Preemption resource-constrained project scheduling problems with fuzzy random duration and resource availabilities

Modeling data envelopment analysis by chance method in hybrid uncertain environments

Structural reliability analysis with fuzzy random variables using error principle

In structural reliability calculation, there are fuzzy uncertainties in the distribution parameters of random variables, which bring the problem of large computation and poor precision. In order to improve accuracy and efficiency of structural reliability, a novel structural reliability calculation method with fuzzy random variables is proposed from the perspective of perturbation principle. First, the fuzzy characteristic parameters of the structural fuzzy random variables are expressed as the sums of their true values and fuzzy perturbations. At the same time, the perturbations are equivalently selected. Second, the probability density function and the performance function are decomposed into a series of intervals under different level cut sets, and the Taylor series is expanded on the upper and lower limits of the intervals. Finally, according to the definition of structural reliability, based on the direct integration method, the sigmoid function is introduced into the reliability function to approximate the step function, and the fuzzy reliability is obtained. The simulation results show the effectiveness and accuracy of the proposed method, and it provides a feasible way for structural reliability analysis with fuzzy variables or fuzzy random variables.

In this paper, a dynamic programming model is proposed for a joint pricing construction materials procurement problem with multiple suppliers (JPCMPPMS) in a fuzzy random environment. In this model, the objective of the leader is to minimize total costs by deciding the purchase quantity. Demand and transport price are assumed to be fuzzy random variables in this paper. A dynamic programming-based genetic algorithm (DP-based GA) is developed to find feasible solutions and a dynamic programming-based initialization, crossover and mutation are designed to avoid infeasible solutions. The model and the proposed solution procedure are very practical and effective, and raw material purchasing system will achieve the overall best economic interests.

A class of random fuzzy programming and its application to supply chain design

A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

Ordered fuzzy random variables: Definition and the concept of normality

Resource constrained project scheduling problems (RCPSPs) are complex optimization problems that aim to minimize project completion time after considering limited resources and precedence-related activities with known durations. However, due to the dynamic nature of real-world applications, activity durations are vulnerable to change. In addition, resource demands along with resource availability at any stage of a project can also vary due to disruptions, which compel practitioners to re-think existing scheduling methodologies. Consequently, to mitigate the conjoint effect of those uncertainties and/or disruptions, this paper proposes a real-time reactive scheduling approach. To deal with uncertain activity durations, a chance constrained based approach is followed, which is later solved by an advanced meta-heuristic based approaches called IGFBIS and IGFBID. After solving an exhaustive list of stochastic RCPSP instances, this paper proves the efficacy of the proposed approaches, which is proven to be more useful to mitigate uncertainty or disruption while executing real-life projects.

In this paper, some essential stochastic inequalities and several convergence theorems were investigated for fuzzy random variables. The classical counterpart relationship between the proposed convergence theorems was also discussed in the fuzzy environment. The main advantage of the proposed method is its minimal requirements for such limit theorems and inequalities compared to the conventional methods used in the fuzzy environments. The previous methods mostly rely on the lower and upper bounds of the $$\alpha $$-cuts of fuzzy random variables, while the proposed method utilizes a unified quantity called $$\alpha $$-value.

This paper considers bilevel linear programming with fuzzy random variables. Through the introduction of a novel optimisation model that is to minimise the absolute deviation of degree of possibility and necessity that each fuzzy goal is fulfilled, the original bilevel programming problems with fuzzy random variables can be transformed into deterministic bilevel fractional programming problems. It is shown that the extended Stackelberg solutions can be obtained by solving the transformed bilevel linear programming problem through the combined use of the variable transformation method and the Kth best algorithm. A numerical example of bilevel purchase problem for food retailing is provided to illustrate the usefulness of the proposed methods.

This paper develops life insurance pricing with stochastic representation of mortality and fuzzy quantification of interest rates following the methodology by Andrés and González-Vila (2012). We show that modelling the present value of life insurance contracts with fuzzy random variables allows a well-founded quantification of their fair price and the risk resulting from the uncertainty of mortality and discounting rates. So, we firstly describe fuzzy random variables and define some associated measures: the mathematical expectation, the variance, distribution function and quantiles. Subsequently the present value of life insurance policies is modelled with fuzzy random variables. We finally show how an actuary can quantify the price and the risk of a life insurance portfolio when the contracts present value is given by fuzzy random variables.KeywordsFuzzy financeFuzzy random variablesLife insurance mathematics

Material transportation problems in construction projects under an uncertain environment

In this paper, a Pre-emptive Resource Constrained Project Scheduling Problem (PRCPSP) mathematical model is proposed to schedule a production project by considering uncertainty of time parameter for each activity. At last to evaluate the validity of the model, the mathematical model is implemented in a production factory and the results have been evaluated. In addition, some analyses are implemented to assess the behavior of the model and extract managerial insights.

Fuzzy random variable has been defined in several ways in literature. This paper presents a new definition of fuzzy random variable, and gives a novel definition of scalar expected value operator for fuzzy random variables. Some properties concerning the measurability of fuzzy random variable are also discussed. In addition, the concept of independent and identically distributed fuzzy random variables is introduced. Finally, a type of law of large numbers is proved.

ABSTRACTEffective management of municipal solid waste (MSW) is critical for urban planning and development. This study aims to develop an integrated type 1 and type 2 fuzzy sets chance-constrained programming (ITFCCP) model for tackling regional MSW management problem under a fuzzy environment, where waste generation amounts are supposed to be type 2 fuzzy variables and treated capacities of facilities are assumed to be type 1 fuzzy variables. The evaluation and expression of uncertainty overcome the drawbacks in describing fuzzy possibility distributions as oversimplified forms. The fuzzy constraints are converted to their crisp equivalents through chance-constrained programming under the same or different confidence levels. Regional waste management of the City of Dalian, China, was used as a case study for demonstration. The solutions under various confidence levels reflect the trade-off between system economy and reliability. It is concluded that the ITFCCP model is capable of helping decision makers to generate reasonable waste-allocation alternatives under uncertainties.