A system and method for determining minimum operation and startup for a generator are described herein. A method and system according to the invention may include assigning a binary value to one or more commitment status variables each associated with an increment of time. The method and system may also assign a binary value to a time-dependent startup status variable. The method and system may implement the following constraints. The startup status variable minus the current commitment variable plus the subsequent previous commitment status variable is greater than or equal to zero, the startup status variable plus the subsequent previous commitment status variable is less than or equal to one, and the startup status variable minus the current commitment status variable is less than or equal to zero. The method and system may also include a constraint that a sum of all commitment status variables is greater than or equal to the product of the startup status variable and a minimum time-on variable wherein the minimum time-on variable is equal to a minimum operation time for the generator.