Fuzzy Demand Research Articles

A study of an EOQ model with public-screened discounted items under cloudy fuzzy demand rate

This article deals with an economic order quantity inventory model of imperfect items under non-random uncertain demand. Here we consider the customers screen the imperfect items during the selling period. After a certain period of time, the imperfect items are sold at a discounted price. We split the model into three cases, assuming that the demand rate increases, decreases, and is constant in the discount period. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the dense fuzzy, parabolic fuzzy, degree of fuzziness and cloudy fuzzy for a comparative study. The basic novelty of this paper is that a computer-based algorithm and flow chart have been given for the solution of the proposed model. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.

On Solving Bi-level Multi-Objective Fully Quadratic Fractional Optimization Model with Fuzzy Demands

This paper has been designed to introduce the method for solving the Bi-level Multi-objective (BL-MO) Fully Quadratic Fractional Optimization Model through Fuzzy Goal Programming (FGP) approach by utilising non-linear programming. In Fully Quadratic Fractional Optimization Model, the objective functions are in fractional form, having quadratic functions in both numerator and denominator subject to quadratic constraints set. The motive behind this paper is to provide a solution to solve the BL-MO optimization model in which number of decision-makers (DM) exists at two levels in the hierarchy. First, the fractional functions with fuzzy demand, which are in the form of fuzzy numbers, are converted into crisp models by applying the concept of α-cuts. After that, membership functions are developed which are corresponding to each decision-maker’s objective and converted into simpler form to avoid complications due to calculations. Finally, the model is simplified by applying FGP approach, and a compromised solution to the initial model is obtained. An algorithm, flowchart and example are also given at the end to explain the study of the proposed model.

Optimising a mathematical model for a multi-sized public bicycle sharing system considering built-in control centres under fuzzy demand, a case study

A public bicycle sharing system makes bikes available for users to travel from one station to another in a city. Bicycles are repaired after getting used by users at the control centres if needed and then returned to their source bike station. There are very essential decision criteria to build a bicycle sharing system, the most important of which are the exact number and location of bike stations and control centres, the number of bicycles, and the number of docks in each station. This paper presents a single-objective nonlinear mathematical model for the bicycle sharing problem to minimise the system's total cost considering built-in control centres. Subjective distance is mentioned in this article so that distance-dependent costs become closer to real urban conditions. In this article, two exact and – heuristic methods are considered for solving the problem. Also, the applicability of the proposed model is examined through a real case study. After validating the model in a small dimension, the model is solved by a grasshopper optimisation algorithm in a large scale, and different numerical tests are developed.

Designing a single-vendor and multiple-buyers’ integrated production inventory model for interval type-2 fuzzy demand and fuzzy rule based deterioration

In this paper, a single-vendor and multiple-buyers’ integrated production inventory model is investigated where demand of the item at the buyers’ location is considered as interval type-2 fuzzy number (IT2FN). Deterioration rate of the item is assumed to change in accordance with the weather conditions of a particular region. It relies upon the values of certain attributes that have a direct influence on the extent of deterioration. These parameter values are easily forecasted and thereby can be utilized to determine the item depletion rate, which is executed here using Mamdani fuzzy inference scheme. Besides, a nearest interval approximation formula for the defuzzification of IT2FN is developed and applied in the proposed integrated production inventory model. The model optimizes the total number of shipments to be made to the buyers within a complete cycle so as to minimize the overall integrated cost incurred. A detailed illustration of the theoretical results is further demonstrated with the help of numerical example, followed by sensitivity analysis which provides insights into better decision making.

An integrated model for solving production planning and production capacity problems using an improved fuzzy model for multiple linear programming according to Angelov's method

Decision making has become a part of our everyday lives. The main apprehension is that almost all decision difficulties include certain criteria, which usually can be multiple or conflicting. Certainly, the production planning and production capacity development includes several parameters uncertainty such as fuzzy resource capacity, fuzzy demand and fuzzy production rate. This situation makes decision maker challenging to describe the objective crisply and at the end the real optimum solution cannot attained correctly. The Fuzzy model for multi-objective linear programming should be an suitable approach for dealing with the production planning and production capacity (PP& PC) problems. The PP& PC problem based on the fuzzy environment becomes even more sophisticated as decision makers try to consider multi-objectives, Therefore, this study attempts to propose a novel scheme which is capable of dealing with these obstacles in PP& PC problem. Intuitionistic Fuzzy Optimization (1FO) by implementing the optimization problem in an Intuitionistic Fuzzy Set (IFS) environment and considered the degrees of rejection of objective(s) and of constraints as the complement of satisfaction degrees. The aim of the research is to propose a new method capable of dealing with these obstacles in the PP & PC problem. It takes into account uncertainty and makes trade-offs between multiple conflicting goals simultaneously. To verify the validity of the proposed method, a case study of the fuzzy multi-objective model of the PP&PC is used. This research takes into account uncertainty and makes a comparison between multiple conflicting goals at the same time. Therefore, this study attempts to propose a new scheme which is the modified Angelov’s approach.

A supply chain model with service level constraints and strategies under uncertainty

In the current socio-economic situation, the daily demand for essential goods in the business sector is always changing owing to various unavoidable reasons. As a result, choosing the right method for profitable business has become quite tricky. This study introduces different business strategies based on constant and fuzzy demands. There are two types of constraints considered in this model to avoid the backorder cost. However, combining the service-level constraints with the constant and fuzzy demand, this study compares the total costs, and finally, the best strategy is established. Moreover, investing a small amount, this model improves the quality of the products and reduces the vendor’s setup cost. Depending on the number of transported products, this model follows the transportation discount policy for hassle-free delivery of the products with a minimum delivery rate. The Kuhn-Tucker optimization technique is employed, and global optimality is verified numerically, analytically using the Hessian matrix. This model’s robustness is discussed through a comparative study, numerical examples, sensitivity analysis, graphical representation, and managerial insights. Finally, some concluding remarks along with future extensions are discussed.

Research on Path Optimization Problem Based on Satisfaction Degree in Fuzzy Demand Environment

Aiming at the vehicle routing problem with fuzzy demand, this paper takes the fuzzy demand of the customer as the starting point, and first defines the demand satisfaction function; takes the maximum satisfaction and the minimum cost as the goal, constructs the fuzzy demand path optimization multi-objective planning model (MORG-FD), and the characteristics of MORG-FD are analyzed; combined with the actual case of a dairy product distribution for simulation analysis, considering the changes in the distribution plan under different demand parameters, and compared with the commonly used methods, the results show that MORG-FD has good structural characteristics, strong applicability, can provide a way of thinking for solving the problem of fuzzy demand vehicle routing, and can also provide guidance for actual distribution route planning.

Multi-objective vendor managed inventory system with interval type-2 fuzzy demand and order quantities

PurposeThe proposed IT2FMOVMI model intends to concurrently minimize total cost and warehouse space for the single vendor-retailer, multi-item and a consolidated vendor store. Regarding demand and order quantities with the deterministic and type-1 fuzzy numbers, we have also formulated the classic/crisp MOVMI model and type-1 fuzzy MOVMI (T1FMOVMI) model. The suggested solution technique can solve both crisp MOVMI and T1FMOVMI problems. By finding the optimal ordered quantities and backorder levels, the Pareto-fronts are constructed to form the solution sets for the three models.Design/methodology/approachA multi-objective vendor managed inventory (MOVMI) is the most recognized marketing and delivery technique for the service provider and the retail in the supply chain in Industry 4.0. Due to the evolving market conditions, the characteristics of the individual product, the delivery period and the manufacturing costs, the demand rate and order quantity of the MOVMI device are highly unpredictable. In such a scenario, a MOVMI system with a deterministic demand rate and order quantity cannot be designed to estimate the highly unforeseen cost of the problem. This paper introduces a novel interval type-2 fuzzy multi-objective vendor managed inventory (IT2FMOVMI) system, which uses interval type-2 fuzzy numbers (IT2FNs) to represent demand rate and order quantities. As the model is an NP-hard, the well-known meta-heuristic algorithm named NSGA-II (Non-dominated sorted genetic algorithm-II) with EKM (Enhanced Karnink-Mendel) algorithm based solution method has been established.FindingsThe experimental simulations for the five test problems that demonstrated distinct conditions are considered from the real-datasets of SAPCO company. Experimental study concludes that T1FMOVMI and crisp MOVMI schemes are outclassed by IT2FMOVMI model, offering more accurate Pareto-Fronts and efficiency measurement values.Originality/valueUsing fuzzy sets theory, a significant amount of work has been already done in past decades from various points of views to model the MOVMI. However, this is the very first attempt to introduce type-2 fuzzy modelling for the problem to address the realistic implementation of the imprecise parameters.

An imperfect production model with energy consumption, GHG emissions and fuzzy demand under a sustainable supply chain

ABSTRACT In this article, an integrated two-level supply chain model is described in two different scenarios by treating the demand rate as a triangular fuzzy number. In the first scenario, the retailer offers a price discount for customers on the backorders; it encourages the customer to wait for the product. In the second scenario, the retailer does not provide any discount; instead, an investment is made to reduce lost sales during the stock-out. In both scenarios, the shortages are allowed, and it is partially back-ordered. Two different cases are discussed within these scenarios with two different production functions related to the process quality and production rate. The signed distance method is employed to handle the fuzzified parameter. This research aims to minimize the total expected cost of the supply chain model under each scenario with energy consumption and greenhouse gas emissions during the production process. Moreover, to investigate how changes in the production rate affect the quality of products produced and the entire model’s total cost under the effects of backorder price discounts and lost sales reduction. An iterative algorithm is followed to acquire numerical results. To demonstrate the model, some numerical instances, sensitivity analysis and managerial insights are provided.

A profit jump inventory model for imperfect quality items with receiving reparative batch and order overlapping in dense fuzzy environment

This paper presents an economic order quantity (EOQ) inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a dense fuzzy environment Here, the imperfect items are identified by screening and are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterwards, the items are returned to the supplier to be reworked. Also, discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error free. An order overlapping scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. However, we assume the total monthly demand quantity as the dense fuzzy number because of learning effect. Moreover, first of all a profit maximization deterministic model is developed and solve by classical method. Fuzzifying the final optimized function via dense fuzzy demand quantity we have employed extended ranking index rule for its defuzzification. During the process of defuzzification we make an extensive study on the paradoxical unit square of the left and right deviations of dense fuzzy numbers. A comparative study is made after splitting the model into general fuzzy and dense fuzzy environment. Finally numerical and graphical illustrations and sensitivity analysis have been made for its global justifications.

A Multi-Item Sustainable Manufacturing Model with Discrete Setup Cost and Carbon Emission Reduction Under Deterministic and Trapezoidal Fuzzy Demand

A Multi-Item Sustainable Manufacturing Model with Discrete Setup Cost and Carbon Emission Reduction Under Deterministic and Trapezoidal Fuzzy Demand

A FEPQ model of sustainable items with time and stock dependent demand under trade credit policy

Nowadays sustainable fuzzy economic production quantity (s-FEPQ) models gets more highlighted over classical fuzzy economic production quantity (EPQ) models. In this paper, we developed a fuzzy inventory model of sustainable items under time dependent quadratic rate of fuzzy demand and exponential holding cost where shortages are allowed and are fully backlogged considering obsolescence cost and carbon emission cost. Also the developed model is compared with stock dependent fuzzy demand. The proposed fuzzy inventory model is solved via generalised Hukuhara derivative approach. Two different cases are considered by using generalised Hukuhara: differentiability and generalised Hukuhara. For the first time, in this sustainable fuzzy EPQ model, an alternative approach of payment is proposed. After that, the proposed model has been solved by using multi-objective genetic algorithm. The proposed model and technique are lastly illustrated by providing numerical examples. The results from the two methods are compared and some sensitivity analyses both in tabular and graphical forms are presented and discussed.

Inventory control techniques in a two-echelon supply chain model with fuzzy demand and learning effect

Inventory control techniques in a two-echelon supply chain model with fuzzy demand and learning effect

Inventory control techniques in a two-echelon supply chain model with fuzzy demand and learning effect

Inventory control techniques in a two-echelon supply chain model with fuzzy demand and learning effect

Optimizing an Imperfect Production Model with Varying Setup Cost, Price Discount, and Lead Time Under Fuzzy Demand

This article considers the two-tier supply chain based on the single setup multiple delivery (SSMD) policy between a single vendor and a single buyer. The entire production process is performed in a single setup and the logarithmic reduction function is employed to reduce the expense of this setup. As the machine switches from the in-control stage to the out-of-control stage, the output of the manufactured item is found to be defective. Continuous investment has been made to reduce this imperfect production by improving the quality of the item. Furthermore, this model takes into account incomplete product restructuring. In some cases, due to certain issues, such as lead time, the order quantity may not be received on time. The buyer’s lead time duration is controlled by adding the crashing cost. The purpose of this research is to achieve optimum setup cost and defective item percentage with minimum total supply chain cost under a triangular fuzzy demand. Two numerical examples have been considered to evaluate this model. Moreover, sensitivity analysis, graphical representation, and managerial insights are given. Finally, the model obtains the minimum supply chain cost with decision variables as demonstrated by the numerical study.

A super-network equilibrium optimization method for operation architecture with fuzzy demands

From the view of information flow, a super-network equilibrium optimization model is proposed to compute the solution of the operation architecture which is made up of a perceptive level, a command level and a firepower level. Firstly, the optimized conditions of the perceptive level, command level and firepower level are analyzed respectively based on the demand of information relation, and then the information supply-and-demand equilibrium model of the operation architecture super-network is established. Secondly, a variational inequality transformation (VIT) model for equilibrium optimization of the operation architecture is given. Thirdly, the contraction projection algorithm for solving the operation architecture super-network equilibrium optimization model with fuzzy demands is designed. Finally, numerical examples are given to prove the validity and rationality of the proposed method, and the influence of fuzzy demands on the super-network equilibrium solution of operation architecture is discussed.

A multi-constrained supply chain model with optimal production rate in relation to quality of products under stochastic fuzzy demand

For the production of complex products, this study investigates a flexible production system with a variable production rate as an alternative method to overcome the stock-out risk because of the uncertainty of fuzzy-stochastic demand in an integrated model. The variable production rate enables vendors to fulfill demand uncertainties and reduce the lead time. To establish the relationship between the process quality and production rate three functions, linear, quadratic, and cubic, have been introduced in the mode. The development of such an advanced flexible production system requires a considerably higher setup cost and increases the supply chain cost. To overcome this, the authors introduce a discrete investment function to control setup costs. Authors utilize a crashing cost to reduce the duration of the lead time within the supply chain (SC) structure. In real-life, vendors and buyers face different constraints and set some targets for themselves. Here, the authors consider the storage space and budget constraint for the vendor and customers’ service level constraint for the buyer. An SC model is proposed to find the optimal order quantity, reorder point, lead time, investment for setup cost reduction, and production rate with the minimized total expected cost of the chain. To get the optimal solutions to decision variables, the authors employed a classical optimization technique in the proposed model. An improved algorithm for the global minimum expected cost of SC is designed under the flexible production system. Three numerical examples with comparative study to the previous model and the sensitivity analysis are included to test and validate the proposed model. The numerical analysis and comparative study prove that the proposed model attains the minimum SC cost at the decision variables' optimal values.

A Fuzzy Demand-Profit Model for the Sustainable Development of Electric Vehicles in China from the Perspective of Three-Level Service Chain

Electric vehicles have great potential in dramatically reducing environmental pollution, which has become an important strategic direction for future sustainable development. With the influence of policy support and market, the construction of new energy supply infrastructure in China has achieved remarkable outcomes. However, according to the actual use of the new energy supply facilities, there is still a severe imbalance between long queues and unattended charging stations in some areas. Therefore, this paper aims to establish a fuzzy demand-profit model to accurately optimize new energy supply from the perspective of the three-level service chain. Then, based on authoritative historical sales data of electric vehicles in China in 2011–2018, the model is used to analyze the fuzzy demand for electric vehicle charging capacity. The research results indicate that the fuzzy demand-profit model is an effective tool to promote the coordination of new energy supply, which will provide support for the sustainable development of electric vehicles in China.

An intelligent design for remanufacturing method based on vector space model and case-based reasoning

Design for Remanufacturing (DfRem) plays an important role in remanufacturing, which promotes the product remanufacturability, and enhance the efficiency of remanufacturing processes. However, due to the large and fuzzy demand data, it is difficult to accurately extract DfRem targets from the customer demand data. Moreover, the process of DfRem scheme generation includes conceptual design, general design and detailed design. The remanufacturability of products needs be considered at the design process, which makes the DfRem scheme solution process very complicated. For the purpose of accurately extracting DfRem targets and shortening design cycle, it is necessary to apply intelligent technology for customer demand analysis and DfRem solution. To address this, an intelligent DfRem method based on vector space model (VSM) and case-based reasoning (CBR) is proposed. Firstly, for accurate extraction of DfRem targets, VSM is employed to extract customer demand data features from the mass customer demand data embedded with remanufacturing information, and K-means technique is applied to classify customer demand data features thus to extract DfRem targets. After extraction of DfRem targets, CBR is utilized to retrieve the case that is most similar to the DfRem targets from DfRem and remanufacturing process knowledge bases. In order to improve the accuracy of the retrieval, ontology is used to construct standard knowledge expression. Finally, this method has been evaluated utilizing the DfRem of clutch remanufacturing as case studies. The results show that the method can accurately generate design scheme to satisfy the customer demands. In this paper, the intelligent DfRem method has been developed by Visual Studio and Microsoft SQL Server, which can quickly generate the most suitable solution.

Simulative study of a novel fuzzy demand controlled ventilation for façade-integrated decentralized systems in renovated residential buildings

Decentralized mechanical ventilation systems had a sustainable growth in the past ten years in order to guarantee air exchange in highly airtight renovated residential buildings. Smart control strategies could provide a solution to the tradeoff between energy efficiency, hygrothermal comfort and indoor air quality. In this paper, a novel fuzzy demand controlled ventilation strategy is proposed, using state-of-the-art sensors often available in ventilation systems. The proposed controller is tested using a co-simulation approach and is compared to other typical mechanical ventilation control strategies. Results show that this approach provides around 25% energy savings in comparison to a constant airflow strategy, and around 12% against typical smart ventilation systems. The obtained differences regarding hygrothermal comfort and indoor air quality are negligible, and the proposed controller succeeds on keeping the indoor environment in the acceptable range. Finally, the developed fuzzy controller could potentially allow control systems to adapt to different occupant preferences, by tailoring the membership functions to each user.