An application of parametric mixed‐integer linear programming to hydropower development

The problem consists in selecting the sites on the river where reservoirs and hydroelectric power plants are to be built and then determining the type and size of the projected installations. The solution obviously depends on the amount of money the utility is willing to invest, which itself is a function of what the new installations will produce. It is therefore necessary to solve the problem for all possible amounts of firm energy produced, since it is not known at the outset which production level the utility will select. This is done in the paper by a parametric mixed‐integer linear programming (MILP) method whose efficiency derives from the fact that the branch‐and‐bound algorithm for selecting the sites to be developed (and consuming most of the computer time) is solved a minimum number of times. Between the points where the MILP problem is solved, LP parametric analysis is applied.