The paper investigates the influence of tolerating the shortage of energy supplies on the economy of cogeneration systems in consideration of energy demands as random variables. To make a reasonable investigation into the influence, an optimal unit sizing method proposed by the authors is adopted after it is extended to this case so that it enables probability distributions of energy demands to be considered. In the method, equipment capacities and maximum contract demands of utilities such as electricity and natural gas are determined so as to minimize the expected value of the annual total cost in consideration of operational strategies for all the estimated energy demands under the toleration for the shortage of energy supplies. Numerical studies are carried out on cogeneration systems installed in a hotel or an office building with changing shortage rates of energy supplies as parameters. Through the studies, it is found that the expected systems＇ economy is improved even if the shortage rates of energy supplies are very small, and that the improvement for the office building is larger than that for the hotel.