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stochastic dynamic resource allocation for HIV prevention and treatment: An approximate dynamic programming approach

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 118卷 423-439页

作者： Cosgun, Ozlem Buyuktahtakin, I. Esra Wichita State Univ Dept Ind & Mfg Engn Wichita KS 67260 USA New Jersey Inst Technol Dept Mech & Ind Engn Newark NJ 07102 USA

Human immunodeficiency virus (HIV) is a key global health concern, with 33 million people living with HIV worldwide and 2.7 million new infections occurring annually. To prevent the spread of this widely prevalent epidemic disease, prevention and treatment intervention strategies urgently need to be implemented. The goal of this study is to propose stochastic dynamic programming (SDP) and approximate dynamic programming (ADP) algorithms that will optimally allocate the limited intervention budget among the HIV disease compartments and determine the best set of interventions that should be applied to each disease compartment, while minimizing the number of HIV-infected and people diagnosed with acquired immune deficiency syndrome (AIDS) as well as related deaths over a multi-year planning horizon. A compartmental model is constructed and formulated as a nonstationary Markov decision process (MDP) in order to capture the progression of the disease among the highest risk group-African American/black men who have sex with men (BMSM). In order to alleviate the computational difficulties arising from the exponentially growing state space in the SDP, we propose ADP algorithms that determine the approximately optimal budget allocation policies over six years. Our results suggest a greater allocation of the limited budget to prevention measures rather than treatment interventions, such as antiretroviral therapy (ART). As opposed to traditional policies that allocate the budget only once at the beginning of the time horizon, the ADP model suggests using a dynamic proportional budget strategy, allocating the budget dynamically over a multi-period planning period as the uncertainty in disease transmission is revealed. Results show that our ADP approach provides significant increases in health benefits and cost savings in HIV prevention and intervention.

关键词： HIV epidemic disease Resource allocation Interventions Approximate dynamic programming stochastic dynamic programming Disease transmission uncertainty Markov decision process (MDP)

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Strategy maps: Generalised giving-up densities for optimal foraging

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ECOLOGY LETTERS 2023年第3期26卷 398-410页

作者： Arehart, Emerson Reimer, Jody R. Adler, Frederick R. Univ Penn Dept Biol Philadelphia PA USA Univ Utah Sch Biol Sci Dept Math Salt Lake City UT USA Dept Biol 433 S Univ Ave Philadelphia PA 19104 USA

Finding a common currency for benefits and hazards is a major challenge in optimal foraging theory, often requiring complex computational methods. We present a new analytic approach that builds on the Marginal Value Theorem and giving-up densities while incorporating the nonlinear effect of predation risk. We map the space of all possible environments into strategy regions, each corresponding to a discrete optimal strategy. This provides a generalised quantitative measure of the trade-off between foraging rewards and hazards. This extends a classic optimal diet choice rule-of-thumb to incorporate the hazard of waiting for better resources to appear. We compare the dynamics of optimal decision-making for three foraging life-history strategies: One in which fitness accrues instantly, and two with delays before fitness benefit is accrued. Foragers with delayed-benefit strategies are more sensitive to predation risk than resource quality, as they stand to lose more fitness from a predation event than instant-accrual foragers.

关键词： diet choice giving up density landscape of fear Markov decision process optimal foraging stochastic dynamic programming

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dynamic hedging in incomplete markets using risk measures

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2022年第2期33卷 345-367页

作者： Gaillardetz, Patrice Hachem, Saeb Concordia Univ Dept Math & Stat Montreal PQ H3G 1M8 Canada

In this paper, we consider the pricing of financial derivatives that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), guaranteed investment certificates (GICs) and American and barrier options are typical examples of these products. Our exploration involves the use and comparison of alternative models that use risk measures. Although the hedging is done for each observation of the input stochastic process, the appropriate mix of risk measures and state dynamic equations helps the issuer to appropriately tailor the overall risk exercise. These different models are solved by a unified backward stochastic dynamic programming framework that we imbed with parametric techniques to shorten the running time and manage the curse of dimensionality in dynamic programming. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs. Finally, by using sampling techniques, optimal hedging strategies and specific indicators of the hedging performance, we make recommendations on how to fine tune the risk measure parameters.

关键词： partial hedging local risk-minimizing strategies stochastic dynamic programming linear programming parametric linear programming risk measures

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Robotic mobile fulfillment systems: a mathematical modelling framework for e-commerce applications

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2022年第11期60卷 3589-3605页

作者： Rimele, Adrien Gamache, Michel Gendreau, Michel Grangier, Philippe Rousseau, Louis-Martin Polytech Montreal Dept Math & Ind Engn Montreal PQ Canada CIRRELT Interuniv Res Ctr Enterprise Networks Logist & Tr Montreal PQ Canada GERAD Grp Res Decis Anal Montreal PQ Canada IVADO Labs Montreal PQ Canada

Robotic Mobile Fulfillment Systems (RMFSs) are a recent type of automated warehouse deployed in e-commerce. In this parts-to-picker system, a fleet of small robots is tasked with retrieving and storing shelves of items in the warehouse. Due to the nature of the e-commerce market, and the high flexibility of RMFSs, there are many opportunities to improve the productivity of the warehouse by optimising operational decisions. Online retailers promise extremely fast deliveries, which requires that new orders be included in the set of requests to fulfil as soon as they are revealed. For this reason, and because of the very dynamic nature of the robots' cycles, decision-making needs to be done in real time, in an uncertain environment. Because such a problem often lacks a formal description, we propose a mathematical framework that models the operational decisions taking place in an RMFS as a stochastic dynamic program. Our objective is to formalise optimisation opportunities, to allow researchers to develop more advanced methods in a well-defined environment. Embedded in a discrete event simulator, this model is illustrated by simulations to compare against standard storage decision rules.

关键词： warehouse e-commerce robotic mobile fulfillment system stochastic dynamic programming mathematical modelling simulations

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Fully polynomial time (Sigma, Pi)-approximation schemes for continuous nonlinear newsvendor and continuous stochastic dynamic programs

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MATHEMATICAL programming 2022年第1-2期195卷 183-242页

作者： Halman, Nir Nannicini, Giacomo Bar Ilan Univ Ramat Gan Israel IBM TJ Watson Res Ctr IBM Quantum Yorktown Hts NY USA

We study the nonlinear newsvendor problem concerning goods of a non-discrete nature, and a class of stochastic dynamic programs with several application areas such as supply chain management and economics. The class is characterized by continuous state and action spaces, either convex or monotone cost functions that are accessed via value oracles, and affine transition functions. We establish that these problems cannot be approximated to any degree of either relative or additive error, regardless of the scheme used. To circumvent these hardness results, we generalize the concept of fully polynomial-time approximation scheme allowing arbitrarily small additive and multiplicative error at the same time, while requiring a polynomial running time in the input size and the error parameters. We develop approximation schemes of this type for the classes of problems mentioned above. In light of our hardness results, such approximation schemes are "best possible". A computational evaluation shows the promise of this approach.

关键词： Newsvendor problem stochastic inventory control Hardness of approximation Approximation algorithms stochastic dynamic programming K -approximation sets and functions

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Co-optimizing Consumption and EV Charging under Net Energy Metering

Co-optimizing Consumption and EV Charging under Net Energy M...

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IEEE-Power-and-Energy-Society General Meeting (PESGM)

作者： Jeon, Minjae Tong, Lang Zhao, Qing Cornell Univ Sch Elect & Comp Engn Ithaca NY 14850 USA

ISBN: (纸本)9781665464413

We consider the co-optimization of flexible household consumption, electric vehicle charging, and behind -the meter distributed energy resources under the net energy metering tariff. Using a stochastic dynamic programming formulation, we show that the optimal co -optimization follows a procrastination threshold policy that delays and minimizes electricity purchasing for EV charging. The policy thresholds can be computed off-line, simplifying the continuous action space dynamic optimization. Empirical studies using renewable, consumption, and EV data demonstrate 30 c7t and 65 % improvements in customer surplus over the state-of-the-art for the typical 6 and 8 -hour scheduling horizons, respectively. The impacts of net energy metering parameters on the household surplus are also demonstrated.

关键词： EV charging distributed energy resources stochastic dynamic programming net energy metering

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A hybrid model based on fuzzy VIKOR and the classical optimal search to detect illegal chemical warehouses

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JOURNAL OF ENVIRONMENTAL SCIENCE AND HEALTH PART A-TOXIC/HAZARDOUS SUBSTANCES & ENVIRONMENTAL ENGINEERING 2022年第3期57卷 229-241页

作者： Sotoudeh-Anvari, Alireza Sadi-Nezhad, Soheil Islamic Azad Univ Dept Ind Engn Sci & Res Branch Tehran Iran Univ Waterloo Dept Stat & Actuarial Sci Waterloo ON Canada

The use of chemical weapons has turned into an increasing risk for the world. In this study, a hybrid approach on the basis of fuzzy VIKOR and the optimal search model to cope with an important case study called the detection of illegal chemical warehouses is introduced. It is obvious that such illegal activities are accomplished under high secret considerations. Therefore, we have several types of ambiguity and uncertainty in this problem. First, fuzzy VIKOR is used to prioritize the suspicious warehouses based on time and cost of a search under fuzzy environment. Also the probability of existence of chemical agents in each warehouse (P-i) and the probability of detection (alpha(i)) in case materials exist in warehouse, are estimated. Next, the output of VIKOR i.e., Q is assumed as an input of optimal search model and optimal strategy for searching is achieved by solving a stochastic dynamic programming. According to this hybrid approach, we start from the location that has the maximum value of alpha P-i(i)/Q(i). Although we get benefits of fuzzy logic, VIKOR, and classical optimal search, the suggested method is easy to understand and straightforward to utilize in real-world problems. Also this model can enhance the robust nature of hybrid approach and reduces its sensitivity to the change of weights.

关键词： Illegal chemical warehouses optimal search VIKOR fuzzy sets stochastic dynamic programming

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On the Optimality of Procrastination Policy for EV Charging under Net Energy Metering 62

On the Optimality of Procrastination Policy for EV Charging ...

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62nd IEEE Conference on Decision and Control (CDC)

作者： Jeon, Minjae Tong, Lang Zhao, Qing Cornell Univ Sch Elect & Comp Engn Ithaca NY 14853 USA

ISBN: (纸本)9798350301243

We address the problem of behind-the-meter EV charging by a prosumer, co-optimized with rooftop solar, electric battery, and flexible consumption devices such as water heaters and HVAC systems. We consider a scenario involving a time-of-use net energy metering tariff, alongside stochastic solar production and random EV charging demand, a finite-horizon surplus-maximization problem is formulated. We show that a procrastination threshold policy that delays EV charging to the last possible moment is optimal when EV charging is co-optimized with flexible demand, and the policy thresholds can be easily computed offline. When battery storage is part of the co-optimization, we show that the prosumer's net consumption is a two-threshold piecewise linear function of the behind-the-meter renewable generation under the optimal policy, and the procrastination threshold policy remains optimal, although the thresholds cannot be computed easily. We propose a straightforward myopic solution which becomes optimal strategy when the storage state of charge doesn't reach boundary, and demonstrate in a numerical simulation that involves real-world data.

关键词： EV charging distributed energy resources stochastic dynamic programming net energy metering

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A simple but powerful simulated certainty equivalent approximation method for dynamic stochastic problems

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QUANTITATIVE ECONOMICS 2023年第2期14卷 651-687页

作者： Cai, Yongyang Judd, Kenneth L. Ohio State Univ Dept Agr Environm & Dev Econ Columbus OH 43210 USA Stanford Univ Hoover Inst Stanford CA USA

We introduce a novel simulated certainty equivalent approximation (SCEQ) method for solving dynamic stochastic problems. Our examples show that SCEQ can quickly solve high-dimensional finite- or infinite-horizon, stationary or nonstationary dynamic stochastic problems with hundreds of state variables, a wide state space, and occasionally binding constraints. With the SCEQ method, a desktop computer will suffice for large problems, but it can also use parallel tools efficiently. The SCEQ method is simple, stable, and can utilize any solver, making it suitable for solving complex economic problems that cannot be solved by other algorithms.

关键词： stochastic dynamic programming competitive equilibrium large-scale model integrated assessment model new Keynesian model zero lower bound occasionally binding constraint nonstationary problem parallelism C61 C63 C68 Q54 Q58

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An evolutionary model of sensitive periods when the reliability of cues varies across ontogeny

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BEHAVIORAL ECOLOGY 2022年第1期33卷 101-114页

作者： Walasek, Nicole Frankenhuis, Willem E. Panchanathan, Karthik Radboud Univ Nijmegen Behav Sci Inst Thomas van Aquinostr 4 NL-6525 GD Nijmegen Netherlands Univ Utrecht Dept Psychol Heidelberglaan 1 NL-3584 CS Utrecht Netherlands Max Planck Inst Study Crime Secur & Law Gunterstalstr 73 D-79100 Freiburg Germany Univ Missouri Dept Anthropol 225 Swallow Hall Columbia MO 65211 USA

Sensitive periods are widespread in nature, but their evolution is not well understood. Recent mathematical modeling has illuminated the conditions favoring the evolution of sensitive periods early in ontogeny. However, sensitive periods also exist at later stages of ontogeny, such as adolescence. Here, we present a mathematical model that explores the conditions that favor sensitive periods at later developmental stages. In our model, organisms use environmental cues to incrementally construct a phenotype that matches their environment. Unlike in previous models, the reliability of cues varies across ontogeny. We use stochastic dynamic programming to compute optimal policies for a range of evolutionary ecologies and then simulate developmental trajectories to obtain mature phenotypes. We measure changes in plasticity across ontogeny using study paradigms inspired by empirical research: adoption and cross-fostering. Our results show that sensitive periods only evolve later in ontogeny if the reliability of cues increases across ontogeny. The onset, duration, and offset of sensitive periods-and the magnitude of plasticity-depend on the specific parameter settings. If the reliability of cues decreases across ontogeny, sensitive periods are favored only early in ontogeny. These results are robust across different paradigms suggesting that empirical findings might be comparable despite different experimental designs. Phenotypic plasticity, the ability to tailor development to different conditions, typically declines with age. However, some traits have sensitive periods, windows of heightened plasticity, at later life stages, such as adolescence. The evolution of such windows is not well understood. Using mathematical modeling we find that changes in the reliability of information available to developing organisms may influence when sensitive periods evolve. Specifically, when the reliability of information increases across ontogeny, sensitive periods evolve later.

关键词： cues development evolution modeling phenotypic plasticity sensitive periods stochastic dynamic programming

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