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Understanding the data and reaching accurate conclusions are of paramount importance in the present era of big data. Machine learning and probability theory methods have been widely used for this purpose in various fields. One critically important yet less explored aspect is capturing and analyzing uncertainties in the data and model. Proper quantification of uncertainty helps to provide valuable information to obtain accurate diagnosis. This paper reviewed related studies conducted in the last 30 years (from 1991 to 2020) in handling uncertainties in medical data using probability theory and machine learning techniques. Medical data is more prone to uncertainty due to the presence of noise in the data. So, it is very important to have clean medical data without any noise to get accurate diagnosis. The sources of noise in the medical data need to be known to address this issue. Based on the medical data obtained by the physician, diagnosis of disease, and treatment plan are prescribed. Hence, the uncertainty is growing in healthcare and there is limited knowledge to address these problems. Our findings indicate that there are few challenges to be addressed in handling the uncertainty in medical raw data and new models. In this work, we have summarized various methods employed to overcome this problem. Nowadays, various novel deep learning techniques have been proposed to deal with such uncertainties and improve the performance in decision making. [ABSTRACT FROM AUTHOR]

Mutual fund (MF) is one of the applicable and popular tools in investment market. The aim of this paper is to propose an approach for performance evaluation of mutual fund by considering internal structure and financial data uncertainty. To reach this goal, the robust network data envelopment analysis (RNDEA) is presented for extended two-stage structure. In the RNDEA method, leader–follower (non-cooperative game) and robust optimization approaches are applied in order to modeling network data envelopment analysis (NDEA) and dealing with uncertainty, respectively. The proposed RNDEA approach is implemented for performance assessment of 15 mutual funds. Illustrative results show that presented method is applicable and effective for performance evaluation and ranking of MFs in the presence of uncertain data. Also, the results reveal that the discriminatory power of robust NDEA approach is more than the discriminatory power of deterministic NDEA models. [ABSTRACT FROM AUTHOR]

Stochastic multicriteria acceptability analysis (SMAA) is a family of multiple criteria decision making (MCDM) methods dealing with incomplete, imprecise, and uncertain information on the evaluations and preference model parameters. As it provides a general framework that has extensions to deal with various specificities in MCDM problems, the development of SMAA methods and their applications in real-life decision-making problems have been increased over the recent years. This paper provides an up-to-date literature review of different SMAA methods and their applications in various areas. First, we selected, from different on-line data base, 118 articles published between 1998 and 2017. We categorized the selected papers into theoretical and applied. While the theoretical papers were analyzed based on the method's aggregation procedure, type of problem, type of method's outputs and inputs, the applied papers were separated and analyzed by application areas. Then, we provide some descriptive statistics, analyzing the papers regarding to publication year and journals of publication. Finally, we provide some guidelines to assist decision-makers in the choice of a SMAA method on a specific decision-making context and some future research directions. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has given rise to a spike in financial market volatility. In this paper, we attempt to assess the effects of financial & news-driven uncertainty shocks in growing Asian economies, using country-specific bond volatility shocks as a measure of local interest rate uncertainty. Also, we contrast the effects of local uncertainty with global stock market uncertainty. Using bond market data from nine Asian markets, we uncover a transmission mechanism of uncertainty shocks via the bond market. The mechanism works as a crowding-out effect due to government-led excessive market borrowing with supply-side consequences for the private sector, as opposed to economic policy or global stock market uncertainty which works more like a demand shock as in the literature. We conclude that countries with growing fiscal deficits that entail a larger government bond market or higher current account deficits, tend to experience an increase in the cost of borrowing due to this bond market volatility or interest rate uncertainty shocks. [ABSTRACT FROM AUTHOR]

Multiple and usually conflicting objectives subject to data uncertainty are main features in many real-world problems. Consequently, in practice, decision-makers need to understand the trade-off between the objectives, considering different levels of uncertainty in order to choose a suitable solution. In this paper, we consider a two-stage bi-objective single source capacitated model as a base formulation for designing a last-mile network in disaster relief where one of the objectives is subject to demand uncertainty. We analyze scenario-based two-stage risk-neutral stochastic programming, adaptive (two-stage) robust optimization, and a two-stage risk-averse stochastic approach using conditional value-at-risk (CVaR). To cope with the bi-objective nature of the problem, we embed these concepts into two criterion space search frameworks, the ϵ -constraint method and the balanced box method, to determine the Pareto frontier. Additionally, a matheuristic technique is developed to obtain high-quality approximations of the Pareto frontier for large-size instances. In an extensive computational experiment, we evaluate and compare the performance of the applied approaches based on real-world data from a Thies drought case, Senegal. [ABSTRACT FROM AUTHOR]

This paper investigates the uncertain stochastic resource allocation problem in which the results of a given allocation of resources are described as probabilities and these probabilities are considered to be uncertain from practical aspects. Here uncertainties are introduced by assuming that these probabilities depend on random parameters which are impacted by various factors. The redundancy allocation problem (RAP) and the multi-stage weapon-target assignment (MWTA) problem are special cases of stochastic resource allocation problems. Bi-objective models for the uncertain RAP and MWTA problem in which the conditional value-at-risk measure is used to control the risk brought by uncertainties are presented in this paper. The bi-objective formulation covers the objectives of minimizing the risk of failure of completing activities and the resulting cost of resources. With the aim of determining referenced Pareto fronts, a linearized formulation and an approximated linear formulation are put forward for RAPs and MWTA problems based on problem-specific characteristics, respectively. Two state-of-the-art decomposition-based multi-objective evolutionary algorithms (i.e., MOEA/D-AWA and DMOEA- ε C ) are used to solve the formulated bi-objective problem. In view of differences between MOEA/D-AWA and DMOEA- ε C , two matching schemes inspired by DMOEA- ε C are proposed and embedded in MOEA/D-AWA. Numerical experiments have been performed on a set of uncertain RAP and MWTA instances. Experimental results demonstrate that DMOEA- ε C outperforms MOEA/D-AWA on the majority of test instances and the superiority of DMOEA- ε C can be ascribed to the ε -constraint framework. [ABSTRACT FROM AUTHOR]

Decision support for Supplier Selection and Order Allocation (SSOA) is an important application area of multiple criteria decision making (MCDM) problems. In Amid et al. (Int J Prod Econ 131(1):139–145, 2011) proposed and developed a weighted maximin model to ensure the weight-consistent solution for SSOA in an MCDM problem under an uncertain environment. Essentially, this model is based on a weight-consistent constraint and a maximin aggregation operator. This paper reanalyzes the weighted maximin model in terms of the weight-consistent constraint, and then proposes a general weight-consistent model for SSOA in MCDM problems under uncertainty. In this paper, two existing models are reviewed and compared with the proposed model. Three datasets with different ranges of fuzzy demand and full factorial patterns of criteria weights are used to test the performances of the related models. The results showed that the proposed model always generates a weight-consistent Pareto-optimal solution in all cases, while the other existing models do not. [ABSTRACT FROM AUTHOR]

Effective and efficient care of hospital patients relies on well-coordinated resource allocation. Determining the number of beds and nurses in clinical units depends, among other considerations, on admission volumes, lengths of stay, and staffing availability, all of which are stochastic in practice. Given these uncertainties, this paper develops two robust optimization models to help plan the most effective bed and nurse resource allocation in terms of costs and access in a single clinical unit while allowing resources to be shared between units for flexibility. Ellipsoidal, budgeted, and data-driven formulations are compared for "conservatism," a measure of costs incurred to achieve robustness. In addition to existing formulations we develop uncertainty sets based on least-squares ellipsoidal fitting, which produces better solutions in our application. A case study involving different patient types and care levels reduces the number of patients that cannot be admitted (non-admissions) by up to 85% for the budgeted model and up to 100% for the data-driven model, with resource sharing reducing costs by 1% and 2%, respectively, compared to the non-sharing models. While the least-squares ellipsoidal model increases costs from the current scenario by 2% to achieve robustness, the budgeted and data-driven counterparts increase costs by 54% and 57%, respectively. These results have important implications for how uncertainty sets are formed when applying robust optimization to healthcare problems. [ABSTRACT FROM AUTHOR]

Robust multi-stage linear optimization is hard computationally and only small problems can be solved exactly. Hence, robust multi-stage linear problems are typically addressed heuristically through decision rules, which provide upper bounds for the optimal solution costs of the problems. We investigate in this paper lower bounds inspired by the perfect information relaxation used in stochastic programming. Specifically, we study the uncapacitated robust lot-sizing problem, showing that different versions of the problem become tractable whenever the non-anticipativity constraints are relaxed. Hence, we can solve the resulting problem efficiently, obtaining a lower bound for the optimal solution cost of the original problem. We compare numerically the solution time and the quality of the new lower bound with the dual affine decision rules that have been proposed by Kuhn et al. (Math Program 130:177-209, 2011). [ABSTRACT FROM AUTHOR]

This paper considers a buyer that procures from its major supplier whose production is subject to random yield risk. To mitigate supply risk, the buyer can procure from another reliable supplier who provides quantity flexibility (QF) contract. Under both deterministic and stochastic demand, we study the buyer’s optimal procurement decisions. We analyze the structural properties of optimal solutions and identify the conditions under which the quantity flexibility procurement policy should be used. We also examine the effect of supply risk, flexibility, wholesale price and demand risk on the procurement decisions. We find that the higher supply risk and demand risk reduce the buyer’s profit but have different impact on the buyer’s order policy. For the QF supplier, it may not obtain more orders by providing larger flexibility to the buyer, on the contrary, doing this may benefit the risky supplier. For the QF supplier or risky supplier, given its competitor’s wholesale price, it can increase its order share by lower wholesale price. [ABSTRACT FROM AUTHOR]

The earliest documented analytical approach to portfolio selection is Markowitz’s mean-variance analysis, which attempts to find the portfolio with optimal performance by considering the tradeoff between return and risk. The performance of mean-variance analysis has been the subject of many studies and compared to other portfolio construction approaches such as a naïve equally-weighted allocation scheme. In recent years, several approaches have been proposed to improve the mean-variance model by reducing the sensitivity of the portfolio selection process in order achieve robust performance. Although robust portfolio optimization has been one of the most researched methods for improving portfolio robustness, the performance of robust portfolios has not been the major focus of studies. In this paper, a comprehensive analysis on robust portfolio performance is presented for equity portfolios constructed in the U.S. market during the period 1980 and 2014, and results confirm the advantage of robust portfolio optimization for controlling uncertainty while efficiently allocating investments. [ABSTRACT FROM AUTHOR]

Risk based portfolio construction and particular risk parity or equally weighted risk contribution became popular among practitioners. These approaches focus only on risk and are agnostic with respect to the expected returns. In this paper, we consider risk budgeting; a generalization of risk parity. We propose an alternative formulation that is more efficient computationally. We introduce the robust risk budgeting, a robust variant of the standard risk budgeting that deals with the uncertainty in the input parameters. We show that the problem remains tractable under different types of uncertainty. We evaluate the proposed framework on real data and we observe a positive premium associated with the robust variant. [ABSTRACT FROM AUTHOR]

In this paper a class of combinatorial optimization problems is discussed. It is assumed that a feasible solution can be constructed in two stages. In the first stage the objective function costs are known while in the second stage they are uncertain and belong to an interval uncertainty set. In order to choose a solution, the minmax regret criterion is used. Some general properties of the problem are established and results for two particular problems, namely the shortest path and the selection problem, are shown. [ABSTRACT FROM AUTHOR]

In recent years, reasoning under uncertainty in multi-objective problems has become an active research area. However, solving this kind of problems reveals many performance and robustness issues that have been so far been neglected. Most of existing studies in this area are focused on dealing with robustness in the field of mono-objective optimization. The aim of the present paper is to address robustness of multi-objective optimization problems over uncertain inputs data. In particular, we focus on the specific case of fuzziness propagation to the multiple objectives in such problems. Then in order to avoid the loss of efficiency of fuzzy-valued objective values, we introduce new robustness techniques combining fuzziness and multi-objective context. [ABSTRACT FROM AUTHOR]

In the scheduling problem of logistics service supply chain (LSSC), the uncertainties of the functional logistics service provider's (FLSP's) operation time and customer requirement time will directly influence the logistics service integrator's (LSI's) time scheduling plan. In this paper, we explored the influences of time windows of the FLSP's operation and customer requirement on the scheduling decision. A multi-objective programming model of the LSSC time scheduling is established, aiming to minimize total order operation cost of the LSSC, minimize the difference between the total expected operation time and customer requirement time, and maximize the satisfaction of functional logistics service providers. To simplify the model solution, this multi-objective model is changed into a single-objective model with ideal point method. In the following numerical analysis for a specific example, genetic algorithm is applied. The influences of some relevant parameters on the scheduling performance are discussed. Firstly, with the increases of FLSPs' operation time range and the postponement proportionality coefficient of customer requirement time, the optimal scheduling performance of LSSC will increase and then tend to be stable. Secondly, the customer requirement time could not be compressed too much and have a minimum in order to obtain a feasible solution. Thirdly, the time windows of the FLSP's operation and customer requirement have significant interactions. The time window of customer requirement will expand with the increase of the time window of the FLSP's operation. [ABSTRACT FROM AUTHOR]

Decision making in health technology assessment (HTA) involves multiple criteria (clinical outcomes vs. cost) and risk (criteria measured with estimation error). A survey conducted among Polish HTA experts shows that opinions how to trade off health against money should be treated as fuzzy. We propose an approach that allows to introduce fuzziness into decision making process in HTA. Specifically, in the paper we (i) define a fuzzy preference relation between health technologies using an axiomatic approach; (ii) link it to the fuzzy willingness-to-pay and willingness-to-accept notions and show the survey results in Poland eliciting these; (iii) incorportate uncertainty additionally to fuzziness and define two concepts to support decision making: fuzzy expected net benefit and fuzzy expected acceptability (the counterparts of expected net benefit and cost-effectiveness acceptability curves, CEACs, often used in HTA). Illustrative examples show that our fuzzy approach may remove some problems with other methods (CEACs possibly being non-monotonic) and better illustrate the amount of uncertainty present in the decision problem. Our framework can be used in other multiple criteria decision problems under risk where trade-off coefficients between criteria are subjectively chosen. [ABSTRACT FROM AUTHOR]

This paper addresses the one-dimensional cutting stock problem when demand is a random variable. The problem is formulated as a two-stage stochastic nonlinear program with recourse. The first stage decision variables are the number of objects to be cut according to a cutting pattern. The second stage decision variables are the number of holding or backordering items due to the decisions made in the first stage. The problem’s objective is to minimize the total expected cost incurred in both stages, due to waste and holding or backordering penalties. A Simplex-based method with column generation is proposed for solving a linear relaxation of the resulting optimization problem. The proposed method is evaluated by using two well-known measures of uncertainty effects in stochastic programming: the value of stochastic solution— VSS—and the expected value of perfect information— EVPI. The optimal two-stage solution is shown to be more effective than the alternative wait-and-see and expected value approaches, even under small variations in the parameters of the problem. [ABSTRACT FROM AUTHOR]

Traditionally, long-term investment planning models have been the apparent tool to analyse future developments in the energy sector. With the increasing penetration of renewable energy sources, however, the modelling of short-term operational issues becomes increasingly important in two respects: first, in relation to variability and second, with respect to uncertainty. A model that includes both may easily become intractable, while the negligence of variability and uncertainty may result in sub-optimal and/or unrealistic decision-making. This paper investigates methods for aggregating data and reducing model size to obtain tractable yet close-to-optimal investment planning decisions. The aim is to investigate whether short-term variability or uncertainty is more important and under which circumstances. In particular, we consider a generation expansion problem and compare various representations of short-term variability and uncertainty of demand and renewable supply. The main results are derived from a case study on the Danish power system. Our analysis shows that the inclusion of representative days is crucial for the feasibility and quality of long-term power planning decisions. In fact, we observe that short-term uncertainty can be ignored if a sufficient number of representative days is included. [ABSTRACT FROM AUTHOR]

Choosing the right professional that has to meet indeterminate requirements is a critical aspect in humanitarian development and implementation projects. This paper proposes a hybrid evaluation methodology for some non-governmental organizations enabling them to select the most competent expert who can properly and adequately develop and implement humanitarian projects. This methodology accommodates various stakeholders' perspectives in satisfying the unique requirements of humanitarian projects that are capable of handling a range of uncertain issues from both stakeholders and project requirements. The criteria weights are calculated using a two-step multi-criteria decision-making method: (1) fuzzy analytical hierarchy process for the evaluation of the decision maker weights coupled with (2) technique for order preference by similarity to ideal solution to rank the alternatives which provide the ability to take into account both quantitative and qualitative evaluations. Sensitivity analysis have been developed and discussed by means of a real case of expert selection problem for a non-profit organisation. The results show that the approach allows a decrease in the uncertainty associated with decision-making, which proves that the approach provides robust solutions in terms of sensitivity analysis. [ABSTRACT FROM AUTHOR]

Supply chains (SCs) can be managed at many levels. The use of tactical SC planning models with multiple flexibility options can help manage the usual operations efficiently and effectively, whilst improve the SC resiliency in response to inherent environmental uncertainties. This paper defines tactical SC flexibility and identifies tactical flexibility measures and options for development of flexible SC planning models. A classification of the existing literature of SC planning is introduced that highlights the characteristics of published flexibility inclusive models. Additional classifications from the reviewed literature are presented based on the integration of flexibility options used, solution methods utilized, and real world applications presented. These classifications are helpful for identifying research gaps in the current literature and provide insights for future modeling and research efforts in the field. [ABSTRACT FROM AUTHOR]

Open Source Software (OSS) is one of the most trusted technologies for implementing industry 4.0 solutions. The study aims to assist a community of OSS developers in quantifying the product's reliability. This research proposes reliability growth models for OSS by incorporating dynamicity in the debugging process. For this, stochastic differential equation-based analytical models are developed to represent the instantaneous rate of error generation. The fault introduction rate is modeled using exponential and Erlang distribution functions. The empirical applications of the proposed methodology are verified using the real-life failure data of the Open Source Software projects, GNU Network Object Model Environment, and Eclipse. A soft computing technique, Genetic Algorithm, is applied to estimate model parameters. Cross-validation is also performed to examine the forecasting efficacy of the model. The predictive power of the developed models is compared with various benchmark studies. The data analysis is conducted using the R statistical computing software. The results demonstrate the proposed models' efficacy in parameter estimation and predictive performance. In addition, the optimal release time policy based on the proposed mathematical models is presented by formulating the optimization model that intends to minimize the total cost of software development under reliability constraints. The numerical illustration and sensitivity analysis exhibit the proposed problem's practical significance. The findings of the numerical analysis exemplify the proposed study's capability of decision-making under uncertainty. [ABSTRACT FROM AUTHOR]

This paper reviews recently developed theories that generalize the von Neumann - Morgenstern theory of preference under risk and Savage's theory of preference under uncertainty. The new theories are designed to accommodate systematic and predictable violations of previous theories while not giving up too much of the mathematical elegance of their expected utility representations. The material in the paper is adapted from the author's book Nonlinear Preference and Utility Theory. [ABSTRACT FROM AUTHOR]

This paper is based on an invited lecture given by the author at the ORSA/TIMS Special Interest Group on Applied Probability Conference on Statistical and Computational Problems in Probability Modeling, held at Williamsburg, Virginia. January 7–9, 1985. The theme of this paper is twofold. First, that members of the above group should be seriously concerned with issues of statistical inference - they should not stop short upon proposing a probability model. Second, that inference be undertaken via a strict adherence to the rules of probability - the Bayesian paradigm. To underscore a need for emphasizing the first theme, it may be pertinent to note that an overwhelming majority of the papers dealing with statistical and inferential issues that were presented at this conference were authored by members who did not claim to belong to the ORSA/TIMS Special Interest Group on Applied Probability. The lecture was followed by a panel discussion, with Drs. Lyle Broemeling and Edward Wegman of the Office of Naval Research as discussants. Dr. Robert Launer of the Army Research Office served as a moderator. Discussions from the floor included comments by Professors D. Harrington of Harvard University, E. Parzen of Texas A&M University, and R. Smith of imperial College, London, England. This paper, and the comments of the panelists, are published in this volume of the Annals of Operations Research, which is going to serve as a Proceedings of the Conference. [ABSTRACT FROM AUTHOR]

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper “Large-scale Unit Commitment under uncertainty: a literature survey” that appeared in 4OR 13(2):115-171 (2015); this version has over 170 more citations, most of which appeared in the last 3 years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject. [ABSTRACT FROM AUTHOR]

In this paper, we first present a market environment with a conventional two settlement mechanism. We show that when we add some wind generation to the system, the steady-state market conditions yield lower social and consumer welfare and higher use of fossil fuels. We also present results of a counterfactual stochastic settlement market which improves social and consumer welfare after the introduction of new intermittent generation. Thus, we conclude that the choice of market mechanism is a critical factor for capturing the benefits of large-scale wind integration. We also introduce a method to compute analytical equilibria of games in which the payoff functions of players depend on the optimal solution to an optimization problem with inequality constraints. [ABSTRACT FROM AUTHOR]

Optimization models have been used to support decision making in the forest industry for a long time. However, several of those models are deterministic and do not address the variability that is present in some of the data. Robust Optimization is a methodology which can deal with the uncertainty or variability in optimization problems by computing a solution which is feasible for all possible scenarios of the data within a given uncertainty set. This paper presents the application of the Robust Optimization Methodology to a Sawmill Planning Problem. In the particular case of this problem, variability is assumed in the yield coefficients associated to the cutting patterns used. The main results show that the loss in the function objective value (the 'Price of Robustness'), due to computing robust solutions, is not excessive. Moreover, the computed solutions remain feasible for a large proportion of randomly generated scenarios, and tend to preserve the structure of the nominal solution. We believe that these results provide an application area for Robust Optimization in which several source of uncertainty are present. [ABSTRACT FROM AUTHOR]

Robust optimization has become a widely implemented approach in investment management for incorporating uncertainty into financial models. The first applications were to asset allocation and equity portfolio construction. Significant advancements in robust portfolio optimization took place since it gained popularity almost two decades ago for improving classical models on portfolio optimization. Recently, studies applying the worst-case framework to bond portfolio construction, currency hedging, and option pricing have appeared in the practitioner-oriented literature. Our focus in this paper is on recent advancements to categorize robust optimization models into asset allocation at the asset class level and portfolio selection at the individual asset level, and we further separate robust portfolio selection approaches specific to each asset class. This organization provides a clear overview on how robust optimization is extensively implemented in investment management. [ABSTRACT FROM AUTHOR]

This paper studies option investors’ tendency to deviate from risk-neutrality around extreme financial events. We incorporate ambiguity into Black–Scholes theory and analyze the lead–lag association between option and stock markets during 2006–2008. Our findings from the Standard and Poor’s 500 index options reveal that investors’ option implied ambiguity moderates the lead–lag relationship between implied and realized volatility. We find that implied ambiguity contains predictive realized volatility information (beyond constant and stochastic implied volatilities), and that implied volatility is a less biased predictor of realized market variance when accounting for ambiguity in option pricing. We are also able to track changing investors’ ambiguity perceptions (pessimism or optimism) prior to severe volatility events and document shifts in ambiguity aversion among put option holders in the period leading to the fall 2008 global market crash. Our results hold under multiple-priors and Choquet ambiguity specifications. [ABSTRACT FROM AUTHOR]

It is shown that a cost function subject to internal costs of adjustment induces a stochastic discount factor (pricing kernel) that is a function of random output, input and output prices, existing capital stock, and investment. The only assumption on firm preferences is that they are increasing in current period consumption and future stochastic consumption. This ensures that the firm will always act to minimize current period cost of providing future consumption, and it is the first-order conditions for this cost minimization problem that generate the stochastic discount factor, which itself can be interpreted as the marginal variable cost of varying stochastic output. A cost-based pricing kernel is estimated using annual time-series data on macroeconomic variables and returns data for the S&P 500 and commercial paper. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cell formation has received much attention from academicians and practitioners because of its strategic importance to modern manufacturing practices. Existing research on cell formation problems using integer programming (IP) has achieved the target of solving problems that simultaneously optimise: (a) cell formation, (b) machine-cell allocation, and (c) part-machine allocation. This paper will present extensions of the IP model where part-machine assignment and cell formation are addressed simultaneously, and also a significant number of constraints together with an enhanced objective function are considered. The main study examines the integration of inter-cell movements of parts and machine set-up costs within the objective function, and also the combination of machine set-up costs associated with parts revisiting a cell when part machine operation sequence is taken into account. The latter feature incorporates a key set of constraints which identify the number of times a part travels back to a cell for a later machine operation. Due to two main drawbacks of IP modelling for cell formation, i.e. (a) only one objective function can be involved and (b) the decision maker is required to specify precisely goals and constraints, fuzzy elements like fuzzy constraints and fuzzy goals will be considered in the proposed model. Overall the paper will not only include an extended and enhanced integer programming model for assessing the performance of cell formation, but also perform a rigorous study of fuzzy integer programming and demonstrate the feasibility of achieving better and faster clustering results using fuzzy theory. [ABSTRACT FROM AUTHOR]

A framework for modelling the safety of an engineering system using a fuzzy rule-based evidential reasoning ( FURBER) approach has been recently proposed, where a fuzzy rule-base designed on the basis of a belief structure (called a belief rule base) forms a basis in the inference mechanism of FURBER. However, it is difficult to accurately determine the parameters of a fuzzy belief rule base (FBRB) entirely subjectively, in particular for complex systems. As such, there is a need to develop a supporting mechanism that can be used to train in a locally optimal way a FBRB initially built using expert knowledge. In this paper, the methods for self-tuning a FBRB for engineering system safety analysis are investigated on the basis of a previous study. The method consists of a number of single and multiple objective nonlinear optimization models. The above framework is applied to model the system safety of a marine engineering system and the case study is used to demonstrate how the methods can be implemented. [ABSTRACT FROM AUTHOR]

This paper models a retailer’s response to temporary manufacturer’s trade deals characterized by a time interval of random length and of uncertain duration. Uncertainty is handled primarily through the establishment of a reordering point, which serves as a trigger mechanism for new special orders. The timing at which this point is activated becomes another decision variable to be determined optimally. The model generates relatively easy-to-implement ordering policies, applicable to any probability distribution. [ABSTRACT FROM AUTHOR]

The electricity industry is undergoing a substantial process of restructuring, with an emphasis on the introduction of competition in the generation sector. Traditional planning methods are not necessarily appropriate for this new environment. This paper extends a previously developed linear programming model to the problem of optimal expansion planning in the face of uncertainty. The model explicitly accounts for equipment availability and load duration curves in selecting optimal investment. The use of the model is illustrated with a simple 2-region problem calibrated with data from Hydro-Québec and the northeastern United States that suggests how the LP model can help decision makers. [ABSTRACT FROM AUTHOR]

This paper presents a robust optimization model for the design of a supply chain facing uncertainty in demand, supply capacity and major cost data including transportation and shortage cost parameters. We first present a base model that aims to determine the strategic 'location' and tactical 'allocation' decisions for a deterministic four-tier supply chain. The model is then extended to incorporate uncertainty in key input parameters using a robust optimization approach that can overcome the limitations of scenario-based solution methods in a tractable way, i.e. without excessive changes in complexity of the underlying base deterministic model. The application of the approach is investigated in an actual case study where real data is utilized to design a bread supply chain network. Numerical results obtained from model implementation and sensitivity analysis experiments arrive at important managerial insights and practical implications. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present in a unified framework a survey of some results related to Choquet Expected Utility (CEU) models, a promising class of models introduced separately by Quiggin [35], Yaari [48] and Schmeidler [40, 41] which allow to separate attitudes towards uncertainty (or risk) from attitudes towards wealth, while respecting the first order stochastic dominance axiom. [ABSTRACT FROM AUTHOR]

A basic and distinctive prediction of regret theory is that certain variations in the juxtaposition of the consequences of alternative actions will tend to affect preferences between them in a particular way. This paper presents a body of experimental evidence which tests that prediction. [ABSTRACT FROM AUTHOR]

Contrary to most formal models of decision making under risk and uncertainty that are built on the basis of prescriptive behavioral principles or axioms, this paper derives a descriptive model of decision making under ambiguity based on principles of behavior, i.e. principles that describe how people behave as opposed to how they should behave. The model assumes that people evaluate the impact of ambiguous probabilities by first anchoring on a given value of the unknown probability and then adjusting this by the net effect of imagining or "trying out" other values the probability could take. The mental simulation process incorporates giving differential weight to the ranges of probability values above and below the anchor where such weight reflects individual and situational variables. In particular, the assumption that people are cautious as opposed to reckless in making decisions leads to attributing more weight to possible values of probabilities below the anchor when considering potential gains, and the reverse when faced with potential losses. Two experiments test implications of the model for situations involving competitive decisions. The first concerns legal decision making, the second involves the purchase and sale of industrial equipment. Both experiments validate predictions that (a) the effects of ambiguity depend on both the sign of payoffs and the level of probabilities, and (b) two parties to a negotiation or transaction may be differentially sensitive to ambiguity. Finally, the model is compared to other models of ambiguity proposed in the literature, and directions are suggested for future work. [ABSTRACT FROM AUTHOR]

In solving real life transportation problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, we formulate a transportation problem in which costs are triangular intuitionistic fuzzy numbers. We have defined accuracy function using score functions for membership and non membership functions of triangular intuitionistic fuzzy numbers. Then ordering of triangular intuitionistic fuzzy numbers using accuracy function has been proposed. We have utilized this ordering to develop methods for finding starting basic feasible solution in terms of triangular intuitionistic fuzzy numbers. Also the same ordering is utilized to develop intuitionistic fuzzy modified distribution method for finding the optimal solution. Finally the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding. [ABSTRACT FROM AUTHOR]

It has been suggested that stock exchanges may be tested for market efficiency by using tests for assessing random number generators. This paper uses such a test to assess the efficiency of small, mid and large cap indices on the Johannesburg Stock Exchange, while making adjustments for thin trading which occurs during the sample period. The efficiency of these indices is examined using individual share level data as well as index level data over a stable period and a period containing the 2008 financial crisis. This study finds evidence suggesting that small cap stocks exhibit a high degree of non-randomness in price movements. Some inefficiencies also appear to be present in mid and large cap stocks, however to a much lesser extent, with large cap stocks exhibiting higher levels of efficiency. Many of the stocks investigated appear to exhibit lower levels of efficiency during the crisis period. This may be a result of increased irrationality during periods of uncertainty. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]