Determine which plants to operate in each period to

Question

Formulate the following problem using linear disjunctions, variable indices, and stretch-cycle constraints.

The week is divided into n periods, and in each period t, dt megawatts of electricity must be generated.

Each power plant i generates at most qi megawatts while operating.

Once plant i is started, it must run for at least li periods, and once shut down, it must remain idle for at least li periods. The cost of producing one megawatt of power for one period at planti is gi, and the cost of starting up the plant is ci.

Determine which plants to operate in each period to minimize cost while meeting demand.

The schedule must follow a weekly cycle.

Indicate how to replace the variable indices with element constraints.

Hint: let yit = 1 if plant i operates in period t, and let the setup cost incurred by plant i in period t be c_iyi, t-1yit, where c_i01 = c_i and c_i00 = c_i01 = c_i11 = 0. 1