Minimum Spillage from Reservoirs using Mixed Integer Linear Programming

The use of the traditional linear programming is not possible when an if-condition is to be imposed on the model unless some modifications are made. The difficulty arises due to the fact that the inclusion of if-condition to the generic formulation of the linear programming and its mechanism called simplex method is not a trivial task. The mixed integer linear programming seems to be a good candidate to achieve this goal. However, two issues should be satisfied beforehand if one would like to minimize the spill. 1. the reservoir should be full up to the spillway crest level in order for the spillage to occur. 2. the next state of the reservoir after the spill has been occurred should be full as well. Adding binary integer variables to the model helps in achieving the optimal solution in terms of minimum sum of spillage without violating any of the underlying constraints. When the input to the model being altered, the results showed that the model can cope with the uncertainty inherent in any natural inflow process in terms of spillage minimization.

Automated summary

This article discusses the difficulties of adding if-condition to traditional linear programming models and proposes the use of mixed integer linear programming to address this issue, while also outlining the two prerequisites needed to minimize spillage.