Multivariate Gaussian criteria in SMAA

We consider stochastic multicriteria decision-making problems with multiple decision makers. In such problems, the uncertainty or inaccuracy of the criteria measurements and the partial or missing preference information can be represented through probability distributions. In many real-life problems the uncertainties of criteria measurements may be dependent. However, it is often difficult to quantify these dependencies. Also, most of the existing methods are unable to handle such dependency information.In this paper, we develop a method for handling dependent uncertainties in stochastic multicriteria group decision-making problems. We measure the criteria, their uncertainties and dependencies using a stochastic simulation model. The model is based on decision variables and stochastic parameters with given distributions. Based on the simulation results, we determine for the criteria measurements a joint probability distribution that quantifies the uncertainties and their dependencies. We then use the SMAA-2 stochastic multicriteria acceptability analysis method for comparing the alternatives based on the criteria distributions. We demonstrate the use of the method in the context of a strategic decision support model for a retailer operating in the liberated European electricity market.     

Characteristics of Decisions in Decision Analysis Practice

This paper presents summary statistics regarding the characteristics of decisions identified in a recent review of 86 applications of decision analysis. The goals of this summary are (1) to identify values for important parameters which characterize the structure of decisions which have been analysed using decision analysis; (2) to see what proportion of studies use the various available analysis tools; and (3) to draw implications from these results, particularly in terms of simplifying applied decision analysis. The results show that decisions tend to be multiattributed, involve a modest number of alternatives, and uncertainties appear to be the major source of influence on the chosen alternative. Furthermore, applications generally appear to take advantage of tools dealing with problem structuring, assessing uncertainty and performing sensitivity analysis.     

Robustness of mechanical systems against uncertainties

In this paper, one can propose a method which takes into account the propagation of uncertainties in the finite element models in a multi-objective optimization procedure. This method is based on the coupling of stochastic response surface method (SRSM) and a genetic algorithm provided with a new robustness criterion. The SRSM is based on the use of stochastic finite element method (SFEM) via the use of the polynomial chaos expansion (PC). Thus, one can avoid the use of Monte Carlo simulation (MCS) whose costs become prohibitive in the optimization problems, especially when the finite element models are large and have a considerable number of design parameters.The objective of this study is on one hand to quantify efficiently the effects of these uncertainties on the responses variability or the cost functions which one wishes to optimize and on the other hand, to calculate solutions which are both optimal and robust with respect to the uncertainties of design parameters.In order to study the propagation of input uncertainties on the mechanical structure responses and the robust multi-objective optimization with respect to these uncertainty, two numerical examples were simulated. The results which relate to the quantification of the uncertainty effects on the responses variability were compared with those obtained by the reference method (REF) using MCS and with those of the deterministic response surfaces methodology (RSM).In the same way, the robust multi-objective optimization results resulting from the SRSM method were compared with those obtained by the direct optimization considered as reference (REF) and with RSM methodology.The SRSM method application to the response variability study and the robust multi-objective optimization gave convincing results.     

Optimal sequential forestry decisions under risk

This paper is a summary of central and typical concepts, ideas and results in the field of sequential optimization and stochastic phenomena in forestry. The sequential optimization methods can be applied to all forestry decisions. The text covers forestry decisions and forest economics issues that are based on sequential decision making. An illustration covers optimal decisions in the presence of stochastic market prices. Stochastic (and/or deterministic but for different reasons unpredictable) changes in the economic and physical environments can be considered in decision making over time as soon as they are revealed. For this reason, the information and decision processes are sequential.     

Multi-Level Strategic Evaluation of Hospital Plans and Decisions

Strategic decision making in hospitals involves the assessment of linkages between decisions that are typically made in a hierarchical fashion. In hospitals, as in most large organizations, overall system performance is a function of how well the critical decisions are integrated. This paper focuses on the multi-level nature of the decisions and policies that typically need to be evaluated in hospital planning, highlighting that both optimization and simulation approaches may be required. An application involving a large general purpose urban hospital is used to illustrate the interdependency between the levels in the planning hierarchy. An optimization model is formulated to deal with facility layout and capacity allocation while a simulation model is proposed to capture the complexities of hospital operations. The linkages and information feedback between the models are shown to be critical in the design of a system that performs well and facilitates strategic hospital planning.     

Robust planning of blending activities at refineries

Refinery operation planning is a complex task since refinery processes and inventories are tightly interconnected. We study refinery planning when ships are loaded with a blend of components and where arrival times of ships are uncertain. Any delay in ship arrival may result in overfull component tanks which results in less efficient blending alternatives, reduced process operations or even shut downs. We propose a planning approach where we use robust optimization as a decision tool. By using robust optimization uncertainty in arrival times is explicitly dealt with and the resulting plan and schedule will always be feasible. The approach includes a flexible way to describe and model uncertainties. To compare the robust approach with a traditional deterministic approach, we use a simulation process. Computational results from a case study and simulations show that the proposed methodology is substantially better than a deterministic approach.     

An approach to the valuation and decision of ERP investment projects based on real options

The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making in multistage ERP projects investment is also complex, due mainly to the uncertainties involved and the various managerial and/or physical constraints to be enforced. This paper tackles the problem using a real-option analysis framework, and applies multistage stochastic integer programming in formulating an analytical model whose solution will yield optimum or near-optimum investment decisions for ERP projects. Traditionally, such decision problems were tackled using lattice simulation or finite difference methods to compute the value of simple real options. However, these approaches are incapable of dealing with the more complex compound real options, and their use is thus limited to simple real-option analysis. Multistage stochastic integer programming is particularly suitable for sequential decision making under uncertainty, and is used in this paper and to find near-optimal strategies for complex decision problems. Compared with the traditional approaches, multistage stochastic integer programming is a much more powerful tool in evaluating such compound real options. This paper describes the proposed real-option analysis model and uses an example case study to demonstrate the effectiveness of the proposed approach.     

Heterogeneous uncertainties in cholesterol management

Physicians use clinical guidelines to inform judgment about therapy. Clinical guidelines do not address three important uncertainties: (1) uncertain relevance of tested populations to the individual patient, (2) the patient’s uncertain preferences among possible outcomes, and (3) uncertain subjective and financial costs of intervention. Unreliable probabilistic information is available for some of these uncertainties; no probabilities are available for others. The uncertainties are in the values of parameters and in the shapes of functions. We explore the usefulness of info-gap decision theory in patient-physician decision making in managing cholesterol level using clinical guidelines. Info-gap models of uncertainty provide versatile tools for quantifying diverse uncertainties. Info-gap theory provides two decision functions for evaluating alternative therapies. The robustness function assesses the confidence—in light of uncertainties—in attaining acceptable outcomes. The opportuneness function assesses the potential for better-than-anticipated outcomes. Both functions assist in forming preferences among alternatives. Hypothetical case studies demonstrate that decisions using the guidelines and based on best estimates of the expected utility are sometimes, but not always, consistent with robustness and opportuneness analyses. The info-gap analysis provides guidance when judgment suggests that a deviation from the guidelines would be productive. Finally, analysis of uncertainty can help resolve ambiguous situations.     

An insurance risk management framework for disaster relief and supply chain disruption inventory planning

Government agencies, not-for-profit organizations, and private corporations often assume leading roles in the delivery of supplies, equipment, and manpower to support initial response operations after a disaster strikes. These organizations are faced with challenging logistics decisions to ensure that the right supplies (including equipment and personnel) are in the right places, at the right times, and in the right quantities. Such logistics planning decisions are further complicated by the uncertainties associated with predicting whether or not a potential threat will materialize into an emergency situation. This paper introduces newsvendor variants that account for demand uncertainty as well as the uncertainty surrounding the occurrence of an extreme event. The optimal inventory level is determined and compared to the classic newsvendor solution and the difference is interpreted as the insurance premium associated with proactive disaster-relief planning. The insurance policy framework represents a practical approach for decision makers to quantify the risks and benefits associated with stocking decisions related to preparing for disaster relief efforts or supply chain disruptions.     

Supporting complex group decisions: A probabilistic multi-dimensional scaling approach

Groups often face complex decisions; decisions in which the decision alternatives are not clearly defined and the criteria for choosing an alternative are subject to dispute within the group. We present a Group Decision Support System that will use judgments from the group to visualize the decision problem in a probabilistic geometric space. In this geometric representation, actual decision alternatives and an ideal alternative—an artificial alternative that identifies the ideal solution to the group's decision dilemma—are portrayed as distributions in a multi-dimensional space. Dispersions of the distributions measure the uncertainties of the decision process. The psychometric theory used to develop the probabilistic geometric representation is described. Preliminary research is presented which demonstrates that geometric representations of this type help groups both to understand better the decision they face and to find better solutions.     

Factors which influence decision making in new product evaluation

New product development is indeed very important for companies. However, developing new products is a risky and uncertain process. In order to reduce the risks and uncertainties, companies need to evaluate their new product initiatives carefully and make accurate decisions. Although the outcome of a new product evaluation decision can be influenced by the environmental uncertainties that are beyond a company’s control, companies can successfully improve the accuracy of their new product evaluation decisions. This article presents an integrated framework for understanding how various factors affect decision making in new product evaluation and provides guidelines for reducing their negative impacts on new product decisions. The results indicate that the quality of new product evaluation decisions is affected by four major sets of factors, namely the nature of the task, the type of individuals who are involved in the decisions, the way the individuals’ opinions are elicited and the way the opinions are aggregated.     

A fuzzy linear programming based approach for tactical supply chain planning in an uncertainty environment

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a fuzzy linear programming model for tactical supply chain planning in a multi-echelon, multi-product, multi-level, multi-period supply chain network. In this approach, the demand, process and supply uncertainties are jointly considered. The aim is to centralize multi-node decisions simultaneously to achieve the best use of the available resources along the time horizon so that customer demands are met at a minimum cost. This proposal is tested by using data from a real automobile SC. The fuzzy model provides the decision maker (DM) with alternative decision plans with different degrees of satisfaction.     

Performance analysis of automatic assembly systems with in-line parallel stations

An automatic assembly system—a key tool for mass production—isgenerally composed of a number of workstations and a transportsystem. One common problem associated with automatic assemblysystems is that some assembly operations may have relativelylong cycle times. As a consequence, productivity, which is determinedby the operations with the longest cycle time, can be reducedsignificantly. Therefore a special form of parallel workstationknown as an in-line parallel (tandem-gated) station was developedto improve the performance of an automatic assembly system.In this design, stations working in parallel are installed ina serial structure and perform identical operations. Thus, morethan one assembly may be processed simultaneously—a typeof design especially beneficial when a stage requires a longoperation cycle time. A typical example is a computer assemblysystem which performs long inspection operations to ensure thatthe quality level of each product is up to the acceptance level. In this paper, we describe a simulation study of the performancecharacteristics of this type of system, with a statistical analysisof each decision factor. Phenomena affecting the performanceof in-line parallel stations, identified by the assistance ofthe computer graphical display, will then be discussed. An analyticalmodel based on these phenomena identified is then developed.The results generated by the analytical model developed arevalidated by comparisons with the simulation results. Finally,guidelines for optimization of buffer size are presented.     

Energy efficiency and risk management in public buildings: strategic model for robust planning

Due to deregulations of the energy sector and the setting of targets such as the 20/20/20 in the EU, operators of public buildings are now more exposed to instantaneous (short-term) market conditions. On the other hand, they have gained the opportunity to play a more active role in securing long-term supply, managing demand, and hedging against risk while improving existing buildings’ infrastructures. Therefore, there are incentives for the operators to develop and use a Decision Support System to manage their energy sub-systems in a more robust energy-efficient and cost-effective manner. In this paper, a two-stage stochastic model is proposed, where some decisions (so-called first-stage decisions) regarding investments in new energy technologies have to be taken before uncertainties are resolved, and some others (so-called second-stage decisions) on how to use the installed technologies will be taken once values for uncertain parameters become known, thereby providing a trade-off between long- and short-term decisions.     

A fuzzy theoretic approach to simulation metamodeling

In this paper, we explore the potential application of fuzzy linear regression in developing simulation metamodels. It should be noted that the basic construct for simulation metamodels involves uncertainties and ambiguities that may be better addressed through fuzzy linear regression application. The solution techniques employed by fuzzy linear regression are very familiar, and the generation of fuzzy outputs may offer a wide range of solution space to the decision maker, thereby reducing the risk of making an incorrect economic decision. A numerical example is presented to show how a possibility distribution is used to capture the vagueness in a dependent variable for a regression metamodel.     

合作竞争条件下R&D项目投资决策分析

R&D项目的成功会为高新技术企业带来巨大收益,但是其研发过程中存在着技术风险、商业风险和突发风险等所带来的多种不确定性。为了应对这些不确定性,一些高新技术企业往往结成追求联盟整体利益最大化的成本共享联盟来进行R&D项目投资,然而由于不进行技术共享并争夺研发成功后的收益,联盟中的企业又会在合作的同时进行竞争,这就需要企业对R&D项目的估值非常的精确,以便在合作竞争条件下做出收益最大的最优投资决策。市场中两个合作竞争的高新技术企业各自拥有四种投资决策:成为市场先行者或跟随者,立刻与另一企业共同投资,与另一企业共同选择先等待时机再进行投资。本文以这两个高新技术企业为例,利用欧式期权理论量化了多种不确定性,建立相应的R&D项目投资决策数学模型,对R&D项目的投资时机和决策收益进行评估。当成本共享联盟整体收益最大时,得到的两个高新技术企业做出的投资决策即为在合作竞争条件下R&D项目投资中各自的最优投资决策,最后通过Shapley值的计算可对联盟中企业各自的收益进行合理分配。     

Patrones de Turing sobre superficies sometidas a deformación: un acercamiento desde el método lagrangiano total

In this work we have developed several numerical examples of reaction-diffusion equations with growing domain. For this purpose we have used the Schnakenberg reaction model with parameters in space Turing. Therefore numerical tests are performed on the appearance of Turing patterns on surfaces that have high deformation rate. For the solution of reaction diffusion equations is presented a solution method on surfaces in three dimensions using the finite element method under the use of the total Lagrangian formulation. The results show that the formation of Turing patterns depends on the features of surface deformation and the rate at which change in position of each point of the domain. These results can explain some phenomena of change of pattern on the surface of the skin of animals that exhibit characteristic spots.     

Application of gradient based algorithms for robust shape optimization of a tensile test specimen

In case of technical applications such as automotive or aeronautic part optimization, uncertainties in design variables and other parameters have to be taken into account. Especially, scattering of material properties and mechanical loads have large influences on the component behavior. Due to the difficulty in calculating of sensitivities, usually stochastic algorithms are used for robust and reliability optimization. That entails a large number of function calls and long computation time. Therefore, the stochastic responses with expectation value and variances will be approximated by response surfaces in this contribution. Based on the practical example of a tensile test specimen a deterministic optimization and optimization under uncertainties will be done. The results of the different optimizations will be compared and the influence of the uncertainties will be shown and discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A multi-parametric programming approach for constrained dynamic programming problems

In this work, we present a new algorithm for solving complex multi-stage optimization problems involving hard constraints and uncertainties, based on dynamic and multi-parametric programming techniques. Each echelon of the dynamic programming procedure, typically employed in the context of multi-stage optimization models, is interpreted as a multi-parametric optimization problem, with the present states and future decision variables being the parameters, while the present decisions the corresponding optimization variables. This reformulation significantly reduces the dimension of the original problem, essentially to a set of lower dimensional multi-parametric programs, which are sequentially solved. Furthermore, the use of sensitivity analysis circumvents non-convexities that naturally arise in constrained dynamic programming problems. The potential application of the proposed novel framework to robust constrained optimal control is highlighted.     

Project Ranking in the Armenian Energy Sector Using a Multicriteria Method for Groups

Project ranking is a complex problem that is often faced by the decision makers involved in the planning process. The necessity to take into account several decision parameters apart from purely economic ones, such as socio-political, technical, institutional and environmental, lead to the use of multicriteria methods instead of single uni-criterion ones. Moreover, most of the times such decisions are taken in a group environment. A hybrid of ELECTRE III and PROMETHEE methods, MURAME, has been specially developed and constitutes the main part of an integrated project ranking methodology for groups. The experience of the application of the methodology in the Armenian energy sector is presented.