Interactive Multiple Criteria Programming Applied to Wide Area Water Supply Scheduling

Abstract

We propose a hybrid method using interactive multiple criteria programming and minimum cost flow analysis to make a useful schedule for waterworks. In case of constructing a mathematical model, it is difficult to adjust the model parameters in the actual application, and to make the user satisfied with the solution under the predetermined parameters. In our research, the parameters are generated automatically based on the abstract plan, in which interactive multiple criteria programming is employed, and then the minimum cost flow is calculated under the generated parameters.
Flexible water supply scheduling is indispensable to assign water using the limited facilities efficiently in various situations. Traditionally, it is a common approach to formulate the minimum cost flow problem to make a schedule. However, good modeling is an essential premise to make a useful plan to distribute water, and elaborate work is necessary for good modeling. It is also difficult to adjust the solution, reflecting the user's aspiration. Multiple criteria programming(MCP) has been proposed to overcome these disadvantages of single-objective optimization. Nevertheless, it is not quite effective to apply MCP to large-scale problem like water supply scheduling because of complexity and formulation difficulty. Using our proposed method, the whole problem can be divided into two parts. In abstract planning, interactive multiple criteria programming is applied to extract the user's request for the intake flow amount by using aspiration levels. Then, cost coefficients of the multi-layered network model are generated automatically based on the abstract plan. Since the minimum cost flow is defined as the flow which can nearly reproduce the abstract plan and minimize the deviation of flow rate, resulting minimum cost flow can satisfy requirements of both reservoir level recovery and flow smoothing. As a result, the proposed method can make an applicable schedule quickly, reflecting the user's aspiration flexibly.