  The current formulation of the optimal scheduling of appliance energy
consumption uses as optimization variables the vectors of appliances' scheduled
energy consumption over equally-divided time slots of a day, which does not
take into account the atomicity of appliances' operations (i.e., the
unsplittable nature of appliances' operations and resulting energy
consumption). In this paper, we provide a new formulation of atomic scheduling
of energy consumption based on the optimal routing framework; the flow
configurations of users over multiple paths between the common source and
destination nodes of a ring network are used as optimization variables, which
indicate the starting times of scheduled energy consumption, and optimal
scheduling problems are now formulated in terms of the user flow
configurations. Because the atomic optimal scheduling results in a
Boolean-convex problem for a convex objective function, we propose a successive
convex relaxation technique for efficient calculation of an approximate
solution, where we iteratively drop fractional-valued elements and apply convex
relaxation to the resulting problem until we find a feasible suboptimal
solution. Numerical results for the cost and peak-to-average ratio minimization
problems demonstrate that the successive convex relaxation technique can
provide solutions close to, often identical to, global optimal solutions.
