Performance bounds on optimal fixed prices

Cataloged from PDF version of article.We consider the problem of selling a fixed stock of items over a finite horizon when the buyers arrive following a Poisson process. We obtain a general lower bound on the performance of using a fixed price rather than dynamically adjusting the price. The bound is 63.21% for one unit of inventory, and it improves as the inventory increases. For the one-unit case, we also obtain tight bounds: 89.85% for the constantelasticity and 96.93% for the linear price-response functions. © 2013 Elsevier B.V. All rights reserved

Online Modified Greedy Algorithm for Storage Control under Uncertainty

This paper studies the general problem of operating energy storage under uncertainty. Two fundamental sources of uncertainty are considered, namely the uncertainty in the unexpected fluctuation of the net demand process and the uncertainty in the locational marginal prices. We propose a very simple algorithm termed Online Modified Greedy (OMG) algorithm for this problem. A stylized analysis for the algorithm is performed, which shows that comparing to the optimal cost of the corresponding stochastic control problem, the sub-optimality of OMG is bounded and approaches zero in various scenarios. This suggests that, albeit simple, OMG is guaranteed to have good performance in some cases; and in other cases, OMG together with the sub-optimality bound can be used to provide a lower bound for the optimal cost. Such a lower bound can be valuable in evaluating other heuristic algorithms. For the latter cases, a semidefinite program is derived to minimize the sub-optimality bound of OMG. Numerical experiments are conducted to verify our theoretical analysis and to demonstrate the use of the algorithm.Comment: 14 page version of a paper submitted to IEEE trans on Power System