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Fixed-time schedules for the processing of jobs when service completions are not observable

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2005年第1期62卷 77-97页

作者： Glazebrook, KD Punton, EL Univ Edinburgh Sch Management Edinburgh EH8 9JY Midlothian Scotland

We argue the importance of studying service systems in which the successful completion of job/customer service cannot be observed contemporaneously. Military and other applications are cited. The allocation of a large amount of processing to a job may make its (unobservable) successful completion more likely but will impose a burden on other jobs awaiting service. A fixed-time schedule specifies both the order in which jobs should be processed and how much processing each should receive. The goal is to find schedules which maximise the total expected reward earned from all jobs served. While this problem is intractable in general, a range of characterisations of optimal fixed-time schedules is achieved for given scenarios. The development of effective heuristics is also discussed.

关键词： Gittins index restless bandit stochastic dynamic programming stochastic scheduling

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Reproductive skipping as an optimal life history strategy in the southern elephant seal, Mirounga leonina

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ECOLOGY AND EVOLUTION 2018年第18期8卷 9158-9170页

作者： Griffen, Blaine D. Brigham Young Univ Dept Biol Provo UT 84602 USA

Intermittent breeding by which organisms skip some current reproductive opportunities in order to enhance future reproductive success is a common life history trade-off among long-lived, iteroparous species. The southern elephant seal Mirounga leonina engages in intermediate breeding when body condition is low. While it is anticipated that this strategy may increase the lifetime reproductive output of this species, the conditions under which reproductive skipping are predicted to occur are not clear. Here I develop a dynamic state variable model based on published data that examines when southern elephant seals are predicted to optimally skip reproduction in order to maximize lifetime reproductive output as a function of current body mass, maternal age, and survivorship. I demonstrate that the optimal reproductive strategy for this species can include reproductive skipping, and that the conditions where this is optimal depend on patterns of mass-dependent adult female survival. I further show that intermittent breeding can increase lifetime reproductive output, and that the magnitude of this benefit increases with the ability of individual animals to replenish depleted body mass through foraging. Finally, I show that when the environment is variable and foraging is reduced in bad years, the benefit of adopting an optimal strategy that includes reproductive skipping increases asymptotically with the frequency of bad years. These results highlight the importance of characterizing the pattern of adult survival in this species, as well as the need to identify other factors that may influence the prevalence and benefits of reproductive skipping.

关键词： body mass dynamic state variable model individual heterogeneity intermittent breeding life history lifetime reproductive output marine mammal reproductive skipping stochastic dynamic programming survival

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A brokered market with heterogeneous suppliers and consumers

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JOURNAL OF APPLIED PROBABILITY 1999年第2期36卷 512-522页

作者： Righter, R Santa Clara Univ Dept Operat & Management Informat Syst Santa Clara CA 95053 USA

We consider a brokered market with heterogeneous suppliers and consumers of identical items or services. Each supplier determines a minimum acceptable price for the items it supplies, based on its costs and target rate of return. The broker begins with a fixed set of items from the suppliers. Customers arrive periodically to the market and offer a bid for an item. If a customer wants more than one item, a set of bids is made. If the broker accepts a bid it must be assigned an item with minimum accceptable price less than or equal to the bid, and the price paid is the bid price. The broker has the option of rejecting a bid. The broker makes acceptance and assignment decisions to maximize the total expected discounted revenue. We show the optimal policy has a simple threshold structure where thresholds can be easily determined by finding the individually optimal policies subject to priorities.

关键词： sequential assignment stochastic dynamic programming efficient markets heterogeneous markets

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Lazy Planning under Uncertainty by Optimizing Decisions on an Ensemble of Incomplete Disturbance Trees

Lazy Planning under Uncertainty by Optimizing Decisions on a...

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8th European Workshop on Reinforcement Learning

作者： Defourny, Boris Ernst, Damien Wehenkel, Louis Univ Liege Dept Elect Engn & Comp Sci B-4000 Liege Belgium

ISBN: (纸本)9783540897217

This paper addresses the problem of solving discrete-time optimal sequential decision making problems having a disturbance space W composed of a finite number of elements. In this context, the problem of finding from an initial state x(0) all optimal decision strategy can be stated as all optimization problem which aims at finding an optimal combination of decisions attached to the nodes of a disturbance tree modeling all possible sequences of disturbances w(0), w(1),..., W(T-1) C W(T) over the optimization horizon T. A significant drawback of this approach is that the resulting optimization problem has a search space which is the Cartesian product of O(vertical bar W vertical bar(T-1)) decision spaces U, which makes the approach computationally impractical as soon as the optimization horizon grows, even if W has just a handful of elements. To circumvent this difficulty, we propose to exploit an ensemble of randomly generated incomplete disturbance trees of controlled complexity, to solve. their induced optimization problems in parallel, and to combine their predictions at time t = 0 to obtain a (near-)optimal first-stage decision. Because this approach postpones the determination of the decisions for subsequent stages until additional information about the realization of the uncertain process becomes available, we. call it lazy. Simulations carried out on a robot corridor navigation problem show that even for small incomplete trees, this approach can lead to near-optimal decisions.

关键词： stochastic dynamic programming Ensemble methods

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Optimal Translocation Strategies for Threatened Species

Optimal Translocation Strategies for Threatened Species

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International Congress on Modelling and Simulation (MODSIM05)

作者： Rout, T. M. Hauser, C. E. Possingham, H. P. Univ Queensland Ctr Ecol Brisbane Qld 4072 Australia

ISBN: (纸本)9780975840023

Translocation-the deliberate, human-mediated movement of organisms-is a useful conservation tool most often employed in attempts to increase persistence of threatened or depleted species. Translocation projects involve difficult management decisions regarding the allocation of animals between sites. This research provides a rational scientific basis for these decisions. We use a stochastic population model and stochastic dynamic programming to determine optimal translocation strategies for theoretical populations, and apply this framework to a case study on the Bridled Nailtail Wallaby (Onychogalea fraenata). The translocation problem is defined as follows: in each time step of the translocation program, a set number of individuals are sourced from a captive population and translocated to two sites. Management decisions involve the allocation of these individuals between the two sites, over time. We use a first-order Markov chain stochastic population model to simulate each translocated population. This model follows females only, and does not consider age structure. Translocated populations A and B are limited by carrying capacities K-A and K-B, with population dynamics governed by Markov chain transition matrices A(A) and A(B). In the time step of their translocation, translocated individuals are governed by a separate transition matrix A(T) with a higher mortality rate and no reproduction. The stochastic dynamic Program (SDP) has three states: the number of individuals in the first site (n(A) = 0,...,K-A), the number of individuals in the second site (n(B) = 0,...,K-B), and the time period of the translocation project (t = 0,...,T). Populations can change state by natural processes-as captured in the transition matrices-or by receiving translocated individuals. With X individuals available in each time step, Population A receives d individuals and Population B receives X-d individuals. The SDP steps backwards from the terminal time T where the final reward, given

关键词： threatened and endangered species wildlife management translocation decision theory stochastic dynamic programming

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Valuing flexible operating strategies in nickel production under uncertainty 20

Valuing flexible operating strategies in nickel production u...

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20th International Congress on Modelling and Simulation (MODSIM)

作者： Bao, C. Mortazavi-Naeini, M. Northey, S. Tarnopolskaya, T. Monch, A. Zhu, Z. CSIRO Computat Informat Minerals Flagship Melbourne Vic Australia CSIRO Proc Sci & Engn Minerals Flagship Melbourne Vic Australia

ISBN: (纸本)9780987214331

With increasing global demand for nickel (which is a key component of stainless steel) the focus of mineral industry is currently on the abundant low-grade nickel laterite reserves. The extraction of nickel from the low-grade laterites is a technically difficult and expensive process and, as a result, the profitability of nickel production projects is highly affected by uncertainty over future market conditions. The project value can be increased by utilizing flexible operating strategies in response to changing future market conditions and Real Options analysis provides a suitable tool for optimizing flexible operating strategies over a long planning horizon in the face of uncertainty. This paper presents the first study on the valuation of flexible operating strategies in a realistic nickel laterite production system under uncertainty of nickel price and exchange rate. In this paper, the production of ore from the three hypothetical nickel laterite mines being fed to a central processing facility is studied. The common features of nickel laterite production, such as a two-fraction (limonite and saprolite) structure of the laterite ore body, layering of each fraction, with different ore grades (concentration of nickel) in each layer, and a simultaneous mining of several ore bodies, are incorporated into the model. It is common in the minerals industry that the ore from each mine is blended to provide as constant a feed rate and grade as possible to the processing facility. However, such a constant feed strategy may not generate the best financial return. In this paper, we investigate whether higher returns can be achieved by adopting a flexible strategy of switching, at prescribed intervals of time, between different feed rates of ore from the three mines that have different quality of nickel laterite. Such flexible strategy allows the operator to change the production rate of nickel in response to changing projected market conditions. In this paper, we use an appr

关键词： Real options stochastic dynamic programming Least Squares Monte Carlo (LSM) nickel laterite multiple mine-site operation genetic algorithm

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Optimization under uncertainty: state-of-the-art and opportunities

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COMPUTERS & CHEMICAL ENGINEERING 2004年第6-7期28卷 971-983页

作者： Sahinidis, NV Univ Illinois Dept Chem & Biomol Engn Urbana IL 61801 USA

A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space that is huge and frequently leads to very large-scale optimization models. Decision-making under uncertainty is often further complicated by the presence of integer decision variables to model logical and other discrete decisions in a multi-period or multi-stage setting. This paper reviews theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty. We discuss and contrast the classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming. The advantages and shortcomings of these models are reviewed and illustrated through examples. Applications and the state-of-the-art in computations are also reviewed. Finally, we discuss several main areas for future development in this field. These include development of polynomial-time approximation schemes for multi-stage stochastic programs and the application of global optimization algorithms to two-stage and chance-constraint formulations. (C) 2003 Elsevier Ltd. All rights reserved.

关键词： stochastic programming fuzzy programming stochastic dynamic programming global optimization approximation algorithms

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A modeling framework for optimizing the flow-level scheduling with time-varying channels

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PERFORMANCE EVALUATION 2010年第11期67卷 1014-1029页

作者： Ayesta, Urtzi Erausqum, Martin Jacko, Peter BCAM Bilbao 48170 Spain IKERBASQUE Basque Fdn Sci Bilbao 48011 Spain Univ Basque Country UPV EHU Bilbao Spain

We introduce a comprehensive modeling framework for the problem of scheduling a finite number of finite-length jobs where the available service rate is time-varying The main motivation comes from wireless data networks where the service rate of each user varies randomly due to fading We employ recent advances on the restless bandit problem that allow us to obtain an opportunistic scheduling rule for the system without arrivals When the objective is to minimize the mean number of users in the system or to minimize the mean waiting time, we obtain a priority-based policy which we call the Potential Improvement (PI) rule, since the priority index equals the ratio between the current available service rate and the expected potential improvement of the service rate We also show that for certain objective functions the index rule takes the form of known opportunistic scheduling rules like Relatively Best (RB) or Proportionally Best" (PB) Thus our model provides a formal justification for the deployment of opportunistic scheduling rules in order to improve the flow-level performance in the presence of time-varying capacities We further analyze the performance of the PI rule in the presence of randomly arriving users When the service rates are constant PI is equivalent to the c mu-rule which is known to be optimal with any distribution of arrivals Using a recent characterization for the stability region of flow-level scheduling rules under random arrivals we show that PI achieves the maximum stability region We perform numerical experiments in a wide range of scenarios and compare the performance of PI with other popular disciplines like RB PB Score-Based (SB) and the c mu-rule Our results show that RB PB SB or the c mu-rule might outperform the others depending on the scenario, but regardless of this the performance of PI is always superior or equivalent to the best of these opportunistic rules (C) 2010 Elsevier B V All rights reserved

关键词： Multi-armed restless bandit problem Markov Decision Process stochastic dynamic programming Opportunistic scheduling Optimal scheduling c mu-rule Index policy

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Assessing Operational Behaviour of a Hybrid Hydro-Solar Power Plant Providing Security of Supply Under Weather Uncertainty in the Nordics 20

Assessing Operational Behaviour of a Hybrid Hydro-Solar Powe...

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20th International Conference on the European Energy Market (EEM)

作者： Trondsen, Benjamin Johansen Steen, Oscar Martinius Host Sheppard, Alexandra Jane NTNU Dept Elect Energy Trondheim Norway

ISBN: (纸本)9798350381757;9798350381740

This paper presents a medium-term scheduling model of a hybrid hydro-solar power plant. The study examines how hybridization enhances the security of supply of a hydro-only system, particularly in Nordic weather conditions. A stochastic dynamic programming (SDP) algorithm is implemented to properly address the uncertainty of Nordic weather conditions and calculate water values. With solar power modeled as a photovoltaic (PV) installation, a hybrid system was created to optimize the load fulfillment. The results from the hybrid system were compared with the reference hydro-only system and an energy-upgraded hydro-only system using a creek inlet. The Ormsetfossen power plant, a Norwegian hydropower system with two reservoirs, is used as a reference for the data collection and topology modeling. Scenarios from 30 weather years of inflow and solar irradiation data were used to produce production plans for the hybrid and hydro-only configurations. Results indicate that hybridization enhances the security of supply to a greater extent than the energy-upgraded hydro-only system. The energy-upgraded hydro-only system is on the other hand more self-sufficient and less reliant on power imported from the market.

关键词： Hybrid power plants PV/hydro power plants uncertainty modeling stochastic dynamic programming hydropower scheduling optimization security of supply

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stochasticALLY MAXIMIZING THE NUMBER OF SUCCESSES IN A SEQUENTIAL ASSIGNMENT PROBLEM

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JOURNAL OF APPLIED PROBABILITY 1990年第2期27卷 351-364页

作者： RIGHTER, R Santa Clara University

In the classical sequential assignment problem as introduced by Derman et al. (1972) there are n workers who are to be assigned a finite number of sequentially arriving jobs. If a worker of value p is assigned a job of value x the return is px, where we interpret the return as the probability that the given worker correctly completes the given job. The job value is a random value that is observed upon arrival, and jobs must be assigned or rejected when they arrive. Each worker can only do one job. Derman et al. showed that when the objective is to maximize the expected return, i.e., the expected number of correctly completed jobs, the optimal policy is a simple threshold policy, which does not depend on the worker values. Their result was extended by Albright (1974) to allow job arrivals according to a Poisson process and a single random deadline for job completion (which is equivalent to discounting). Righter (1987) further extended the result to permit workers to have independent random deadlines for job completions. Here we show that when there are independent deadlines a simple threshold policy that is independent of the worker values stochastically maximizes the number of correctly completed jobs, and therefore maximizes the expected number of correctly completed jobs. We also show that there is no policy that stochastically maximizes the number of correctly completed jobs when there is a single deadline. However, when there is single deadline and the objective is to maximize the probability that n jobs are done correctly by n workers, then the optimal policy is determined by a single threshold that is independent of n and of the worker values.

关键词： SEQUENTIAL stochastic ASSIGNMENT stochastic dynamic programming RESOURCE ALLOCATION MULTIPROCESSOR SCHEDULING

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