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1. Aid Allocation for Camp‐Based and Urban Refugees with Uncertain Demand and Replenishments

   https://doi.org/10.1111/poms.13531  

   Azizi, Shima; Bozkir, Cem Deniz; Trapp, Andrew C.; Kundakcioglu, O. Erhun; Kurbanzade, Ali Kaan (June 2021, Production and Operations Management)

   null (Ed.)

   There are 26 million refugees worldwide seeking safety from persecution, violence, conflict, and human rights violations. Camp-based refugees are those that seek shelter in refugee camps, whereas urban refugees inhabit nearby, surrounding populations. The systems that supply aid to refugee camps may suffer from ineffective distribution due to challenges in administration, demand uncertainty and volatility in funding. Aid allocation should be carried out in a manner that properly balances the need of ensuring sufficient aid for camp-based refugees, with the ability to share excess inventory, when available, with urban refugees that at times seek nearby camp-based aid. We develop an inventory management policy to govern a camp’s sharing of aid with urban refugee populations in the midst of uncertainties related to camp-based and urban demands, and replenishment cycles due to funding issues. We use the policy to construct costs associated with: i) referring urban populations elsewhere, ii) depriving camp-based refugee populations, and iii) holding excess inventory in the refugee camp system. We then seek to allocate aid in a manner that minimizes the expected overall cost to the system. We propose two approaches to solve the resulting optimization problem, and conduct computational experiments on a real-world case study as well as on synthetic data. Our results are complemented by an extensive simulation study that reveals broad support for our optimal thresholds and allocations to generalize across varied key parameters and distributions. We conclude by presenting related discussions that reveal key managerial insights into humanitarian aid allocation under uncertainty. 

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2. Fridge Compiler: Optimal Circuits from Molecular Inventories

   https://doi.org/10.1007/978-3-031-42697-1_16  

   Wathieu, Lancelot; Smith, Gus; Ceze, Luis; Thachuk, Chris (September 2023, Proceedings of Computational Methods in Systems Biology. CMSB 2023.)

   Pang, J. (Ed.)

   Rationally designed molecular circuits describable by well-mixed chemical reaction kinetics can realize arbitrary Boolean function computation yet differ significantly from their electronic counterparts. The design, preparation, and purification of new molecular components poses significant barriers. Consequently, it is desirable to synthesize circuits from an existing “fridge” inventory of distinguishable parts, while satisfying constraints such as component compatibility. Heuristic synthesis techniques intended for large electronic circuits often result in non-optimal molecular circuits, invalid circuits that violate domain-specific constraints, or circuits that cannot be built with the current inventory. Existing “exact” synthesis techniques are able to find minimal feedforward Boolean circuits with complex constraints, but do not map to distinguishable inventory components. We present the Fridge Compiler, an SMT-based approach to find optimal Boolean circuits within a given molecular inventory. Empirical results demonstrate the Fridge Compiler’s versatility in synthesizing arbitrary Boolean functions using three different molecular architectures, while satisfying user-specified constraints. We showcase the successful synthesis of all 256 three-bit and 65,536 four-bit predicate functions using a large custom inventory, with worst-case completion times of only seconds on a modern laptop. In addition, we introduce a unique class of cyclic molecular circuits that cover a larger number of Boolean functions than their conventional counterparts over a common inventory, often with significantly smaller implementations. Importantly, and absent in previous approaches specific to molecular circuits, the Fridge Compiler is logically sound, complete, and optimal for the user-specified cost function and component inventory. 

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3. Robust Dynamic Pricing with Demand Learning in the Presence of Outlier Customers

   https://doi.org/10.1287/opre.2022.2280  

   Chen, Xi; Wang, Yining (April 2022, Operations Research)

   This paper studies a dynamic pricing problem under model misspecification. To characterize model misspecification, we adopt the ε-contamination model—the most fundamental model in robust statistics and machine learning. In particular, for a selling horizon of length T, the online ε-contamination model assumes that demands are realized according to a typical unknown demand function only for [Formula: see text] periods. For the rest of [Formula: see text] periods, an outlier purchase can happen with arbitrary demand functions. The challenges brought by the presence of outlier customers are mainly due to the fact that arrivals of outliers and their exhibited demand behaviors are completely arbitrary, therefore calling for robust estimation and exploration strategies that can handle any outlier arrival and demand patterns. We first consider unconstrained dynamic pricing without any inventory constraint. In this case, we adopt the Follow-the-Regularized-Leader algorithm to hedge against outlier purchase behavior. Then, we introduce inventory constraints. When the inventory is insufficient, we study a robust bisection-search algorithm to identify the clearance price—that is, the price at which the initial inventory is expected to clear at the end of T periods. Finally, we study the general dynamic pricing case, where a retailer has no clue whether the inventory is sufficient or not. In this case, we design a meta-algorithm that combines the previous two policies. All algorithms are fully adaptive, without requiring prior knowledge of the outlier proportion parameter ε. Simulation study shows that our policy outperforms existing policies in the literature. 

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4. STOCHASTIC SETUP-COST INVENTORY MODEL WITH BACKORDERS AND QUASICONVEX COST FUNCTIONS

   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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5. Optimal Policy for Inventory Management with Periodic and Controlled Resets

   https://doi.org/10.1287/msom.2022.0318  

   Lee, Yoon; Mintz, Yonatan; Aswani, Anil; Shen, Zuo-Jun Max; Yang, Cong (June 2025, Manufacturing & Service Operations Management)

   Problem definition: Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and dynamically optimizing endcap promotion duration in retail outlets. In this paper, we consider a set of sequential decision problems in which the decision maker must not only balance holding and shortage costs but discard all inventory before a fixed number of decision epochs with the option for an early inventory reset. Methodology/results: Finding optimal policies for these problems through dynamic programming presents unique challenges because of the nonconvex nature of the resulting value functions. Moreover, this structure cannot be readily analyzed even with extended convexity definitions, such as K-convexity. Managerial implications: Our key contribution is to present sufficient conditions that ensure the optimal policy has an easily interpretable structure, which generalizes the well-known [Formula: see text] policy from the operations management literature. Furthermore, we demonstrate that, under these rather mild conditions, the optimal policy exhibits a four-threshold structure. We then conclude with computational experiments, thereby illustrating the policy structures that can be extracted in various inventory management scenarios. Funding: This work was supported by the National Science Foundation [Grant CMMI-1847666] and the Division of Graduate Education [Grant DGE-2125913]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0318 . 

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