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Scheduling the operation of thermal generating units involves the selection of units to be placed in operation and the allocation of the load among them- These two decisions must be taken so as to minimize the sum of tile startup, banking, and expected riming costs subject to the demand, spinning-reserve, and minimum down-time and up-time constraints and, sometimes, to the following two additional limitations: a unit should not be started up more than once a day; and no more than two units of the same plant should be started up simultaneously. This optimization problem is formulated in this paper as a mixed-integer nonlinear programming problem. Then, by following the Bender's approach, the problem is partitioned into a nonlinear and a pure-integer nonlinear programming problem- The First problem, which represents the economic dispatch problem, is not solved here. The second problem, usually called the unit commitment problem, is solved by a variational method and a branch-and-bound algorithm. Numerical results obtained for a network of ten generating units are presented.