Demonstration of probabilistic ordinal optimization concepts for continuous-variable optimization under uncertainty

A very general and robust approach to solving optimization problems involving probabilistic uncertainty is through the use of Probabilistic Ordinal Optimization. At each step in the optimization problem, improvement is based only on a relative ranking of the probabilistic merits of local design alternatives, rather than on precise quantification of the alternatives. Thus, we simply ask the question: “Is that alternative better or worse than this one?” to some level of statistical confidence we require, not: “HOW MUCH better or worse is that alternative to this one?”. In this paper we illustrate an elementary application of probabilistic ordinal concepts in a 2-D optimization problem. Two uncertain variables contribute to uncertainty in the response function. We use a simple Coordinate Pattern Search non-gradient-based optimizer to step toward the statistical optimum in the design space. We also discuss more sophisticated implementations, and some of the advantages and disadvantages versus other approaches to optimization under uncertainty.     

Quality-driven recovery decisions for used components in reverse logistics

Reverse logistics has emerged as a promising strategy for enhancing environmental sustainability through remanufacturing, reusing, or recycling used components. It is crucial to pursue quality-driven decision-making for component recovery because quality is a dominant factor for component salvage value and its recoverability. To maximise the profit from component recovery, a quality-driven decision model was proposed in this study. Remaining useful life (RUL) was utilised as a measure of quality in the proposed model, where conditional RUL distribution was predicted by utilising both the failure data and condition monitoring data based on a proportional hazard model. Under RUL uncertainty, an interval decision-making approach was developed to suggest recovery strategies for the decision-makers to identify a satisfactory solution according to their risk preferences. Compared to the existing approaches for quality-driven recovery decision-making based on RUL prediction, this work provides a more accurate and powerful approach to managing and mitigating decision risk. Numerical experiments demonstrated the effectiveness and superiority of the proposed model.     

Summary from the epistemic uncertainty workshop: consensus amid diversity

The ‘Epistemic Uncertainty Workshop’ sponsored by Sandia National Laboratories was held in Albuquerque, New Mexico, on 6–7 August 2002. The workshop was organized around a set of Challenge Problems involving both epistemic and aleatory uncertainty that the workshop participants were invited to solve and discuss. This concluding article in a special issue of Reliability Engineering and System Safety based on the workshop discusses the intent of the Challenge Problems, summarizes some discussions from the workshop, and provides a technical comparison among the papers in this special issue. The Challenge Problems were computationally simple models that were intended as vehicles for the illustration and comparison of conceptual and numerical techniques for use in analyses that involve: (i) epistemic uncertainty, (ii) aggregation of multiple characterizations of epistemic uncertainty, (iii) combination of epistemic and aleatory uncertainty, and (iv) models with repeated parameters. There was considerable diversity of opinion at the workshop about both methods and fundamental issues, and yet substantial consensus about what the answers to the problems were, and even about how each of the four issues should be addressed. Among the technical approaches advanced were probability theory, Dempster–Shafer evidence theory, random sets, sets of probability measures, imprecise coherent probabilities, coherent lower previsions, probability boxes, possibility theory, fuzzy sets, joint distribution tableaux, polynomial chaos expansions, and info-gap models. Although some participants maintained that a purely probabilistic approach is fully capable of accounting for all forms of uncertainty, most agreed that the treatment of epistemic uncertainty introduces important considerations and that the issues underlying the Challenge Problems are legitimate and significant. Topics identified as meriting additional research include elicitation of uncertainty representations, aggregation of multiple uncertainty representations, dependence and independence, model uncertainty, solution of black-box problems, efficient sampling strategies for computation, and communication of analysis results.     

基于成本的职能型组织决策体制模型选择

一个企业的组织是由若干个职能部门组成的。为了降低组织的决策成本,建立了度量决策成本的模型,该模型的成本与用来进行决策的信息振荡相关。该模型给出了在不同的情况下选择决策模式的方法。该模型显示：在系统振荡比个别振荡大得多的情况下,如果对部门之间的协调要求比较高,则适宜采用同化信息体制,如部门之间的竞争关系大于协调要求,则采用信息异化体制;相反,在个别振荡比系统振荡大得多的情况下,采用分权体制成本更低。在系统振荡与个别振荡相差不大的情况下,如对部门之间的协调要求比较高,则适宜采用水平体制,反之信息分散化体制成本较低。     

Newsvendor decisions under supply uncertainty

We analyse the impact of supply uncertainty on newsvendor decisions. First, we derive a solution for a newsvendor facing stochastic supply yield, in addition to stochastic demand. While earlier research has considered independent uncertainties, we derive the optimal order quantity for interdependent demand and supply and provide a closed-form solution for a specific copula-based dependence structure. This allows us to give insights into how dependence impacts the newsvendor’s decision, profit and risk level. In addition to the theory, we present experimental results that show how difficult newsvendor decisions under supply uncertainty are for human subjects. In our experiment, the control group replicated a well-known newsvendor experiment, whereas the test group faced additional supply yield uncertainty. Comparison of these results shows that under low-profit condition, subjects are able to incorporate supply uncertainty quite well in their decisions. Under high-profit condition, the deviation from the optimum is much more significant. We discuss this asymmetry and also propose some ways to improve newsvendor decision-making.     

疫情演变不确定情境下考虑多参考点的应急医疗用品生产决策模型

针对疫情演变不确定情境下考虑多种决策信息和企业社会责任的应急医疗用品生产决策问题，提出一种基于累积前景理论的考虑多个参考点的应急医疗用品生产决策模型。综合考虑企业经济目标和社会责任对生产决策的影响，基于决策者的风险规避、参考依赖和损失厌恶等心理特征，建立多个参考点以表征疫情演变方向不确定时决策者期望的不确定性。将含有多种评价信息的决策矩阵归一化处理，利用不同演变方向的参考点，建立益损决策矩阵。根据决策者面对收益和损失的态度，建立主观价值矩阵，依据主观概率函数得到扭曲后演变方向的概率。计算各个生产方案的累积前景值并对其进行优先排序。通过算例验证模型的有效性，进行对比分析和敏感性分析证明模型的优越性。     

Solving black box computation problems using expert knowledge theory and methods

The challenge problems for the Epistemic Uncertainty Workshop at Sandia National Laboratories provide common ground for comparing different mathematical theories of uncertainty, referred to as General Information Theories (GITs). These problems also present the opportunity to discuss the use of expert knowledge as an important constituent of uncertainty quantification. More specifically, how do the principles and methods of eliciting and analyzing expert knowledge apply to these problems and similar ones encountered in complex technical problem solving and decision making? We will address this question, demonstrating how the elicitation issues and the knowledge that experts provide can be used to assess the uncertainty in outputs that emerge from a black box model or computational code represented by the challenge problems. In our experience, the rich collection of GITs provides an opportunity to capture the experts' knowledge and associated uncertainties consistent with their thinking, problem solving, and problem representation. The elicitation process is rightly treated as part of an overall analytical approach, and the information elicited is not simply a source of data. In this paper, we detail how the elicitation process itself impacts the analyst's ability to represent, aggregate, and propagate uncertainty, as well as how to interpret uncertainties in outputs. While this approach does not advocate a specific GIT, answers under uncertainty do result from the elicitation.     

Selective critique of risk assessments with recommendations for improving methodology and practise

Risk assessments are often criticised for defending activities that could harm the environment and human health. The risk assessments produce numbers which are used to prove that the risk associated with the activity is acceptable. In this way, risk assessments seem to be a tool generally serving business. Government agencies have based their regulations on the use of risk assessment and the prevailing practise is supported by the regulations. In this paper, we look more closely into this critique. Are risk assessments being misused or are risk assessments simply not a suitable tool for guiding decision-making in the face of risks and uncertainties? Is the use of risk assessments not servicing public interests? We argue that risk assessments may provide useful decision support but the quality of the risk assessments and the associated risk assessment processes need to be improved. In this paper, three main improvement areas (success factors) are identified and discussed: (1) the scientific basis of the risk assessments needs to be strengthened, (2) the risk assessments need to provide a much broader risk picture than what is typically the case today. Separate uncertainty analyses should be carried out, extending the traditional probabilistic-based analyses and (3) the cautionary and precautionary principles need to be seen as rational risk management approaches, and their application would, to a large extent, be based on risk and uncertainty assessments.     

Science and sustainability: who knows best?

Sustainability is a worthy ideal. Deciding between the priorities associated with the sustainable development needed to work towards sustainability, specific objectives to be met, methods for meeting them and criteria for success will be governed primarily by politics, perspective and probably power. Effective decision-making, however, involves identifying and deciding between a variety of options, assessing the existing state of knowledge, uncertainty and ignorance and the time that might be needed usefully to improve knowledge and reduce uncertainty. It also requires objectivity, open-mindedness, scepticism and clarity of thought. Knowledge is necessary (but not sufficient) for rational decision-making. Some knowledge (but not all) relates to a developing understanding of the physical and natural world, i.e. scientific knowledge. Are there absolutes in this knowledge? With what authority can (or should) science speak? Is science too much confused with technology and its application? How should critical scientific and technological controversies be resolved? To what extent should decision-making/adjudication be based on a democratic process or on rational judgement by experts? How can a balance between these be achieved and be made acceptable? What happens when scientists become activists? How can science and democracy be reconciled? The issues raised by these questions will be discussed.     

Combining the cost of reducing uncertainty with the selection of risk assessment models for remediation decision of site contamination

The decision as to whether a contaminated site poses a threat to human health and should be cleaned up relies increasingly upon the use of risk assessment models. However, the more sophisticated risk assessment models become, the greater the concern with the uncertainty in, and thus the credibility of, risk assessment. In particular, when there are several equally plausible models, decision makers are confused by model uncertainty and perplexed as to which model should be chosen for making decisions objectively. When the correctness of different models is not easily judged after objective analysis has been conducted, the cost incurred during the processes of risk assessment has to be considered in order to make an efficient decision. In order to support an efficient and objective remediation decision, this study develops a methodology to cost the least required reduction of uncertainty and to use the cost measure in the selection of candidate models. The focus is on identifying the efforts involved in reducing the input uncertainty to the point at which the uncertainty would not hinder the decision in each equally plausible model. First, this methodology combines a nested Monte Carlo simulation, rank correlation coefficients, and explicit decision criteria to identify key uncertain inputs that would influence the decision in order to reduce input uncertainty. This methodology then calculates the cost of required reduction of input uncertainty in each model by convergence ratio, which measures the needed convergence level of each key input's spread. Finally, the most appropriate model can be selected based on the convergence ratio and cost. A case of a contaminated site is used to demonstrate the methodology.     

Military (in)decision-making process: a psychological framework to examine decision inertia in military operations

Abstract

When understanding how members of the armed forces make decisions in war current military doctrine centers on the military decision-making process (MDMP) – a linear process of identifying, evaluating and choosing the best course of action, while wider theoretical contributions focus on recognition prime models (RPD) of decision-making. In this article, we argue that the SAFE-T model of critical incident decision-making can elucidate the process of decision-making during military operations. The SAFE-T model states that effective decision-making follows a sequential process of situation assessment (SA), plan formulation (F) and plan execution (E) phases, and team learning (T). The central innovation of the SAFE-T model; however, is that it highlights the different ways in which decision-making can de-rail from this optimal strategy, resulting in decision inertia. This article discusses the implications of employing the SAFE-T model as a framework to study military decision-making both in the lab and in the field.     

A quantitative model for ERP investment decision: considering revenue and costs under uncertainty

This paper evaluates ERP investment under uncertainty using a model based on the Real Options theory. We expand the Dixit and Pindyck (Dixit, A.K. and Pindyck, R.S., 1994. Investment under uncertainty. Princeton: Princeton University Press) model, which considers a single source of uncertainty, and apply it to the problem of ERP investment decision. Revenue and costs are well documented in the literature as uncertain and critical factors. We developed a quantitative model using the concept of dynamic programming, which takes into account multiple uncertain factors, to determine the optimal threshold ratio of revenue to cost, as a means to evaluate investment in ERP. In addition, we performed sensitivity analysis on the effects various parameters have on the value of ERP projects. In contrast to conventional wisdom, we showed that the evaluation of ERP based on Real Options theory differs from that of NPV and captures a more realistic valuation of investment in ERP. This paper contributes to the literature by taking both uncertain revenue and costs into account, and makes up for the lack of tools required to quantify investments in ERP under uncertainty.     

Error and uncertainty in modeling and simulation

This article develops a general framework for identifying error and uncertainty in computational simulations that deal with the numerical solution of a set of partial differential equations (PDEs). A comprehensive, new view of the general phases of modeling and simulation is proposed, consisting of the following phases: conceptual modeling of the physical system, mathematical modeling of the conceptual model, discretization and algorithm selection for the mathematical model, computer programming of the discrete model, numerical solution of the computer program model, and representation of the numerical solution. Our view incorporates the modeling and simulation phases that are recognized in the systems engineering and operations research communities, but it adds phases that are specific to the numerical solution of PDEs. In each of these phases, general sources of uncertainty, both aleatory and epistemic, and error are identified. Our general framework is applicable to any numerical discretization procedure for solving ODEs or PDEs. To demonstrate this framework, we describe a system-level example: the flight of an unguided, rocket-boosted, aircraft-launched missile. This example is discussed in detail at each of the six phases of modeling and simulation. Two alternative models of the flight dynamics are considered, along with aleatory uncertainty of the initial mass of the missile and epistemic uncertainty in the thrust of the rocket motor. We also investigate the interaction of modeling uncertainties and numerical integration error in the solution of the ordinary differential equations for the flight dynamics.     

Use of decision criteria based on expected values to support decision-making in a production assurance and safety setting

We consider decision problems related to production assurance and safety. The issue is to what extent we should use decision criteria based on expected values, such as the expected net present value (E[NPV]) and the expected cost per expected number of saved lives (ICAF), to guide the decision. Such criteria are recognised as practical tools for supporting decision-making under uncertainty, but is uncertainty adequately taken into account by these criteria? Based on the prevailing practice and the existing literature, we conclude that there is a need for a clarification of the rationale of these criteria. Adjustments of the standard approaches have been suggested to reflect risks and uncertainties, but can cautionary and precautionary concerns be replaced by formulae and mechanical procedures? These issues are discussed in the present paper, particularly addressing the company level. We argue that the search for such formulae and procedures should be replaced by a more balanced perspective acknowledging that there will always be a need for management review and judgment beyond the realm of the analyses. Most of the suggested adjustments of the E[NPV] and ICAF approaches should be avoided. They add more confusion than value.     

Conceptual framework for designing agri-food supply chains under uncertainty by mathematical programming models

Agri-food sector performance strongly impacts global economy, which means that developing optimisation models to support the decision-making process in agri-food supply chains (AFSC) is necessary. These models should contemplate AFSC’s inherent characteristics and sources of uncertainty to provide applicable and accurate solutions. To the best of our knowledge, there are no conceptual frameworks available to design AFSC through mathematical programming modelling while considering their inherent characteristics and sources of uncertainty, nor any there literature reviews that address such characteristics and uncertainty sources in existing AFSC design models. This paper aims to fill these gaps in the literature by proposing such a conceptual framework and state of the art. The framework can be used as a guide tool for both developing and analysing models based on mathematical programming to design AFSC. The implementation of the framework into the state of the art validates its. Finally, some literature gaps and future research lines were identified.     

The effect of model uncertainty on cooperation in sensorimotor interactions

Decision-makers have been shown to rely on probabilistic models for perception and action. However, these models can be incorrect or partially wrong in which case the decision-maker has to cope with model uncertainty. Model uncertainty has recently also been shown to be an important determinant of sensorimotor behaviour in humans that can lead to risk-sensitive deviations from Bayes optimal behaviour towards worst-case or best-case outcomes. Here, we investigate the effect of model uncertainty on cooperation in sensorimotor interactions similar to the stag-hunt game, where players develop models about the other player and decide between a pay-off-dominant cooperative solution and a risk-dominant, non-cooperative solution. In simulations, we show that players who allow for optimistic deviations from their opponent model are much more likely to converge to cooperative outcomes. We also implemented this agent model in a virtual reality environment, and let human subjects play against a virtual player. In this game, subjects'' pay-offs were experienced as forces opposing their movements. During the experiment, we manipulated the risk sensitivity of the computer player and observed human responses. We found not only that humans adaptively changed their level of cooperation depending on the risk sensitivity of the computer player but also that their initial play exhibited characteristic risk-sensitive biases. Our results suggest that model uncertainty is an important determinant of cooperation in two-player sensorimotor interactions.     

Comments on generalised likelihood uncertainty estimation

The paper presents an application of the generalised likelihood uncertainty estimation methodology to the problem of estimating the uncertainty of predictions produced by environmental models. The methodology is placed in a wider context of different approaches to inverse modelling and, in particular, a comparison is made with Bayesian estimation techniques based on explicit structural assumptions about model error. Using a simple example of a rainfall-flow model, different evaluation measures and their influence on the prediction uncertainty and credibility intervals are demonstrated.     

Addressing imperfect maintenance modelling uncertainty in unavailability and cost based optimization

Optimization of testing and maintenance activities performed in the different systems of a complex industrial plant is of great interest as the plant availability and economy strongly depend on the maintenance activities planned. Traditionally, two types of models, i.e. deterministic and probabilistic, have been considered to simulate the impact of testing and maintenance activities on equipment unavailability and the cost involved. Both models present uncertainties that are often categorized as either aleatory or epistemic uncertainties. The second group applies when there is limited knowledge on the proper model to represent a problem, and/or the values associated to the model parameters, so the results of the calculation performed with them incorporate uncertainty. This paper addresses the problem of testing and maintenance optimization based on unavailability and cost criteria and considering epistemic uncertainty in the imperfect maintenance modelling. It is framed as a multiple criteria decision making problem where unavailability and cost act as uncertain and conflicting decision criteria. A tolerance interval based approach is used to address uncertainty with regard to effectiveness parameter and imperfect maintenance model embedded within a multiple-objective genetic algorithm. A case of application for a stand-by safety related system of a nuclear power plant is presented. The results obtained in this application show the importance of considering uncertainties in the modelling of imperfect maintenance, as the optimal solutions found are associated with a large uncertainty that influences the final decision making depending on, for example, if the decision maker is risk averse or risk neutral.     

Integrated workforce capacity and inventory management under labour supply uncertainty

In a manufacturing environment with volatile demand, inventory management can be coupled with dynamic capacity adjustments for handling the fluctuations more effectively. In this study, we consider the problem of integrated capacity and inventory management under non-stationary stochastic demand and capacity uncertainty. The capacity planning problem is investigated from the workforce planning perspective where the capacity can be temporarily increased by utilising contingent workers from an external labour supply agency. The contingent capacity received from the agency is subject to an uncertainty, but the supply of a certain number of workers can be guaranteed through contracts. There may also be uncertainty in the availability of the permanent and contracted workers due to factors such as absenteeism and fatigue. We formulate a dynamic programming model to make the optimal capacity decisions at a tactical level (permanent workforce size and contracted number of workers) as well as the operational level (number of workers to be requested from the external labour supply agency in each period), integrated with the optimal operational decision of how much to produce in each period. We analyse the characteristics of the optimal policies and we conduct an extensive numerical analysis that helps us provide several managerial insights.     

Risk Evaluation in Decision Making in Risk Situations

We analyze the components of uncertainty in decision making and consider a risk evaluation model in decision making in a risk situation in economic activities. A modified cost-benefit criterion is proposed for decision making for implementing a project, taking into account the average losses due to wrong decisions. __________ Translated from Izmeritel'naya Tekhnika, No. 9, pp. 27–29, September, 2005.