
<div> <div> In classic adversarial online resource allocation problems, such as matching, AdWords, or assortment planning, customers (demand) arrive online, while products (supply) are given offline with a fixed initial inventory. To ensure acceptable revenue guarantees given the uncertainty in future customer arrivals, the decision maker must balance consumption across different products. Motivated by this, the prevalent policy "<i>inventory balancing (IB)" </i>is introduced and studied in the literature and has proved to be optimal or near-optimal competitive in almost all classic settings. However, an important feature that these classic models do not capture are various forms of possible <i>inventory shocks</i> on the supply side, which plays an important role in several real-world applications of online assortment and could significantly impact the revenue performance of the IB algorithm. </div> <div> <br> </div> <div> Motivated by this paradigm, we introduce and study a new variant of online assortment planning with inventory shocks. Our model considers both adversarial exogenous shocks (where supply increases over time in unpredictable fashion) and allocation-coupled endogenous shocks (where an inventory reduction is triggered by the algorithms and is re-adjusted after a usage duration)---combination of which can cause non-monotonic inventory fluctuations. As our main result, we show the robustness of the inventory balancing strategy against inventory shocks and such fluctuations by designing a new family of optimal competitive IB-type algorithms, called <i>Batched Inventory Balancing (BIB)</i>. We develop a novel randomized primal-dual method to bound the competitive ratio of our BIB algorithm against any feasible policy. We show that with the proper choice of a certain parameter, this competitive ratio is asymptotically optimal and converges to (1-1/e) as the initial inventories converge to infinity---in contrast to the original IB which no longer achieves the optimal competitive ratio in this new model. Moreover, we characterize BIB's competitive ratio in its general form (parametric by the penalty function it uses) and show that it matches <i>exactly</i> the competitive ratio of IB in the special case without shocks. To this end, we use a refined analysis that reduces the dual construction to a combinatorial problem called the "interval assignment problem." Our solution to this problem is algorithmic and might be of independent interest. </div> </div>
Computer Science and Game Theory, FOS: Computer and information sciences, Data Structures and Algorithms, Online assortment planning, Online matching, Primal-dual algorithm, Reusable resources, Data Structures and Algorithms (cs.DS), Computer Science and Game Theory (cs.GT)
Computer Science and Game Theory, FOS: Computer and information sciences, Data Structures and Algorithms, Online assortment planning, Online matching, Primal-dual algorithm, Reusable resources, Data Structures and Algorithms (cs.DS), Computer Science and Game Theory (cs.GT)
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