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 present an efficient linear programming formulation for the demand response of such a consumer who could be a price taker, industrial or commercial user of electricity that has some ability to self-generate. We will establish a monotonicity result that indicates fuel supply of S, utilized for self generation, may be spent in successive steps adding to S in total.