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VALUING FIXED PRICE SUPPLY CONTRACTS

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1994年第1期74卷 50-60页

作者： KAMRAD, B RITCHKEN, P CASE WESTERN RESERVE UNIV WEATHERHEAD SCH MANAGEMENT DEPT OPERAT RES CLEVELAND OH 44119 USA

This article considers the problem of valuing a supply contract that requires the manufacturer to deliver fixed quantities of a product according to a predetermined schedule at fixed prices. Given that the raw material costs fluctuate randomly, the producer has capacity constraints, production costs depend on production rates, and that switching production rates result in additional charges, the problem is to establish an optimal production and inventory policy such that the schedule is met, and the value of the contract to the firm is maximized.

关键词： CONTINGENT CLAIMS ANALYSIS (CCA) WIENER PROCESSES ARBITRAGE ITOS LEMMA APPROXIMATING LATTICES stochastic dynamic programming

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Why do hoarding birds gain fat in winter in the wrong way? Suggestions from a dynamic model

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BEHAVIORAL ECOLOGY 2000年第1期11卷 27-39页

作者： Brodin, A Univ Lund Dept Ecol Div Theoret Ecol S-22362 Lund Sweden

In winter, small birds should be fat to avoid starvation and lean and agile to escape predators. This means that they face a tradeoff between the costs and benefits of carrying fat reserves. Every day they must gain enough fat to survive the coming night. Food-hoarding species can afford to carry less fat than nonhoarders because they can store energy outside the body. Furthermore, hoarders should avoid carrying excessive fat during the day because they can gain fat fast by retrieving food late in the afternoon. With no stored supplies, nonhoarders face more unpredictable access to food, and they should start gaining fat earlier in the day. The predicted pattern is then that nonhoarders gain fat early and that hoarders gain fat late in the day. Recent field data show the opposite pattern: hoarders gain relatively more fat reserves in the morning than nonhoarders do. Using a dynamic model that mimics the conditions in a boreal winter forest, I investigated under which conditions this pattern will arise. The only assumption of those investigated that produced this pattern was to relax the effect of mass-dependent predation risk. I did this by introducing a limit under which fat reserves did not affect predation risk. Hoarders then started the day by gaining fat in the morning. Later;when they had reached a safer (but still not risky) level, they switched to hoarding. The pattern I searched would only occur if either. not all food was possible to store, or if retrieval gave less energy than foraging in good weather conditions. If I assumed that low levels of body fat also increased predation risk, hoarders would cache in the morning when they carried least fat. I discuss empirical evidence for how body fat affects predation risk. In summary the factors that produced the pattern I searched were a change in the predation-mortality function combined with restrictions on hoarding.

关键词： dynamic modeling fat reserves food hoarding Paridae predation risk stochastic dynamic programming

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Economics of Integrated Insect Management in Stored Corn

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JOURNAL OF ECONOMIC ENTOMOLOGY 2010年第5期103卷 1896-1908页

作者： Yigezu, Yigezu A. Alexander, Corinne E. Preckel, Paul V. Maier, D. E. Mason, L. J. Woloshuk, C. Lawrence, J. Moog, D. J. Purdue Univ Dept Agr Econ W Lafayette IN 47907 USA Kansas State Univ Dept Grain Sci & Ind Manhattan KS 66506 USA Purdue Univ Dept Entomol W Lafayette IN 47907 USA Purdue Univ Dept Bot & Plant Pathol W Lafayette IN 47907 USA Purdue Univ Dept Agr & Biol Engn W Lafayette IN 47907 USA

Insects can cause substantial damage to stored grain. In addition, consumers and therefore food processors are increasingly interested in chemical-free products. Integrated pest management (IPM) may increase farmers' profits while reducing their use of pesticides. This study uses a stochastic dynamic programming framework to model the economics of optimal insect control in corn, Zea mays L., stored on-farm with multiple controls conditional on the biophysical conditions of the grain in the bin. We find that for farmers who have a contract with a food processor, where there are quality premiums, the optimal management strategy depends on monitoring the biophysical conditions of the grain and the time period under consideration. For farmers who deliver to the commodity market, their current practices are optimal.

关键词： insect management stored corn IPM stochastic dynamic programming

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A safety-first approach to dynamic cropping decisions

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EUROPEAN REVIEW OF AGRICULTURAL ECONOMICS 1997年第1期24卷 47-63页

作者： VanKooten, GC Young, DL Krautkraemer, JA WASHINGTON STATE UNIV PULLMANWA 99164

A risk-sensitive optimal flexible cropping plan for spring barley in southeastern Washington state is identified by stochastic dynamic programming. State transformation equations are determined from data generated by a process simulation model. Katoaka's safety-first criterion is proposed as an operational procedure for discounting payoff values for differential riskiness. Stronger short-run risk aversion leads to the use of more conservative optimal flexcrop strategies which require higher threshold spring soil moisture levels for cropping. The dynamically optimal barley flexcrop strategies generate similar expected net returns but decrease soil loss relative to a fixed winter wheat-fallow rotation;however, annual income risk increases.

关键词： stochastic dynamic programming Katoaka's safety-first criterion flexible cropping and soil loss process simulation models

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Availability maximization under partial observations

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OR SPECTRUM 2013年第3期35卷 691-710页

作者： Jiang, Rui Kim, Michael J. Makis, Viliam Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

In this paper, we propose a new model for availability maximization under partial observations for maintenance applications. Compared with the widely studied cost minimization models, few structural results are known about the form of the optimal control policy for availability maximization models. We consider a failing system with unobservable operational states. Only the failure state is observable. System deterioration is driven by an unobservable, continuous-time homogeneous Markov process. Multivariate condition monitoring data which is stochastically related to the unobservable state of the system is collected at equidistant sampling epochs and is used to update the posterior state distribution for decision making. Preventive maintenance can be carried out at any sampling epoch, and corrective maintenance is carried out upon system failure. The objective is to determine the form of the optimal control policy that maximizes the long-run expected average availability per unit time. We formulate the problem as an optimal stopping problem with partial information. Under standard assumptions, we prove that a control limit policy is optimal. A computational algorithm is developed, illustrated by numerical results.

关键词： Availability maximization Optimal stopping stochastic dynamic programming Partially observable system Control limit structure

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Optimization methods to solve adaptive management problems

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THEORETICAL ECOLOGY 2017年第1期10卷 1-20页

作者： Chades, Iadine Nicol, Sam Rout, Tracy M. Peron, Martin Dujardin, Yann Pichancourt, Jean-Baptiste Hastings, Alan Hauser, Cindy E. CSIRO GPO Box 2583 Brisbane Qld 4001 Australia Univ Melbourne Sch BioSci Parkville Vic 3010 Australia Queensland Univ Technol Sch Math Sci Brisbane Qld 4000 Australia Univ Calif Davis Dept Environm Sci & Policy Davis CA 95616 USA

Determining the best management actions is challenging when critical information is missing. However, urgency and limited resources require that decisions must be made despite this uncertainty. The best practice method for managing uncertain systems is adaptive management, or learning by doing. Adaptive management problems can be solved optimally using decision-theoretic methods;the challenge for these methods is to represent current and future knowledge using easy-to-optimize representations. Significant methodological advances have been made since the seminal adaptive management work was published in the 1980s, but despite recent advances, guidance for implementing these approaches has been piecemeal and study-specific. There is a need to collate and summarize new work. Here, we classify methods and update the literature with the latest optimal or near-optimal approaches for solving adaptive management problems. We review three mathematical concepts required to solve adaptive management problems: Markov decision processes, sufficient statistics, and Bayes' theorem. We provide a decision tree to determine whether adaptive management is appropriate and then group adaptive management approaches based on whether they learn only from the past (passive) or anticipate future learning (active). We discuss the assumptions made when using existing models and provide solution algorithms for each approach. Finally, we propose new areas of development that could inspire future research. For a long time, limited by the efficiency of the solution methods, recent techniques to efficiently solve partially observable decision problems now allow us to solve more realistic adaptive management problems such as imperfect detection and non-stationarity in systems.

关键词： Adaptive management Markov decision process MDP Partially observable Markov decision process POMDP stochastic dynamic programming Value of information Hidden Markov models Natural resource management Conservation

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Adaptive management for improving species conservation across the captive-wild spectrum

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BIOLOGICAL CONSERVATION 2016年 199卷 123-131页

作者： Canessa, Stefano Guillera-Arroita, Gurutzeta Lahoz-Monfort, Jose J. Southwell, Darren M. Armstrong, Doug P. Chades, Iadine Lacy, Robert C. Converse, Sarah J. Zool Soc London Inst Zool Regents Pk London England Univ Melbourne Sch BioSci Melbourne Vic 3010 Australia Massey Univ Inst Nat Resources Palmerston North New Zealand CSIRO Brisbane Qld Australia Chicago Zool Soc Brookfield IL USA US Geol Survey Patuxent Wildlife Res Ctr Laurel MD USA

Conservation of endangered species increasingly envisages complex strategies that integrate captive and wild management actions. Management decisions in this context must be made in the face of uncertainty, often with limited capacity to collect information. Adaptive management (AM) combines management and monitoring, with the aim of updating knowledge and improving decision-making over time. We provide a guide for managers who may realize the potential of AM, but are unsure where to start. The urgent need for iterative management decisions, the existence,of uncertainty, and the opportunity for learning offered by often highly controlled captive environments create favorable conditions for AM. However, experiments and monitoring may be complicated by small sample sizes, and the ability to control the system, including stochasticity and observability, may be limited toward the wild end of the spectrum. We illustrate the key steps to implementing AM in threatened species management using four case studies, including the management of captive programs for cheetah (Acinonyx jubatus) and whooping cranes (Grus americana), of a translocation protocol for Arizona cliffroses Purshia subintegra and of ongoing supplementary feeding of reintroduced hihi (Notiomystis cincta) populations. For each case study, we explain (1) how to clarify whether the decision can be improved by learning (i.e. it is iterative and complicated by uncertainty) and what the management objectives are;(2) how to articulate uncertainty via alternative, testable hypotheses such as competing models or parameter distributions;(3) how to formally define how additional information can be collected and incorporated in future management decisions. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Captive breeding Monitoring Reintroduction stochastic dynamic programming Translocation Uncertainty

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Subpopulation triage: How to allocate conservation effort among populations

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CONSERVATION BIOLOGY 2008年第3期22卷 656-665页

作者： McDonald-Madden, Eve Baxter, Peter W. J. Possingham, Hugh P. Univ Queensland Sch Integrat Biol Appl Environm Decis Anal Ctr Ctr Ecol Brisbane Qld 4072 Australia Univ Canberra CRC Invas Anim Canberra ACT 2601 Australia

Threatened species often exist in a small number of isolated subpopulations. Given limitations on conservation spending, managers must choose from strategies that range from managing just one subpopulation and risking all other subpopulations to managing all subpopulations equally and poorly, thereby risking the loss of all subpopulations. We took an economic approach to this problem in an effort to discover a simple rule of thumb for optimally allocating conservation effort among subpopulations. This rule was derived by maximizing the expected number of extant subpopulations remaining given n subpopulations are actually managed. We also derived a spatiotemporally optimized strategy through stochastic dynamicprogramming. The rule of thumb suggested that more subpopulations should be managed if the budget increases or if the cost of reducing local extinction probabilities decreases. The rule performed well against the exact optimal strategy that was the result of the stochastic dynamic program and much better than other simple strategies (e.g., always manage one extant subpopulation or half of the remaining subpopulation). We applied our approach to the allocation offunds in 2 contrasting case studies: reduction of poaching of Sumatran tigers (Panthera tigris sumatrae) and habitat acquisition for San Joaquin kitfoxes (Vulpes macrotis mutica). For our estimated annual budget for Sumatran tiger management, the mean time to extinction was about 32 years. For our estimated annual management budget for kitfoxes in the San Joaquin Valley, the mean time to extinction was approximately 24 years. Our framework allows managers to deal with the important question of how to allocate scarce conservation resources among subpopulations of any threatened species.

关键词： decision theory financial resource allocation optimal management rule of thumb stochastic dynamic programming Sumatran tiger San Joaquin kit fox threatened species

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Periodic review production models with variable capacity, random yield, and uncertain demand

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MANAGEMENT SCIENCE 1996年第1期42卷 130-137页

作者： Wang, YZ Gerchak, Y UNIV WATERLOO DEPT MANAGEMENT SCIWATERLOOON N2L 3G1CANADA

We investigate a production planning problem in a periodic review environment with variable production capacity, random yields, and uncertain demand. The implications of random yields and variable capacity for lot sizing previously have been explored separately, but not jointly. Many production environments are likely to be subject to both types of uncertainties. To minimize the total discounted expected costs (production, holding, and shortage costs), we formulate the problem as a stochastic dynamic program. For the finite-horizon problem, we prove that the objective function is quasi-convex and that the structure of the optimal policy is characterized by a single critical point for the initial stock level at each period. That is, if the initial stock is greater than this critical point, the optimal planned production is zero;Otherwise, it is greater than zero. Expressions for solving the critical point and the optimal planned production are obtained. We further show that the solution for the finite-horizon problem converges to that of the infinite-horizon problem.

关键词： inventory and production policies stochastic dynamic programming periodic review models

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A note on the economic management of inventory or resource under stochastic prices

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JOURNAL OF STATISTICAL PLANNING AND INFERENCE 2006年第3期136卷 1020-1038页

作者： Jia, SW Oregon State Univ Dept Stat Corvallis OR 97331 USA

The Markovian optimal policies are studied for the problem of economic inventory control or resource management in a finite time horizon. Under some conditions, in particular, when the prices are stochastic and there is a positive fixed setup cost K, the existence of {S, s}-type Markovian optimal management policies is proved. When K = 0, the optimal policies are of (S)-type, in which case a comparison is made between the optimal policies under stochastic and deterministic prices. It turns out that under stochastic prices the optimal policies should be more conservative in order to maximize the present value of expected revenue. (c) 2004 Elsevier B.V. All rights reserved.

关键词： iterated random maps K-concavity S-s optimal policy stochastic dynamic programming stochastic inventory model stochastic price model

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