We develop the first algorithmic approach to compute provably good ordering policies for a multiperiod, capacitated, stochastic inventory system facing stochastic nonstationary and correlated demands that evolve over time. Our approach is computationally efficient and guaranteed to produce a policy with total expected cost no more than twice that of an optimal policy. As part of our computational approach, we propose a novel scheme to account for backlogging costs in a capacitated, multiperiod environment. Our cost-accounting scheme, called the forced marginal backlogging cost-accounting scheme, is significantly different from the period-by-period accounting approach to backlogging costs used in dynamic programming; it captures the long-term impact of a decision on system performance in the presence of capacity constraints. In the likely event that the per-unit order costs are large compared to the holding and backlogging costs, a transformation of cost parameters yields a significantly improved guarantee. We also introduce new semimyopic policies based on our new cost-accounting scheme to derive bounds on the optimal base-stock levels. We show that these bounds can be used to effectively improve any policy. Finally, empirical evidence is presented that indicates that the typical performance of this approach is significantly stronger than these worst-case guarantees.

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We study a fundamental model of resource allocation in which a finite amount of service capacity must be allocated to a stream of jobs of different priorities arriving randomly over time. Jobs incur costs and may also cancel while waiting for service. To increase the rate of service, overtime capacity can be used at a cost. This model has application in healthcare scheduling, server applications, make-to-order manufacturing systems, general service systems, and green computing. We present an online algorithm that minimizes the total cost due to waiting, cancellations and overtime capacity usage. We prove that our scheduling algorithm has cost at most twice of an optimal offline algorithm. This competitive ratio is the best possible for this class of problems. We also provide extensive numerical experiments to test the performance of our algorithm and its variants.