Fuzzy Random Environment Research Articles

A Continuous Review Production-Inventory System with a Variable Preparation Time in a Fuzzy Random Environment

With the increase in the varieties products and the increasing uncertainty about product demand, the production preparation time is a significant factor in addressing these issues. The trade-off between the reduction of the production preparation time and the associated cost remains a critical decision. With this backdrop, this study presents a continuous review production-inventory model with a variable production preparation time and a time-dependent setup cost. The demand during the preparation time is captured through a min-max distribution-free approach. In a stochastic framework, the order quantity, reorder point, and setup time are optimized by minimizing the expected cost considering the time-value effect. Further, a fuzzy model is formulated to tackle the imprecise nature of the production setup time and demand. Two algorithms are developed using an analytical approach to obtain the optimal solution. A numerical illustration is given to present the key insights of the model for effective inventory management. It is observed that order quantity and total cost are more sensitive at the lower side of the optimal setup time rather than at the higher side. The discount rate is also found to be a sensitive factor while minimizing the total expected cost.

A Structural Adjustment optimization model for electric-power system management under multiple Uncertainties—A case study of Urumqi city, China

In this study,a structural adjustment optimization model for electric-power system management under fuzzy-random environment was developed for regional electric power system management in Urumqi, China. The emission control policy andstructural adjustment are considered and quantified in the developed model to tackle the electric power problems of a regional electric-power system. The objective of this study was to develop a power structural adjustment optimization model with fuzzy-random parameters for discussing the effects, merits and defects of structural adjustment and policy adjustment to manage the electric power system of the city Urumqi. Finally, the results and comparisons analysis of the case study demonstrated the practicality and efficiency of the optimization method. The results indicated that the model can provide an effective linkage between conflicting economic cost and the system stability, and different power demand levels correspond to different electricity generation schemes with varied energy policy and power structural adjustment. The power generation schemes, pollution emission and CO2 emission were analyzed. The modeling results are valuable for supporting the adjustment or justification of the energy policies and structures within a complicated power system under uncertainty.

Application of a Bilevel Programming Model in Disposal Site Selection for Hazardous Waste

In this study, a bilevel programming model is proposed for a multiple decision-subject location-routing problem of hazardous waste (HW) under a fuzzy random environment to select the best HW dispos...

Fuzzy Random Chance-Constrained Programming Model for the Vehicle Routing Problem of Hazardous Materials Transportation

As an indispensable necessity in daily routine of citizens, hazardous materials (Hazmat) not only plays an increasingly important role, but also brings a series of transportation uncertainty phenomena, the most prominent of which is a safety problem. When it attempts to find the best vehicle route scheme that can possess the lowest risk attribute in a fuzzy random environment for a single warehouse, the influence of cost should also be taken into account. In this study, a new mathematical theory was conducted in the modeling process. To take a full consideration of uncertainty, vehicle travel distance and population density along the road segment were assumed to be fuzzy variables. Meanwhile, accident probability and vehicle speed were set to be stochastic. Furthermore, based on the assumptions, authors established three chance constrained programming models according to the uncertain theory. Model I was used to seek the achievement of minimum risk of the vehicle route scheme, using traditional risk model; the goal of Model II was to obtain the lowest total cost, including the green cost, and the main purpose of Model III was to establish a balance between cost and risk. To settle the above models, a hybrid intelligent algorithm was designed, which was a combination of genetic algorithm and fuzzy random simulation algorithm, which simultaneously proved its convergence. At last, two experiments were designed to illustrate the feasibility of the proposed models and algorithms.

Production and payment policies for an imperfect manufacturing system with discount cash flows analysis in fuzzy random environments

ABSTRACT This paper considers an imperfect manufacturing system with credit policies in fuzzy random environments. The supplier simultaneously offers the retailer either a permissible delay in payments or a cash discount and retailer in turn provides its customer a permissible delay period. We used an alternate approach – discount cash flow analysis to establish an inventory problem. It is assumed that the elapsed time until the machine shifts from ‘in-control’ state to ‘out-of-control’ state is characterized as a fuzzy random variable. As a function of this parameter, the profit function is also a random fuzzy variable. Based on the credibility measure of fuzzy event, the model with fuzzy random elapsed time can be transformed into a crisp model . We establish several theoretical results to obtain the solution that provides the largest present value of all future cash flows. Finally, numerical example is given to illustrate the results and obtain some managerial insights.

The mean chance conditional value at risk under interval type-2 intuitionistic fuzzy random environment

The interval type-2 intuitionistic fuzzy random variable is an extension of the intuitionistic fuzzy random variable such that it can be a effective tool to determine some high-uncertainty phenomena. In this paper, the interval type-2 intuitionistic fuzzy random variable is introduced for the first time, and then, a scalar expected value operator of interval type-2 intuitionistic fuzzy random variable is proposed. Moreover, the new concepts of mean chance value at risk and mean chance conditional value at risk are discussed for the interval type-2 intuitionistic fuzzy random variables which have application in uncertain optimization, like fuzzy inverse location problems. Finally, it is proven that mean chance value at risk and mean chance conditional value at risk fulfill the convex risk metric properties.

Linear Fractional Programming for Fuzzy Random based Possibilistic Programming Problem

The uncertainty in real-world decision making originates from several sources, i.e., fuzziness, randomness, ambiguous. These uncertainties should be included while translating real-world problem into mathematical programming model though handling such uncertainties in the decision making model increases the complexities of the problem and make the solution of the problem hard. In this paper, a linear fractional programming is used to solve multi-objective fuzzy random based possibilistic programming problems to address the vague decision maker's preference (aspiration) and ambiguous data (coefficient), in a fuzzy random environment. The developed model plays a vital role in the construction of fuzzy multiobjective linear programming model, which is exposed to various types of uncertainties that should be treated properly. An illustrative example explains the developed model and highlights it's effectiveness.

Multi-choice Linear Programming in Fuzzy Random Hybrid Uncertainty Environment and Their Application in Multi-commodity Transportation Problem

In this paper, due to increasing competition in the business world, which makes decision makers dealing with multiple options/information for optimal decisions on a single task, we will look at multi-choice programming in hybrid fuzzy random environment. Alternative choices multi-choice parameters are considered as fuzzy random variables. By using polynomials interpolation for each multi-choice parameter, the model is transformed into a fuzzy random programming problem. Then, to convert this model to its deterministic form, we use the concept of the mean value of fuzzy random variables. Finally, to validate the proposed mathematical operations, we solve a multi-commodity transportation problem with fuzzy random multi-choice parameters.

The survey of data envelopment analysis models in fuzzy stochastic environments

One of the best techniques for evaluating the performance of organizations is data envelopment analysis. Data Envelopment Analysis (DEA) is a non-parametric method for evaluating the performance of decision-making units (DMUs) that recognizes the relative performance of DMUs based on mathematical programming. The classic DEA model was initially formulated for optimal inputs and outputs, But in real-world problems, the values observed from input and output data are often ambiguous and random. In fact, decision-makers may be faced with a specific hybrid environment where there are fuzziness and randomness in the problem. To overcome this problem, data envelopment analysis models in the random fuzzy environment have been proposed. Although the DEA has many advantages, one of the disadvantages of this method is that the classic DEA does not actually give us a definitive conclusion and does not allow random changes in input and output. In this research data envelopment analysis models in fuzzy random environments is reviewed.

A hybrid optimization approach for unequal-sized dynamic facility layout problems under fuzzy random demands

Dynamic facility layout problems involve devising the optimal layout for each different production period. This article studies unequal-area dynamic facility layout problems under fuzzy random environment to minimize the sum of the material handling costs and rearrangement costs. For a more general situation, a novel model of unequal-area dynamic facility layout problems is proposed on the basis of fuzzy random theory, in which uncertain demands are characterized by fuzzy random variables. Unequal-area dynamic facility layout problems are one of the non-deterministic polynomial-time hard problems. Therefore, a hybrid particle swarm optimization and simulated annealing algorithm is innovated to solve the proposed unequal-area dynamic facility layout problems model under fuzzy random environment, in which the shapes and areas of facilities are changed dynamically. Two facility-swapping methods and two local search methods help hybrid algorithm escape from local optima, allowing a more reliable solution. Moreover, a new shifting method is developed to prevent the spatial overlapping between adjacent facilities and save material handling costs. The performance of the hybrid algorithm is confirmed by some test problems available. Finally, the proposed method is extended to a facility layout planning of a new aircraft assembly shop floor. Computational results show that the efficiency and effectiveness of the proposed method, in sharp comparison with other approaches.

The multiple trip vehicle routing problem with backhauls in random fuzzy environment: using (α,β)-cost minimization model under the Hurwicz criterion

ABSTRACTIn the literature on VRP issues, many works have been studied in deterministic environments. Such proposed models cannot show the appropriate demands of different customers in the real world. One of the most important VRP problems that are widely applicable in real life is nondeterministic multiple trip vehicle routing problem with backhauls (MT-VRPB). In this paper, we focus on MT-VRPB in the random fuzzy environment using cost minimization model under the Hurwicz criterion. This model can deal with various MT-VRPB in random, fuzzy and random fuzzy environments. Regarding to the structure of the proposed model and in order to solve it, a hybrid intelligent algorithm based on the integration of the simplex algorithm, fuzzy simulations, and a firefly algorithm is proposed. The effectiveness and sensitive analysis of the proposed algorithm is demonstrated by solving some numerical examples.

On the distribution-free continuous review (Q, r, L) inventory model with lead-time-dependent partial backlogging

ABSTRACTIn this article, we study a distribution-free continuous review inventory system that assembles lost sales and backorders. The order quantity, the reorder point and lead-time are decision variables of the problem. The study under consideration assumes that purchasing cost is order dependent, partial backlogging is lead-time dependent and the distribution of lead-time demand is known partially. The objective of the paper is twofold. First, in the random framework, we provide the optimal order quantity, reorder level and lead-time simultaneously to acquire significant savings in the total costs of the model than Sana and Goyal ((q, r, l) model for stochastic demand with lead-time dependent partial backlogging. Annals of Operations Research. 233(1), 401–410, 2015). Second, we extend the crisp model to the fuzzy random environment employing the uncertain demand rate as a fuzzy random variable. We develop the mathematical methodologies to obtain the optimal solutions such that the total expected cost of the inventory system is minimized in both the cases. An algorithm is proposed with the help of the developed methodologies. We employ the proposed algorithm to solve two numerical examples to demonstrate the effectiveness of the methods.

Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment

In this paper, we investigated a multi-objective inventory model under both stock-dependent demand rate and holding cost rate with fuzzy random coefficients. Chance constrained fuzzy random multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. In addition, the technique of fuzzy random simulation is applied to deal with general fuzzy random objective functions and fuzzy random constraints which are usually difficult to converted into their crisp equivalents. The purposed of this study is to determine optimal order quantity and inventory level such that the total profit and wastage cost are maximized and minimize for the retailer respectively. Finally, illustrate example is given in order to show the application of the proposed model.

Stackelberg game optimization for integrated production-distribution-construction system in construction supply chain

Although construction supply chain management has attracted significant research attention, this field remains somewhat fragmented. This paper examines an integrated production-distribution-construction system consisting of the construction department and material suppliers under a fuzzy random environment with the aim of optimizing the global equilibrium. A novel bi-level multistage programming method with multiple objective optimization is developed to examine the inherent conflicts and complex interactions among decision makers in order to obtain the Stackelberg–Nash equilibrium solution, in which the construction department, as the leader, decides on the material allocations to construction sites, while the material supplier, as the follower, produces and transports the corresponding materials. For dealing with uncertainties, a hybrid crisp approach with an expected value operator is proposed to convert the fuzzy random parameters into definitive parameters. A hybrid algorithm combining an evolved genetic algorithm and particle swarm optimization is developed to solve this novel Stackelberg game model. The results from a practical example demonstrate the practicality and efficiency of the proposed optimization method, highlight the significance of quantitative analysis for the construction supply chain, and provide objective guidelines for its real-world application.

Uncertainty based genetic algorithm with varying population for random fuzzy maximum flow problem

AbstractThis paper investigates the uncertain maximum flow of a network whose capacities are random fuzzy variables. We have developed the expected value model (EVM) and the chance‐constrained model (CCM) for maximum flow problem (MFP) under random fuzzy environment and formulated their crisp equivalent models. To solve these models, we have proposed a varying population genetic algorithm with indeterminate crossover (VPGAwIC). In VPGAwIC, selection of a chromosome depends on its lifetime. An improved lifetime allocation strategy (iLAS) has also been proposed to determine the lifetime of the chromosome. The ages of the chromosomes are defined linguistically as Young, Middle, and Old, which follow some uncertainty distributions. The crossover probability is indeterminate, and it depends on the ages of the parents, which is defined by an uncertain rule base. The number of offspring, generated from a population of parents, is determined by the reproduction ratio. The population is updated in 2 ways: (i) All the chromosomes with ages greater than their lifetimes are discarded from the population, and (ii) the offspring are combined with their parents for the next generation. The proposed VPGAwIC is compared with the genetic algorithm developed by Gen, Cheng, and Lin (2008) for maximum flow problem. Wilcoxon signed‐rank test has been performed to show the superiority of the proposed VPGAwIC.

A Dynamic Programming-Based Sustainable Inventory-Allocation Planning Problem with Carbon Emissions and Defective Item Disposal under a Fuzzy Random Environment

There is a growing concern that business enterprises focus primarily on their economic activities and ignore the impact of these activities on the environment and the society. This paper investigates a novel sustainable inventory-allocation planning model with carbon emissions and defective item disposal over multiple periods under a fuzzy random environment. In this paper, a carbon credit price and a carbon cap are proposed to demonstrate the effect of carbon emissions’ costs on the inventory-allocation network costs. The percentage of poor quality products from manufacturers that need to be rejected is assumed to be fuzzy random. Because of the complexity of the model, dynamic programming-based particle swarm optimization with multiple social learning structures, a DP-based GLNPSO, and a fuzzy random simulation are proposed to solve the model. A case is then given to demonstrate the efficiency and effectiveness of the proposed model and the DP-based GLNPSO algorithm. The results found that total costs across the inventory-allocation network varied with changes in the carbon cap and that carbon emissions’ reductions could be utilized to gain greater profits.

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

In this paper, a multi-objective solid transportation problem (MOSTP) for damageable item is formulated and solved. First, we minimised the total cost of transportation and transportation time and maximise the reliability of transportation system. Here, transportation costs, resources, demands and capacities of conveyances are random fuzzy in natures. The transported item is likely to be damaged during transportation and damageability are different for different conveyances along different roots. The solid transportation problem (STP) is formulated as a decision making model optimising possibilistic value at risk (pVaR) by incorporating the concept of value at risk (VaR) into possibility and necessity measure theory. The reduced deterministic constrained problem is solved using generalised reduced gradient (GRG) method (LINGO-14.0). Some particular models has been presented. The model is illustrated with numerical examples and some sensitivity analysis is made on damageability.

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

A multi-objective solid transportation problem with reliability for damageable items in random fuzzy environment

A distribution-free newsboy problem with fuzzy-random demand

This paper introduces a distribution-free newsboy problem in a fuzzy-random environment. The aim of the paper is to extend the distribution-free newsboy problem to the case where the demand is a fuzzy-random variable. We analyse the distribution-free model in which the mean and variance of the demand are known and the associated probability distribution is unknown. The problem is formulated for finding the simple closed-form solution of the optimal order quantity for the distribution-free newsboy model with fuzzy-random demand and then compared with a similar model where the product demand was considered as a random variable. Finally, some numerical examples are provided to illustrate the utility of the results. The applied sensitivity analysis, by changing the mark-up value, discount rate and demand deviation, demonstrates how a decision-maker can set (increase) his/her target profit using a distribution-free newsboy model under fuzzy-random demand.

A three-layer supply chain inventory model for non-instantaneous deteriorating item with inflation and delay in payments in random fuzzy environment

This article focuses on different types of three-layer supply chain models under inflation for non-instantaneous deteriorating item and the retailer has a pre-specified time to settle the account with the supplier. The total cost of each those integrated models under inflation is minimized to get the value of total cycle time and the credit period of the three-layer supply chain model. A numerical example is extracted to solve the proposed three-layer supply chain models using generalized reduced gradient technique. To test the feasibility of the proposed models, sensitivity analyses are explained under different rates of deterioration and inflation and then optimal results are illustrated numerically and graphically.