestic, industrial, hydropower, and environmental (salinity control) sectors. The NEB is as low as USD 5 per thousand m3 for hydropower sector to as high as USD 412 per thousand m3 for domestic use. The estimated NEB of water use in the agriculture sector is USD 78 per thousand m3. The environmental (salinity control) sector has a NEB of USD 7 per thousand m3.




0 0 vote
Article Rating
Notify of
Inline Feedbacks
View all comments