Large customers in many electric distribution utilities must enter into demand contracts for the ensuing year for defining contracted demand. Customer demand charge equals contracted demand billed at contracted tariff if the peak demand is less than the contracted demand, and, if not, the excess is billed at the uncontracted tariff. Both scenarios lead to economic loss for the customer, as the uncontracted tariff is much higher than the contracted tariff. Further, optimization of demand contracts is also important for utilities, as they plan and operate their system to satisfy customer peak demand. If under planned, it leads to technical challenges, and otherwise, it leads to economic loss. This challenge of determining the best demand to be contracted is known as the demand cost optimization problem and would save US$ 38 billion globally to customers. This work describes the problem through a graphical approach and proposes three mathematical models to find the optimum demand even in the presence of intermittent renewable generation. Each model is verified through a case study and an exhaustive study with 7,000 large customers from a Brazilian utility. The formulations are easily implementable and have the potential to assist large customers and utilities with planning studies.