An approach to group decision making under uncertainty with application to project selection

In this paper we present an approach and interactive procedure for group decision making under imprecision of expert judgements as applied to problems containing explicitly given resource constraints in particular to project selection. Alternatives (projects) are evaluated in a scale with a finite number of levels. Based on these estimates, fuzzy group preferences are determined and projects are divided into domination levels. Necessary quantities of resources are given in the form of intervals. Projects from successive levels are selected until maximum resource utilization is achieved. A numerical example is included to illustrate the proposed approach and procedure.     

A vague set based decision support approach for evaluating research funding programs

Scientific Research Assessment (SRA) is receiving increasing attention in both academic and industry. More and more organizations are recognizing the importance of SRA for the optimal use of scarce resources. In this paper, a vague set theory based decision support approach is proposed for SRA. Specifically, a family of parameterized S-OWA operator is developed for the aggregation of vague assessments. The proposed approach is introduced to evaluate the research funding programs of the National Natural Science Foundation of China (NSFC). It provides a soft and expansive way to help the decision maker in NSFC to make his decisions. The proposed approach can also be used for some other agencies to make similar assessment.     

A multiobjective evolutionary approach for linearly constrained project selection under uncertainty

In the project selection problem a decision maker is required to allocate limited resources among an available set of competing projects. These projects could arise, although not exclusively, in an R&D, information technology or capital budgeting context. We propose an evolutionary method for project selection problems with partially funded projects, multiple (stochastic) objectives, project interdependencies (in the objectives), and a linear structure for resource constraints. The method is based on posterior articulation of preferences and is able to approximate the efficient frontier composed of stochastically nondominated solutions. We compared the method with the stochastic parameter space investigation method (PSI) and illustrate it by means of an R&D portfolio problem under uncertainty based on Monte Carlo simulation.     

Sourcing decision under disruption risk with supply and demand uncertainty: A newsvendor approach

Multi-sourcing is considered as a common practice to hedge against supply disruption risk. In this context, this paper proposes two models for optimal order allocation in newsvendor setting, where both supply and demand are uncertain. The first model considers a risk neutral decision maker who maximizes the total expected profit under disruption risk. The second one is for a risk averse decision maker who does so under service level constraints. Analytical closed form solutions for both the models are derived. To overcome the computational complexity of the exact optimal solution, two algorithms are developed to generate optimal order quantity and the corresponding set of suppliers. The solutions with exact optimization algorithms and the proposed ones are illustrated and compared with numerical examples. The results show that the proposed algorithms give the exact optimal solution while being tractable. Finally, a case study is used to illustrate the applicability of the proposed model.     

A novel two-phase group decision making approach for construction project selection in a fuzzy environment

This paper considers a construction project problem under multiple criteria in a fuzzy environment and proposes a new two-phase group decision making (GDM) approach. This approach integrates a modified analytic network process (ANP) and an improved compromise ranking method, known as VIKOR. To take uncertainty and risk into account, a new decision making approach is presented with multiple fuzzy information by a group of experts, and a risk attitude for each expert is incorporated that can be expressed linguistically. First, a modified fuzzy ANP method is introduced to address the problem of dependence as well as feedback among conflicting criteria and to determine their relative importance. Then, a fuzzy VIKOR method is extended to rank potential projects on the basis of their overall performance. An illustrative example from the literature is provided for the construction project problem to demonstrate the effectiveness and feasibility of the proposed approach. The computational results show that the proposed two-phase GDM approach is suitable to cope with imprecision and subjectivity for the complicated decision making problem. Finally, the associated results of the proposed approach with risk attitudes and without risk attitudes are compared with the results reported by Cheng and Li [1], and the merits are highlighted.     

A decision model for interdependent information system project selection

Existing methods for information system (IS) project selection neglect an important aspect of information technology, namely the interdependencies that exist among various IS applications (projects). Recognizing and modeling these project interdependencies provides valuable cost savings and greater benefits to organizations. In this paper, an IS project selection model is developed that identifies and models benefit, resource and technical interdependencies among candidate projects. The proposed model is formulated as a nonlinear 0–1 programming problem and represents a significant addition to existing IS, capital budgeting and R&D project selection models. The model is converted, using linearization techniques, and tested (validated) by applying it to real-world IS project selection data. By comparing the performance of this model with existing project selection models, the contribution of this model is highlighted.     

A problem-solving approach to product design using decision tree induction based on intuitionistic fuzzy

Customer complaint problem is a product design used to understand customer requirements. Furthermore, product design corresponding to customer requirement does not feel adequately solved for a cause of problem. The cause of the problem affecting product design is solved to prevent customer complaint from reoccurring. However, the problems by customer may have observation uncertainty and fuzzy. Fuzzy concept considers not only the degree of membership to an accept set, but also the degree of non-membership to a rejection set. Therefore, we present a new approach for problem solving using decision tree induction based on intuitionistic fuzzy sets in this paper. Under this approach, we first develop the problem formulation for the symptoms and causes of the problem based on intuitionistic fuzzy sets. Next, we identify the cause of the problem using intuitionistic fuzzy decision tree by the problem formulation. We then provide the approach to find the optimal cause of the problem for the consideration of product design. A numerical example is used to illustrate the approach applied for product design.     

Modelling LGD for unsecured personal loans: decision tree approach

The New Basel Accord, which was implemented in 2007, has made a significant difference to the use of modelling within financial organisations. In particular it has highlighted the importance of Loss Given Default (LGD) modelling. We propose a decision tree approach to modelling LGD for unsecured consumer loans where the uncertainty in some of the nodes is modelled using a mixture model, where the parameters are obtained using regression. A case study based on default data from the in-house collections department of a UK financial organisation is used to show how such regression can be undertaken.     

A DST-based approach for construction project risk analysis

Despite its huge potential in risk analysis, the Dempster–Shafer Theory of Evidence (DST) has not received enough attention in construction management. This paper presents a DST-based approach for structuring personal experience and professional judgment when assessing construction project risk. DST was innovatively used to tackle the problem of lacking sufficient information through enabling analysts to provide incomplete assessments. Risk cost is used as a common scale for measuring risk impact on the various project objectives, and the Evidential Reasoning algorithm is suggested as a novel alternative for aggregating individual assessments. A spreadsheet-based decision support system (DSS) was devised to facilitate the proposed approach. Four case studies were conducted to examine the approach's viability. Senior managers in four British construction companies tried the DSS and gave very promising feedback. The paper concludes that the proposed methodology may contribute to bridging the gap between theory and practice of construction risk assessment.     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

Context tree selection: A unifying view

Context tree models have been introduced by Rissanen in [25] as a parsimonious generalization of Markov models. Since then, they have been widely used in applied probability and statistics. The present paper investigates non-asymptotic properties of two popular procedures of context tree estimation: Rissanen’s algorithm Context and penalized maximum likelihood. First showing how they are related, we prove finite horizon bounds for the probability of over- and under-estimation. Concerning over-estimation, no boundedness or loss-of-memory conditions are required: the proof relies on new deviation inequalities for empirical probabilities of independent interest. The under-estimation properties rely on classical hypotheses for processes of infinite memory. These results improve on and generalize the bounds obtained in Duarte et al. (2006) [12], Galves et al. (2008) [18], Galves and Leonardi (2008) [17], Leonardi (2010) [22], refining asymptotic results of Bühlmann and Wyner (1999) [4] and Csiszár and Talata (2006) [9].     

Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach

Selection of supply chain partners is an important decision involving multiple criteria and risk factors. This paper proposes a fuzzy multi-objective programming model to decide on supplier selection taking risk factors into consideration. We model a supply chain consisting of three levels and use simulated historical quantitative and qualitative data. We propose a possibility approach to solve the fuzzy multi-objective programming model. Possibility multi-objective programming models are obtained by applying possibility measures of fuzzy events into fuzzy multi-objective programming models. Results indicate when qualitative criteria are considered in supplier selection, the probability of a certain supplier being selected is affected.     

Portfolio selection under distributional uncertainty: A relative robust CVaR approach

Robust optimization, one of the most popular topics in the field of optimization and control since the late 1990s, deals with an optimization problem involving uncertain parameters. In this paper, we consider the relative robust conditional value-at-risk portfolio selection problem where the underlying probability distribution of portfolio return is only known to belong to a certain set. Our approach not only takes into account the worst-case scenarios of the uncertain distribution, but also pays attention to the best possible decision with respect to each realization of the distribution. We also illustrate how to construct a robust portfolio with multiple experts (priors) by solving a sequence of linear programs or a second-order cone program.     

Dynamic decision making without expected utility: An operational approach

Non-expected utility theories, such as rank dependent utility (RDU) theory, have been proposed as alternative models to EU theory in decision making under risk. These models do not share the separability property of expected utility theory. This implies that, in a decision tree, if the reduction of compound lotteries assumption is made (so that preferences at each decision node reduce to RDU preferences among lotteries) and that preferences at different decision nodes are identical (same utility function and same weighting function), then the preferences are not dynamically consistent; in particular, the sophisticated strategy, i.e., the strategy generated by a standard rolling back of the decision tree, is likely to be dominated w.r.t. stochastic dominance. Dynamic consistency of choices remains feasible, and the decision maker can avoid dominated choices, by adopting a non-consequentialist behavior, with his choices in a subtree possibly depending on what happens in the rest of the tree. We propose a procedure which: (i) although adopting a non-consequentialist behavior, involves a form of rolling back of the decision tree; (ii) selects a non-dominated strategy that realizes a compromise between the decision maker’s discordant goals at the different decision nodes. Relative to the computations involved in the standard expected utility evaluation of a decision problem, the main computational increase is due to the identification of non-dominated strategies by linear programming. A simulation, using the rank dependent utility criterion, confirms the computational tractability of the model.     

Bi-objective project portfolio selection and staff assignment under uncertainty

We formulate a project portfolio selection problem under uncertainty with two optimization criteria: a weighted average of economic and strategic gains, and a risk measure expressed as the expected total overtime cost. The optimal assignment of personnel with given skills to the tasks of the selected projects is incorporated as a subproblem. Searching for Pareto-optimal portfolios satisfying the given constraints amounts to a stochastic multi-objective combinatorial optimization problem, a problem type for which only a few general solution approaches are available at present. We apply a recently developed technique called adaptive Pareto sampling, solve a linear subproblem with an LP solver and use the NSGA-II algorithm for deterministic multi-objective optimization as an auxiliary procedure. A convergence result applicable in a more general context is also shown. To obtain objective function estimates, importance sampling is applied. The technique is tested on a benchmark derived from a real-world application case provided by the E-Commerce Competence Center Austria.     

A rule-based risk decision-making approach and its application in China's customs inspection decision

This paper addresses a kind of risk decision-making problem existing widely in public administration and business management, which is characterized by (1) occurrence probabilities of states of nature can be estimated by analysing historical observations, but historical observations of different objects are unhomogeneous, (2) the relation between observations and occurrence probabilities of states of nature are affected by some qualitative and quantitative indicators, (3) it is a real-time decision-making problem, that is, there are many decisions for different objects to be made in a limited time, (4) considering decision's execution, impact of resource constrains is an important issue in decision-making process. In this paper, we develop a rule-based approach to address the problem. In the proposed approach, a two-step clustering method is employed to classify objects into categories, and observations in each category can be approximately viewed as homogeneous. For objects in each category, occurrence probabilities of states of nature are estimated by logistic regression, and the decision rule is obtained through solving an optimization model, which is to minimize the total decision risks while satisfying resource constrains. Effect and efficacy of our approach are illustrated through its application to China's customs inspection decision.     

Ordering fuzzy sets over the real line: An approach based on decision making under uncertainty

The ordering of fuzzy sets over the real line is approached from the point of view of ordering intervals rather than ordering numbers. First, the maximax and maximin criteria which are commonly used for ordering intervals are expressed in terms of characteristic functions. These criteria and the Hurwicz criterion for decision making under complete ignorance are then reformulated in a manner that allows for their generalization to the fuzzy case. Transitivity is established for these ordering rules. A criterion based on the principle of diminishing marginal utility is also presented.     

Interactive decision making for uncertain minimum spanning tree problems with total importance based on a risk-management approach

This paper deals with a minimum spanning tree problem where each edge cost includes uncertainty and importance measure. In risk management to avoid adverse impacts derived from uncertainty, a d-confidence interval for the total cost derived from robustness is introduced. Then, by maximizing the considerable region as well as minimizing the cost-importance ratio, a biobjective minimum spanning tree problem is proposed. Furthermore, in order to satisfy the objects of the decision maker and to solve the proposed model in mathematical programming, fuzzy goals for the objects are introduced as satisfaction functions, and an exact solution algorithm is developed using interactive decision making and deterministic equivalent transformations. Numerical examples are provided to compare our proposed model with some previous models.