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   https://doi.org/10.1017/S0269964818000335  

   Feinberg, Eugene A.; Liang, Yan (April 2019, Probability in the Engineering and Informational Sciences)

   This paper studies a periodic-review single-commodity setup-cost inventory model with backorders and holding/backlog costs satisfying quasiconvexity assumptions. We show that the Markov decision process for this inventory model satisfies the assumptions that lead to the validity of optimality equations for discounted and average-cost problems and to the existence of optimal (s,S) policies. In particular, we prove the equicontinuity of the family of discounted value functions and the convergence of optimal discounted lower thresholds to the optimal average-cost lower threshold for some sequence of discount factors converging to 1. If an arbitrary nonnegative amount of inventory can be ordered, we establish stronger convergence properties: (i) the optimal discounted lower thresholds converge to optimal average-cost lower threshold; and (ii) the discounted relative value functions converge to average-cost relative value function. These convergence results previously were known only for subsequences of discount factors even for problems with convex holding/backlog costs. The results of this paper also hold for problems with fixed lead times. 

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2. SmartExchange: Trading Higher-cost Memory Storage/Access for Lower-cost Computation

   https://doi.org/10.1109/ISCA45697.2020.00082  

   Zhao, Yang; Chen, Xiaohan; Wang, Yue; Li, Chaojian; You, Haoran; Fu, Yonggan; Xie, Yuan; Wang, Zhangyang; Lin, Yingyan (May 2020, 2020 ACM/IEEE 47th Annual International Symposium on Computer Architecture (ISCA))
3. Cost Based Nonlinear Pricing

   https://doi.org/10.1145/3580507.3597697  

   Bergemann, Dirk; Heumann, Tibor; Morris, Stephen (July 2023, ACM)

   Hartline, Jason (Ed.)

   The arrival of digital commerce has lead to an increasing use of personalization and differentiation strategies. With differentiated products along the quality dimension and/or the quantity dimension comes the need for nonlinear pricing policies or second degree price discrimination. The optimal pricing strategies for quality and quantity differentiated products were first investigated by Mussa and Rosen (1978) and Maskin and Riley (1984), respectively. The optimal pricing strategies were shown to depend heavily on the prior distribution of the private information regarding the types, and ultimately the willingness-to-pay of the buyers. Yet, frequently the sellers possess only weak and incomplete information about the distribution of demand. This paper aims to develop robust pricing policies that are independent of specific demand distributions and provide revenue guarantees across all possible distributions. 

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4. Generalized Transportation Cost Spaces

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   Ostrovska, Sofiya; Ostrovskii, Mikhail I. (December 2019, Mediterranean Journal of Mathematics)

   null (Ed.)
5. Cost effective active search

   Jiang, Shali; Moseley, Benjamin; Garnet, Roman (January 2019, Advances in Neural Information Processing Systems)

   We study a special paradigm of active learning, called cost effective active search, where the goal is to find a given number of positive points from a large unlabeled pool with minimum labeling cost. Most existing methods solve this problem heuristically, and few theoretical results have been established. We adopt a principled Bayesian approach for the first time. We first derive the Bayesian optimal policy and establish a strong hardness result: the optimal policy is hard to approximate, with the best-possible approximation ratio lower bounded by Ω(n^0.16). We then propose an efficient and nonmyopic policy using the negative Poisson binomial distribution. We propose simple and fast approximations for computing its expectation, which serves as an essential role in our proposed policy. We conduct comprehensive experiments on various domains such as drug and materials discovery, and demonstrate that our proposed search procedure is superior to the widely used greedy baseline. 

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