Optimization of demand response through peak shaving

We consider a consumer of a resource, such as electricity, who must pay a per unit charge to procure the resource, as well as a peak demand charge. We will assume that this consumer has some ability to self-generate and present an efficient linear programming formulation for the demand response of such a consumer. We will establish a monotonicity result that indicates fuel supply of SS, utilized for self-generation, may be spent in successive steps adding to SS.