Exploiting linear partial information for optimal use of forecasts: With an application to U.S. economic policy

Traditionally, the link between forecasting and decision making rests on the assumption of a known distribution for the future values of predicted variables. In practice, however, forecasts tend to offer little more than Linear Partial Information (LPI), typically of the form, ‘State 1 is more likely to prevail than state 2, and state 2 more likely to prevail than state 3, among five possible states’. This paper shows how such fuzzy LPI statements can be exploited in decision making. For an illustration, LPI analysis is used for determining (ex post) the optimal economic policy to be followed by the Carter Administration with a view to ensuring reelection in 1980. An optimal adaption of that policy occasioned by the fallible 1980 forecasts made by the Council of Economic Advisors is also derived.     

A simplified treatment of the theory of optimal regulation of Brownian motion

Consider a stochastic control problem where the state variable follows a Brownian motion. The flow reward is a function of the state, which can be regulated with a lump-sum and linear cost of adjustment. Using a discrete approximation, a simple exposition of the control problem is developed. The value matching conditions that hold for any given control parameters, and the smooth pasting conditions that hold for the optimal control are derived. Some extensions and economic applications of the method are also discussed.     

A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.     

Dynamic advertising and pricing with constant demand elasticities

In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman–Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting – when looking at (immediate) expected prices – is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.     

Periodic learning about a hidden state variable

In active learning models the value function is necessarily convex in the priors. Hence, in combination with a concave objective, the decision problem need not become concave so that nonregularity problems are inherent. This paper considers an objective that unambiguously implies a quasi-convex decision problem and highlights the effect of the inherent nonregularities on active learning. A trigger policy for learning is shown to be optimal: the minimum amount of learning is optimal until uncertainty surpasses a critical value. At this trigger point the maximum amount of learning is chosen, uncertainty falls temporarily, and the cycle then repeats itself.     

Stakeholder value analysis: a methodology for intergrating stakeholder values into corporate enviromental investment decisions

Increasingly, decision‐makers in industry are being faced with complex investment decisions created and made emotive by diverse stakeholder expectations. Investments with the potential to have an impact on a company's environmental performance are a prime example of this since they are driven by multidimensional impacts, many of which are difficult to quantify in scientific and monetary terms. This paper presents a stakeholder value analysis (SVA) model, which can be used to address such problems, using a multiple‐attribute decision methodology. This decision tool has been developed and validated through a series of industrial applications, one of which is outlined here. This application describes the use of the tool in a company context whereby stakeholders from within the company are canvassed for their priorities and views. The SVA tool is used not only to guide and support this process but also to analyse the data and consequently produce output decision metrics, which express the preferences of all relevant stakeholders and which can therefore be more confidently used to support the final decision. Copyright © 1999 John Wiley & Sons, Ltd and ERP Environment.     

On time-consistent policy rules for heterogeneous discounting programs

This article considers a new concept of social optimum for an economy populated by agents with heterogeneous discount factors. It is based upon an approach that constrains decision rules to be temporally consistent: these are stationary and unequivocally ruled by the state variable. For agents who differ only in their discount factors and have equal weights in the planner’s objective, the temporally-consistent optimal solution produces identical consumption for the agents at all time periods. In the long run, the capital stock is determined by a modified golden rule that corresponds to an average-like summation of all discount factors. The general argument is illustrated by various two-agent examples that allow for an explicit determination of the temporally consistent decision rules. Interestingly, this temporally consistent solution can be simply recovered from the characterization of a social planner’s problem with variable discounting and can also be decentralized as a competitive equilibrium through the use of various instruments.     

Transfer prices and incentive contracts in vertically-integrated divisionalized companies

This paper studies a divisionalized firm with sequential transfers in which central management wants to motivate two division managers who receive predecision information. Central management can only contract on the observables price, cost and quantity. Starting with the optimal compensation schemes as a benchmark, the paper considers the question whether using transfer prices to substitute for price and cost, respectively, can replicate the optimal solution or not. This is to say, whether using an aggregate measure comes at a loss. The results are dependent on the design constraints (i) single or ‘dual’ transfer prices and (ii) simultaneous design of the reward functions or exogenously given reward functions. Basically, only in the case that central management is restricted to given reward functions, and wants to use the same single transfer price for both divisions, there is a loss relative to the benchmark solution. In the other cases, generally, there is enough latitude to design the available functions to mimic the benchmark. The paper goes on to discuss special cases. First, it finds conditions when purely cost-based transfer prices are optimal, and second, it derives explicit solutions for given linear compensation schemes over divisional book profits.     

Modeling social,economic, and health perspectives for optimal pandemic policy decision-making

While different control strategies in the early stages of the COVID-19 pandemic have helped decrease the number of infections, these strategies have had an adverse economic impact on businesses. Therefore, optimal timing and scale of closure and reopening strategies are required to prevent both different waves of the pandemic and the negative economic impact of control strategies. This paper proposes a novel multi-objective mixed-integer linear programming (MOMILP) formulation, which results in the optimal timing of closure and reopening of states and industries in each state to mitigate the economic and epidemiological impact of a pandemic. The three objectives being pursued include: (i) the epidemiological impact, (ii) the economic impact on the local businesses, and (iii) the economic impact on the trades between industries. The proposed model is implemented on a dataset that includes 11 states, the District of Columbia, and 19 industries in the US. The solved by augmented ε-constraint approach is used to solve the multi-objective model, and a final strategy is selected from the set of Pareto-optimal solutions based on the least cubic distance of the solution from the optimal value of each objective. The Pareto-optimal solutions suggest that for any control decision (state and industry closure or reopening), the economic impact and the epidemiological impact change in the opposite direction, and it is more effective to close most states while keeping the majority of industries open during the planning horizon.     

Design considerations for neyman-pearson and wald hypothesis testing

Summary The Neyman-Pearson Lemma describes a test for two simple hypotheses that, for a given sample size, is most powerful for its level. It is usually implemented by choosing the smallest sample size that achieves a prespecified power for a fixed level. The Lemma does not describe how to select either the level or the power of the test. In the usual Wald decision-theoretic structure there exists a sampling cost function, an initial prior over the hypothesis space and various payoffs to right/wrong hypothesis selections. The optimal Wald test is a Bayes decision rule that maximizes the expected payoff net of sampling costs. This paper shows that the Wald-optimal test and the Neyman-Pearson test can be the same and how the Neyman-Pearson test, with fixed level and power, can be viewed as a Wald test subject to restrictions on the payoff vector, cost function and prior distribution.     

A model for IPO pricing and contract choice decision

This paper attempts to reconcile the average underpricing phenomenon with the expected wealth maximizing behaviors of market participants. Under the usual informational asymmetry, the optimal offer price for best efforts IPOs is derived as a function of the uncertainty about market’s valuation, the expected return on proposed projects and the size of offerings relative to the firm’s market value. According to these firm-specific characteristics, best efforts IPOs can be underpriced, fairly priced, or overpriced. Employing the investment banker as an outside information producer, the basic pricing model is extended to provide empirical implication for underwriting contract choice decision as well as for the pricing. Consistent with the existing empirical evidences, the model predicts that the issuers with greater uncertainty about market’s valuation choose best efforts contract over firm commitment contract and that the dispersion of initial returns would be greater for best efforts IPOs than for firm commitment IPOs.     

价值工程视角下产品功能——成本的最佳配比研究

产品功能和成本的最佳配比,是消费者和生产商所共同追求的理想状态。这一理想状态能否实现,又将如何实现呢?对此,该文引入价值工程分析法进行了分析和求证,并得出如下结论:产品功能和成本之间不仅存在最佳配比关系,而且最佳配比平衡点也能够通过求解得出,从而为保证产品必要功能前提下的成本控制提供了科学的依据。     

Ultimate 100‐m world records through extreme‐value theory

We use extreme‐value theory to estimate the ultimate world records for the 100‐m running, for both men and women. For this aim we collected the fastest personal best times set between January 1991 and June 2008. Estimators of the extreme‐value index are based on a certain number of upper order statistics. To optimize this number of order statistics we minimize the asymptotic mean‐squared error of the moment estimator. Using the thus obtained estimate for the extreme‐value index, the right endpoint of the speed distribution is estimated. The corresponding time can be interpreted as the estimated ultimate world record: the best possible time that could be run in the near future. We find 9.51 seconds for the 100‐m men and 10.33 seconds for the women.     

Convergence of optimal harvesting policies to a normal forest

This paper extends the forestry maximum principle of Heaps (1984) to allow the benefits of harvesting to be the utility of the volume of the wood harvested as in Mitra and Wan, 1985, Mitra and Wan, 1986. Unlike those authors, however, time is treated as a continuous rather than as a discrete variable. Existence of an optimal harvesting policy is established. Then necessary conditions are derived for the extended model which are also sufficient. The conditions are used to show that under certain boundedness conditions, sequences of optimal harvesting policies contain subsequences which converge pointwise a.e. and in net present value to an optimal harvesting policy. This result is then used to show that any optimal logging policy must converge in harvesting age to a constant rotation period given by modified Faustmann formula. The associated age class distribution converges to a normal forest.     

Learning by a dominant firm

This paper is concerned with the optimal output decisions of a dominant firm in the presence of imperfect information about the rival's reactions. The model is multi-period with the profits in each period being independent of those in other periods. Consequently, if the rival's reaction parameter were known to the dominant firm, a myopic policy would be optimal, In the presence of imperfect information about the rival's unknown reaction parameter, the dominant firm acts in a Bayesian manner by updating its prior distribution based on the observations of the rival's outputs. Because of the multiplicative shape of the rival's reaction function, the Bayesian updating rule is a function of the dominant firm's decision variable, i.e. its output decisions. This creates a dependence of the future value of the dominant firm on the present output decision, and hence a myopic policy is not, in general, optimal. It is shown that through output experimentation the dominant firm will tend to overproduce and, consequently, will increase its expected discounted profits (market value).     

基于确定当量的风险规避零售商最优订货决策分析

在报童模型的基础上,分析了风险规避对零售商订货决策造成的影响。比较了几种常用的供应链风险分析模型．认为确定当量法是一种更有效的分析方法。利用指数效用函数对风险进行定量处理．通过确定当量分析方法,将随机效用值转化为确定的效用值．从而将风险引入收益函数进行订货决策分析。同时,证明了零售商的风险规避将导致其最优订货量下降,而且随着零售商风险规避意愿的增强,最优订货量会不断减少。最后,通过数值实验,对风险中性和风险规避零售商的订货量进行了比较。     

Supporting others and the evolution of influence

In this paper we study environments in which agents can transfer influence to others by supporting them. When planning whom to support, they should take into account the future effect of this, since the receiving agent might use this influence to support others in the future. We show that in the presence of a finite horizon there is an essentially unique optimal support behavior which can be characterized in terms of associated marginal value functions. The analysis of these marginal value functions allows us to derive qualitative properties of optimal support strategies under different specific environments and to explicitly compute the optimal support behavior in some numerical examples. We also investigate the case of an infinite horizon. Examples show that multiple equilibria may appear in this setting, some of which sustaining a degree of cooperation that would not be possible under a finite horizon.     

Planning horizon results for the dynamic warehouse location problem

In the last decade, a number of models for the dynamic facility location problem have been proposed. The various models contain differing assumptions regarding the revenues and costs realized in the opening, operation, and closure of a facility as well as considering which of the facility sites are candidates for acquisition or disposal at the beginning of a time period. Since the problem becomes extremely large for practical applications, much of the research has been directed toward developing efficient solution techniques. Most of the models and solutions assume that the facilities will be disposed of at the end of the time horizon since distant future conditions usually can't be forecasted with any reasonable degree of accuracy. The problem with this approach is that the “optimal” solution is optimal for only one hypothesized post horizon facility configuration and may become nonoptimal under a different configuration. Post-optimality analysis is needed to assure management that the “optimal” decision to open or close a facility at a given point in time won't prove to be “nonoptimal” when the planning horizon is extended or when design parameters in subsequent time periods change. If management has some guarantee that the decision to open or close a facility in a given time period won't change, it can safely direct attention to the accuracy of the design parameters within that time period.This paper proposes a mixed integer linear programming model to determine which of a finite set of warehouse sites will be operating in each time period of a finite planning horizon. The model is general in the sense that it can reflect a number of acquisition alternatives—purchase, lease or rent. The principal assumptions of the model are: a) Warehouses are assumed to have infinite capacity in meeting customer demand, b) In each time period, any non-operating warehouse is a candidate for becoming operational, and likewise any operating warehouse is a candidate for disposal, c) During a given time period, the fixed costs of becoming operational at a site are greater than the disposal value at that site to reflect the nonrecoverable costs involved in operating a warehouse. These costs are separate from the acquisition and liquidation values of the site. d) During a time period the operation of a warehouse incurs overhead and maintenance costs as well as a depreciation in the disposal value.To solve the model, it is first simplified and a partial optimal solution is obtained by the iterative examination by both lower and upper bounds on the savings realized if a site is opened in a given time period. An attempt is made to fix each warehouse open or closed in each time period. The bounds are based on the delta and omega tests proposed by Efroymson and Ray (1966) and Khumawala (1972) with adjustment for changes in the value of the warehouse between the beginning and end of a time period. A complete optimal solution is obtained by solving the reduced model with Benders' decomposition procedure. The optimal solution is then tested to determine which time periods contain “tentative” decisions that may be affected by post horizon data by analyzing the relationship between the lower (or upper) bounds used in the model simplification time period. If the warehouse decisions made in a time period satisfy these relationships and are thus unaffected by data changes in subsequent time periods, then the decisions made in earlier time periods will also be unaffected by future changes.     

Analyzing judicial discrimination

When an individual is treated in a judicial decision in a way that is affected by his race, socioeconomic status or some other legally irrelevant characteristic, he is subjected to discrimination. In this paper, various methods for analyzing discrimination of this type are discussed. Mathematically, the severity of a correct decision can be seen as a function of various characteristics of the individual and his behavior. It is argued that in ordinary cases the form of this function must be known for any analysis of discrimination to be possible. A method is presented for the analysis when the function has linear form but unknown structure.     

变样本容量比例控制图设计及应用

针对单边休哈特比例控制图失控状态下平均报警时间长的问题,提出一种单边变样本容量比例控制图来监控两个正态变量间比例的偏移。采用马尔可夫链方法计算了该控制图的平均运行链长。在保证过程处于受控状态的统计性能基础上,使失控状态下的平均运行链长最小,从而获得控制图的最优决策变量和最优性能指标。仿真结果表明,单边变样本容量比例控制图的性能明显优于单边休哈特比例控制图。最后将该方法应用于港口皮带机配煤比例监控的问题,通过仿真实验说明了该方法能够对煤炭配比过程中的比例偏移做出有效反应。