We consider a model in which a consumer of a resource over several periods must pay a per unit charge for the resource as well as a peak charge. The consumer has the ability to reduce his consumption in any period at some given cost, subject to a constraint on the total amount of reduction possible. His problem is to decide in what periods to reduce his consumption to minimize the total cost of procuring the resource. We formulate this problem as a compact linear programming problem, and obtain structural properties of an optimal solution that enable its efficient solution.
Technical Report, Department of Engineering Science, University of Auckland, NZ, June 2013.