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We develop a variant of the multinomial logit model with impatient customers and study assortment optimization and pricing problems under this choice model. In our choice model, a customer incrementally views the assortment of available products in multiple stages. The patience level of a customer determines the maximum number of stages in which the customer is willing to view the assortments of products. In each stage, if the product with the largest utility provides larger utility than a minimum acceptable utility, which we refer to as the utility of the outside option, then the customer purchases that product right away. Otherwise, the customer views the assortment of products in the next stage as long as the customer’s patience level allows the customer to do so. Under the assumption that the utilities have the Gumbel distribution and are independent, we give a closed-form expression for the choice probabilities. For the assortment-optimization problem, we develop a polynomial-time algorithm to find the revenue-maximizing sequence of assortments to offer. For the pricing problem, we show that, if the sequence of offered assortments is fixed, then we can solve a convex program to find the revenue-maximizing prices, with which the decision variables are the probabilities that a customer reaches different stages. We build on this result to give a 0.878-approximation algorithm when both the sequence of assortments and the prices are decision variables. We consider the assortment-optimization problem when each product occupies some space and there is a constraint on the total space consumption of the offered products. We give a fully polynomial-time approximation scheme for this constrained problem. We use a data set from Expedia to demonstrate that incorporating patience levels, as in our model, can improve purchase predictions. We also check the practical performance of our approximation schemes in terms of both the quality of solutions and the computation times. 

Performing inference on pre-trained neural network models must meet the requirement of low-latency, which is often at odds with achieving high throughput. Existing deep learning systems use batching to improve throughput, which do not perform well when serving Recurrent Neural Networks with dynamic dataflow graphs. We propose the technique of cellular batching, which improves both the latency and throughput of RNN inference. Unlike existing systems that batch a fixed set of dataflow graphs, cellular batching makes batching decisions at the granularity of an RNN "cell" (a subgraph with shared weights) and dynamically assembles a batched cell for execution as requests join and leave the system. We implemented our approach in a system called BatchMaker. Experiments show that BatchMaker achieves much lower latency and also higher throughput than existing systems.