Maker's Risk Attitude Research Articles

Fragility-based lot-sizing in veterinary pharmaceutical plants under demand uncertainty

We study a production lot-sizing problem inspired by a veterinary pharmaceutical plant in which demands are uncertain. First, we develop a deterministic capacitated lot-sizing model for the production of animal pesticides, performed in three machine-specific stages. Second, we propose a traditional robust optimisation formulation following the popular budget-of-uncertainty approach. Third, we derive a novel fragility-based approach that circumvents well-known issues with traditional robust optimisation approaches, such as the estimation of budgets of uncertainty, the over-conservatism of robust solutions and the sensitivity of solutions to the decision maker's risk attitude. The fragility-based approach is grounded in the idea of minimising violations, over the full uncertainty support, from a user-specified cost target. It avoids the estimation of budgets of uncertainty and produces less conservative solutions via explicit modelling of constraint violation. We demonstrate the effectiveness of our approach on instances built upon real data provided by our industrial partner, a major player in the Brazilian veterinary pharmaceutical sector. The results show that our fragility-based approach reduces average total costs across all instances and maintains greater model stability under different target estimations. It also preserves cost savings when bottlenecks are introduced in production and when inventory costs and capacities are varied.

The efficient and stable planning for interrupted supply chain with dual‐sourcing strategy: a robust optimization approach considering decision maker's risk attitude

• Proposing an efficient and robust dual-sourcing model for disrupted supply chain • Considering various risk attitudes and interruption uncertain situations • Processing supply interruption uncertainty with robust optimization method • Applying the real case study to analyze validity and stability of model • Providing useful managerial implications for interrupted supply chain sourcing In the face of the complex market environment and the in-depth development of globalization, ensuring the supply chain's stability and cost leadership by developing a differentiated dual-source procurement strategy is extremely important. The present study contemplates the supply chain as the research object. It also considers disruption uncertainty and decision-makers’ risk attitudes. To minimize costs and shortages, we build a dual-objective robust optimization model for a dual-sourcing strategy under interruption risk. The authors aim to explore efficient and robust planning under supply disruption uncertainty in dual-sourcing strategies by different risk attitudes. The research employs the augmented ε-constraint method to solve the proposed model by transforming the model into a single-objective mixed-integer programming model. Additionally, our study uses enterprise examples to prove the feasibility and effectiveness of the model. Moreover, it conducts risk attitude analysis, dual objective function trade-off analysis, and superiority analysis of procurement strategies. Finally, we put forward some management insights to provide a new decision-making idea for real supply chain enterprises in the case of supply interruption risk.

Shortfall Risk Models When Information on Loss Function Is Incomplete

Utility-based shortfall risk measures effectively captures a decision maker's risk attitude on tail losses. In this paper, we consider a situation where the decision maker's risk attitude toward tail losses is ambiguous and introduce a robust version of shortfall risk, which mitigates the risk arising from such ambiguity. Specifically, we use some available partial information or subjective judgement to construct a set of plausible utility-based shortfall risk measures and define a so-called preference robust shortfall risk as through the worst risk that can be measured in this (ambiguity) set. We then apply the robust shortfall risk paradigm to optimal decision-making problems and demonstrate how the latter can be reformulated as tractable convex programs when the underlying exogenous uncertainty is discretely distributed.

A supply chain network reconfiguration under partial disruptions with capacity recovery

This paper presents a multi-objective supply chain network (SCN) reconfiguration model under disruptions considering cost minimisation and resilience maximisation objectives. Potential disruption scenarios are modelled considering the decision maker's (DM) risk-attitude. At first, the single-objective cost minimisation problem is formulated and extended as a multi-objective problem incorporating responsiveness as another objective. A set of Pareto solutions is obtained using the augmented ε-constraint (AUGMECON) method. The major inferences include: 1) the structural decisions are highly influenced by the SCN facility's failure probability and the DM's risk-attitude; 2) the cost-effectiveness is achieved by incorporating a portfolio of reactive strategies during the post disruption periods, whereas redundancy at design phase is preferred to maximise the resilience; 3) a rapid and radical albeit costly recovery option is favoured to maximise resilience while a slow and incremental recovery is preferred to minimise the cost.

Preference Robust Distortion Risk Measure and Its Application

Distortion risk measure (DRM) plays a crucial role in risk measuring and managing, especially in insurance pricing. Various DRMs have been introduced but little is discussed about which DRM at hand should be chosen to address a decision maker (DM)'s risk attitude. This paper aims to fill out the gap. Specifically we consider a situation where the true distortion function is unknown either because it is difficult to identify/elicit and/or because the DM's risk attitude is ambiguous. We introduce a preference robust distortion risk measure (PRDRM) which is based on the worst-case distortion function from an ambiguity set of distortion functions to mitigate the impact arising from the ambiguity. The ambiguity set is constructed under well-known general principals such as concavity and inverse S-shapedness of distortion functions (over-weighting on events from impossible to possible or possible to certainty and under-weighting on those from possible to more possible) as well as new user-specific information such as sensitivity to tail losses, confidence intervals to some lotteries, and preferences to certain lotteries over others. To calculate the proposed PRDRM, we use the convex and/or concave envelop of a set of points to characterise the curvature of the distortion function and derive a tractable reformulation of the PRDRM when the underlying random loss is discretely distributed. Moreover, we show that the worst-case distortion function is a non-decreasing piece-wise linear function and can be determined by solving a linear programming problem. Finally, we apply the proposed PRDRM to a risk capital allocation problem and carry out some numerical tests to examine the efficiency of the PRDRM model.

Robust Spectral Risk Optimization When Information on Risk Spectrum Is Incomplete

A spectral risk measure (SRM) is a weighted average of value at risk where the weighting function (also known as risk spectrum or distortion function) characterizes a decision maker's risk attitude. In this paper, we consider the case where the decision maker's risk spectrum is ambiguous and introduce a robust SRM model based on the worst risk spectrum from a ball of risk spectra centered at a nominal risk spectrum. When the ball consists of step-like risk spectra, we show that the robust SRM can be computed by solving a linear programming problem. For the general case, we propose a step-like approximation scheme and derive an error bound for the approximation. As an application, we apply the proposed robust SRM to one-stage stochastic optimization with the objective of minimizing the robust SRM and propose an alternating iterative algorithm for solving the resulting minimax optimization problem. Moreover, to examine stability of the robust spectral risk optimization model with respect to perturbation of observed data from the underlying exogenous uncertainty in data-driven environments, we investigate statistical robustness of the model and derive sufficient conditions for the required stability.

Analysis of emission taxes levying on regional electric power structure adjustment with an inexact optimization model - A case study of Zibo, China

In this study, an inexact two-stage chance-constrained programming (ITSCCP) model was provided for multiple electrical power system supply and demand management in Zibo City under uncertainties. Three scenarios about the electric power structure adjustment, renewable power generation, and the emission taxes were designed. Methods of two-stage stochastic programming (TSP) and inexact chance-constrained programming (ICCP) were incorporated into the developed model to tackle uncertainties in terms of various cost coefficients, decision maker's risk attitude which was described by interval values and probability distributions. Moreover, under the objective of cost minimize, the electrical power generation planning for each terms under different feasibility degrees (violating constraints or available resources situations) can be obtained. The results indicated that higher probability of violating system constraints would increase risk of system, but lower the total cost; the proportion of optimized thermal power generation and imported electricity would decrease, which could promote the energy conservation and emissions reduction in some degree. At the same time, the model results are valuable for decision-makers to tackle the uncertainty of the power generation schemes within a complicated energy system and make a desired compromise between the satisfaction degree of the economic benefits and feasibility degree of constraints.

A Three-Phase Method for Group Decision Making With Interval-Valued Intuitionistic Fuzzy Preference Relations

This paper develops a new method for solving group decision making (GDM) problems with interval-valued intuitionistic fuzzy preference relations (IVIFPRs). First, an additive consistency of an IVIFPR is defined by the additive consistency of intuitionistic fuzzy preference relation (IFPR). Based on the additive consistency definition of IVIFPR, two linear programming models are established to extract the most optimistic and pessimistic consistent IFPRs from an IVIFPR, respectively. Especially, if the feasible regions of these two models are empty, two adjusted programming models are constructed. Afterwards, a risk attitudinal-based consistent IFPR is determined considering decision maker's (DM's) risk attitude. To derive the intuitionistic fuzzy priority weights from the risk attitudinal-based consistent IFPR, a multiobjective programming model is established and transformed into a linear goal program to resolve. Subsequently, combining DMs’ subjective and objective importance degrees, the comprehensive importance degrees of DMs are generated. Using comprehensive importance degrees as order inducing variables, a new comprehensive importance interval-valued intuitionistic fuzzy induced ordered weighted averaging (CI-IVIF-IOWA) operator is defined to aggregate the individual IVIFPRs into a collective one. Thereby, a three-phase method is proposed for GDM with IVIFPRs. An example of network system selection is examined to illustrate the practicability and effectiveness of the proposed method.

Explicit cost-risk tradeoff for optimal energy management in CCHP microgrid system under fuzzy-risk preferences

In this paper, a fuzzy risk-explicit interval parameter programming (FREIPP) approach was provided for multiple energy supply and demand management in microgrid system under uncertainties. The FREIPP method integrates risk-explicit interval linear programming and fuzzy theory within a general framework. It can tackle fuzzy and interval uncertainties in terms of various cost coefficients, forecasted load demand, decision maker's risk attitude and other uncertainties in microgrid system management. Compared with traditional interval parameter programming, the proposed method has distinct advantages in minimizing the system cost and risk simultaneously and providing more risk explicit solutions with the regard of obscure risk preference of decision maker. The FREIPP approach was successfully applied in a microgrid system with combined cooling, heating and power (CCHP) generation for three types of decision maker (i.e. defensive, neutral and aggressive). The obtained results indicated that the proposed FREIPP approach could provide optimal operation strategies with explicit cost-risk tradeoff information for decision maker when facing multiple complex uncertainties. Furthermore, it could help decision maker with different risk tolerance select desired optimal risk-aversion strategies, which is more realistic in real-world decision making process.

Risk-Based Comparison of Consolidated and Distributed Satellite Systems

Governments and large private satellite operators face a strategic decision for multipayload satellite programs: whether to use large consolidated satellites with multiple payloads or constellations of a few smaller spacecraft (here a “distributed” system). One advantage of the latter is that it allows faster replacement of failed payloads and more efficient insertion of new technologies. The costs and the benefits of each option are a function of a myriad of uncertain factors, including the sequence of decisions that have to be made during the lifetime of the program. We present a general model based on decision and risk analysis to support the choice between these two satellite architectures for a long-term program in Earth's orbit. This model is built on probabilistic risk analysis of satellite vehicles and includes the operational decisions that may have to be made later, such as the construction and launch of new satellites, either because one fails or because a new technology has become available. The value of each architecture is based on that of the data that the satellite system provides when it is operated according to an optimal policy. We compute the value of each satellite architecture, reflecting the uncertainties involved and the decision maker's risk attitude in optimal management decisions. This model thus yields the sensitivity of both satellite architecture and operational decisions to factors such as risk aversion and the anticipated rate of technology advancement. We find that in many circumstances, more risk-averse decision makers may prefer distributed satellite architectures and the flexibility that they provide, even at a potentially higher initial cost. We also show that distributed systems tend to be preferred when the payload technology is expected to improve rapidly over time.

A group decision making method with interval valued fuzzy preference relations based on the geometric consistency

This paper investigates a group decision making (GDM) method with interval valued fuzzy preference relations (IVFPRs). According to the geometric consistency of IVFPR, the max-consistency index and min-consistency index of an IVFPR are developed respectively. Combining the max-consistency index with min-consistency index, the geometric consistent index of an IVFPR is defined to measure the consistency level of the IVFPR by considering decision maker's (DM's) risk attitude. For improving the unacceptable geometric consistency of an IVFPR, a goal programming model is constructed to derive an acceptable geometric consistent IVFPR. By regarding the geometric consistent conditions of an IVFPR as fuzzy constraints, a fuzzy logarithmic program is established to generate the interval priority weights. In GDM problems, the individual interval priority weights are obtained by solving the corresponding fuzzy logarithmic programs. The similarities between DMs are calculated based on their individual interval priority weights. Subsequently the confidence degrees of DMs are defined to determine DMs' weights. To obtain the collective interval priority weights, a parametric linear program is constructed and transformed into a linear program to resolve. The order of alternatives is generated by the collective interval priority weights. Some examples are analyzed to verify the effectiveness of the proposed method.

Constrained fuzzy arithmetic approach to fuzzy transportation problems with fuzzy decision variables

Most of the existing methods for solving fully fuzzy mathematical programs are based on the standard fuzzy arithmetic operations and/or Zadeh's extension principle. These methods may produce questionable results for many real-life applications. Due to this fact, this paper presents a novel method based on the constrained fuzzy arithmetic concept to solve fully fuzzy balanced/unbalanced transportation problems in which all of the parameters (source capacities, demands of destinations, transportation costs etc.) as well as the decision variables (transportation quantities) are considered as fuzzy numbers. In the proposed method, the requisite crisp and/or fuzzy constraints between the base variables of the fuzzy components are provided from the decision maker according to his/her exact or vague judgments. Thereafter, fuzzy arithmetic operations are performed under these requisite constraints by taking into account the additional information while transforming the fuzzy transportation model into crisp equivalent form. Therefore, various fuzzy efficient solutions can be generated by making use of the proposed method according to the decision maker's risk attitude. In order to present the efficiency/applicability of the proposed method, different types of fully fuzzy transportation problems are generated and solved as illustrative examples. A detailed comparative study is also performed with other methods available in the literature. The computational analysis have shown that relatively more precise solutions are obtained from the proposed method for “risk-averse” and “partially risk-averse” decision makers. The proposed method also successfully provided fuzzy acceptable solutions for “risk seekers” with high degree of uncertainty similar to the other existing methods in the literature.

Decision making framework for optimal SHM planning of ship structures considering availability and utility

Uncertainties associated with modeling and performance prediction of structures may be addressed and subsequently reduced by including, within the performance assessment, information collected from inspections and structural health monitoring (SHM). Under ideal conditions, continuous monitoring is required to accurately assess and predict the performance of deteriorating systems; however, in general, this is neither practical nor financially efficient. Presented herein is an approach that determines cost-effective SHM plans that consider the probability that the performance prediction model based on monitoring data is suitable throughout the life-cycle of ship structures. This probability is used to compute the expected average availability of monitoring data for prediction during the life-cycle of a system. Utility theory is employed to incorporate the influence of the decision maker's risk attitude on the relative desirability of SHM plans. Optimization techniques are utilized to simultaneously maximize the utilities associated with monitoring cost and expected average availability in order to determine optimal monitoring strategies under uncertainty. The effects of the formulation of the utility function, risk attitude of the decision maker, and number of uniform and non-uniform time monitoring intervals on optimal SHM plans are investigated. The capabilities of the proposed decision support framework are illustrated on a naval ship.

Optimization with Reference-Based Robust Preference Constraints

We propose an optimization model using a novel robust preference relationship---reference-based almost stochastic dominance (RSD). The concept of RSD addresses the two problems in utility-based decision making: (i) ambiguity and inaccuracy in characterizing the decision maker's individual risk attitude, and (ii) overconservativeness of stochastic dominance representing general properties of risk aversion. The RSD rule reveals the maximum dominance level quantifying the robustness of the decision maker's preference between alternative choices. We first develop an approximation model using Bernstein polynomials, show the asymptotic convergence of its optimal value and set of optimal solutions to their true counterparts as the degree of Bernstein polynomials increases, and analyze the convergence rate of its feasible region. We next develop a cut-generation algorithm to solve the approximation model. Finally, we further adapt this cut-generation algorithm to seek a valid option most robustly preferable to a random benchmark. The effectiveness and computational complexity of the model have been illustrated using a portfolio optimization problem.

Discrete choice models with q-product random utilities

While most existing closed-form discrete choice models can be regarded as special cases of McFadden's generalized extreme value model, recently, alternative frameworks of McFadden's generalized extreme value model, which maintain closed-form expressions, have been proposed; these include the weibit model, which uses the Weibull distribution for its random component. In this paper, we develop a generalized closed-form discrete choice model which include both logit and weibit models as special cases, by introducing the q-product random utility, in which the relationship between the systematic component and the random component can be either additive, multiplicative, or in-between, depending on the value of the parameter q. We show that, when imposing the Gumbel distribution on its error component (instead of assuming the additive case as the logit model), the parameter q depicts decision maker's risk attitude in the sense of the Arrow–Pratt measure of relative risk aversion, which would be a behavioral foundation of the model. We also show that the model can be straightforwardly extended to incorporate statistical dependence across alternatives. The performance of the proposed model is examined by using two case studies; one on travel-route choices and the other on transport-mode choices.

History-dependent risk attitude

We propose a model of history-dependent risk attitude, allowing a decision maker's risk attitude to be affected by his history of disappointments and elations. The decision maker recursively evaluates compound risks, classifying realizations as disappointing or elating using a threshold rule. We establish equivalence between the model and two cognitive biases: risk attitudes are reinforced by experiences (one is more risk averse after disappointment than after elation) and there is a primacy effect (early outcomes have the greatest impact on risk attitude). In a dynamic asset pricing problem, the model yields volatile, path-dependent prices.

A risk attitudinal ranking method for interval-valued intuitionistic fuzzy numbers based on novel attitudinal expected score and accuracy functions

This article investigates new score and accuracy functions for ranking interval-valued intuitionistic fuzzy numbers (IVIFNs). The novelty of these functions is that they allow the comparison of IVIFNs by taking into account of the decision makers’ attitudinal character. The new attitudinal expected score and accuracy functions extend Xu and Chen's score and accuracy degree functions, and verify the following set of properties: (1) boundedness; (2) monotonicity; (3) commutativity; and (4) symmetry. These novel functions are used to propose a total order on the set of IVIFNs, and to develop an interval-valued intuitionistic fuzzy multi-attribute decision making selection process in which the final result depends on the decision maker's risk attitude. In addition, a ranking sensitivity analysis with respect to the risk attitude is provided.

Private partner's risk response in PPP low-cost housing projects

Purpose – The purpose of this paper is to identify the salient risks borne by private firms and to investigate their effective risk response strategies in public-private partnership (PPP) low-cost housing (LCH) projects in Thailand. Design/methodology/approach – The paper employs grounded theory and case study methodologies to extensively analyze ten private firms’ risks and their strategic risk mitigation. As a result, the matrix of imperative risks’ root causes and the area of the project life cycle most exposed to their impacts were proposed. This included the framework of the risk response strategy application. Findings – The private firm's risk mitigation strategies depended on the salient risks’ impact and the private firms’ predictability and controllability of the risk outcome. This included the private firm's participating objectives and core business, decision maker's risk attitude, risk perception, experience of risk, and risk assessment skill, and the project life cycle phase of risk occurrence. Practical implications – Under the same characteristics of the immature PPP market in developing countries, the contractors’ effective risk management framework can be used as a guideline to complement the contractors’ decision making on risk response strategy selection and resource allocation in the PPP project life cycle. Originality/value – Despite working under the familiar environment of construction risk and generous payment method in PPP-LCH projects, only few contractors were successful. The examination of risks borne and effectively responded by the private sector increases the likelihood of the project success.

Optimal condition-based maintenance decisions for systems with dependent stochastic degradation of components

Components in engineered systems are subjected to stochastic deterioration due to the operating environmental conditions, and the uncertainty in material properties. The components need to be inspected and possibly replaced based on preventive or failure replacement criteria to provide the intended and safe operation of the system. In the present study, we investigate the influence of dependent stochastic degradation of multiple components on the optimal maintenance decisions. We use copula to model the dependent stochastic degradation of components, and formulate the optimal decision problem based on the minimum expected cost rule and the stochastic dominance rules. The latter is used to cope with decision maker's risk attitude. We illustrate the developed probabilistic analysis approach and the influence of the dependency of the stochastic degradation on the preferred decisions through numerical examples.

Optimal Seismic Design Considering Risk Attitude, Societal Tolerable Risk Level, and Life Quality Criterion

The minimum expected life-cycle cost decision rule leads to an optimal design for a risk-neutral decision maker, but fails to incorporate the magnitude of uncertainty in the life-cycle cost and is incapable of coping with risk attitudes. The maximum expected utility decision rule results in a utility function dependent optimal decision that may not be accepted by a decision maker with a different utility function. This study develops a framework for selecting efficient or optimal seismic designs by considering the decision maker's risk attitude, societal tolerable risk level, and societal life quality criterion. Analysis results suggest that use of the developed framework can identify different sets of optimal designs for different risk attitudes. The results also show that the societal life quality criterion, for the considered examples, could only lead to a lower bound on the seismic design level for risk-seeking decision makers, whereas a reasonable tolerable risk level could provide a lower bound on the seismic design level for risk-seeking or risk-averse decision makers, or deny any acceptable designs for risk-neutral and risk-seeking decision makers.