Fuzzy Demand Research Articles

Dynamic Supplier Selection and Its Optimal Strategy Considering Full Truck Load and Fuzzy Demand using Fuzzy Expected Value-Based Programming

This article proposes a linear integer optimization model incorporating fuzzy parameters to find the optimal solution for a dynamic supplier selection problem with uncertain demand. The uncertain demand value is represented using a fuzzy variable. A fuzzy expected value-based linear optimization solver is used to address the optimization problem, to minimize the total cost under fuzzy demand values. Several computational experiments were conducted to evaluate and analyze the model. The results show that the proposed model effectively identifies the optimal suppliers for each product. Additionally, the model determines the optimal purchase volumes for each product type from the selected suppliers, leading to the minimal total expected cost.

Utilizing Multi-vehicle Traveling Purchaser Problem for Multiple-Supplier Selection and Multi-period Lot-Sizing in a Fuzzy Demand Environment

Utilizing Multi-vehicle Traveling Purchaser Problem for Multiple-Supplier Selection and Multi-period Lot-Sizing in a Fuzzy Demand Environment

Decision-making optimization for post-disaster restoration of multimodal transport networks in terms of resilience

IntroductionPublic health emergencies can have a ripple effect on the resilience of multimodal transport network, which will lead to problems such as route disruptions or blockages, route selection change and information transmission delay spreading to the whole network, further hindering the transportation planning and operational efficiency of the network. MethodsThis study constructs a multimodal transport route optimization model under uncertainty with the objective of the sum of transportation cost, transshipment cost, penalty cost and carbon emission cost. To enhance the computational efficiency of the model, a novel invasive weed optimization with memory and encoding value clustering capabilities is proposed. In addition, by fusing the Q-learning algorithm in reinforcement learning with the novel invasive weed algorithm, the action-value function table obtained from the training facilitates the selection of optimal routes. Based on empirical data, explore the sensitivity analysis of node disruptions, time windows, and fuzzy demand on route decision-making under public health emergencies. ResultsThe transport network is affected by public health emergencies, which makes the optimal route deviate from the expected goal, resulting in an increase in the total cost. The proportion of total cost is determined by the position of nodes in the network, with critical nodes suffering more losses than ordinary nodes. Reasonable setting of time windows and fuzzy demand intervals is an effective way to improve the resilience and transportation efficiency of multimodal transport network. ConclusionsThis study provides more applicable decision-making references for enterprises to prevent the risk of supply chain disruptions caused by public health emergencies.

An artificial bee colony optimization algorithms for solving fuzzy capacitated logistic distribution center problem

This paper presents a methodological approach to solving the fuzzy capacitated logistic distribution center problem, with a focus on the optimal selection of distribution centers to meet the demands of multiple plants. The distribution centers are characterized by fixed costs and capacities, while plant demands are modeled using fuzzy triangular membership functions. The problem is mathematically formulated by converting fuzzy demands into crisp values, providing a structured framework for addressing uncertainty in logistic planning. To support future research and facilitate comparative analysis, 20 benchmark problems were generated, filling a gap in the existing literature. Three distinct artificial bee colony algorithm variants were hybridized with a heuristic: one using the best solution per iteration, another incorporating chaotic mapping and adaptive procedures, and the third employing convergence and diversity archives. An experimental design based on Taguchi's orthogonal arrays was employed for optimizing the algorithm parameters, ensuring systematic exploration of the solution space. The developed methods offer a comprehensive toolkit for addressing complex, uncertain demands in logistic distribution, with code provided for reproducibility.Key contributions include:•Development of a fuzzy model for the selection of distribution centers with fixed costs and capacities under uncertain plant demands.•Generation of 20 benchmark problems to advance research in the fuzzy capacitated logistic distribution center problem domain.•Integration of a heuristic approach with three distinct ABC algorithm variants, each contributing unique methodological insights.

A Study of an EOQ Model of Deteriorated Items with Pentagonal Dense Fuzzy Demand Rate

In this project work, we deal with an economic order quantity inventory model of deteriorating items under non-random uncertain demand. Here we consider the customers screen the fresh items during the selling period. After a certain period of time, the deteriorated items are sold at a discounted price. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the pentagonal dense fuzzy, trapezoidal dense fuzzy, and triangular dense fuzzy for a comparative study. We have taken the numerical result using LINGO 18.0 software. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.

A novel fuzzy finite-horizon economic lot and delivery scheduling model with sequence-dependent setups

This paper addresses the economic lot and delivery scheduling problem (ELDSP) within three-echelon supply chains, focusing on the complexities of demand uncertainty, limited shelf-life of products, and sequence-dependency of setups. We develop a novel mixed-integer non-linear programming (MINLP) model for a supply chain comprising one supplier, multiple manufacturers with flexible flow shop (FFS) production systems, and multiple retailers, all operating over a finite planning horizon. The common cycle (CC) strategy is adopted as the synchronization policy. Our model employs fuzzy set theory, particularly the “Me measure,” to effectively handle the retailers’ demand uncertainty. Our findings indicate that total supply chain costs escalate with an increase in demand, final components’ holding costs, and sequence-dependent setup costs, but decrease with increasing production rates. Furthermore, while total costs are significantly sensitive to changes in demand, they are relatively insensitive to fluctuations in sequence-dependent setup times. The models developed offer valuable managerial insights for optimizing costs in synchronized multi-stage supply chains, aiding managers in making informed decisions about production lot sizes and delivery schedules under both deterministic and fuzzy demand scenarios. Additionally, the proposed models bridge key research gaps and provide robust decision-making tools for cost optimization, enhancing supply chain synchronization in practical settings.

An Inventory Model for Deteriorating Items with Price Dependent Demand Under Fuzzy and Neutrosophic Fuzzy Environment

This paper represents an inventory model of deteriorating items under fuzzy and neutrosophic environment without allowing shortages in inventory. Demand is price dependent and is compared between crisp, fuzzy and neutrosophic fuzzy demand. Realistically it is observed that although the cycle time of any supply chain system is uncertain but uncertainty is mainly dependent on the selling price. So, here we have compared the model using crisp, fuzzy and neutrosophic fuzzy demand. The result is illustrated with the help of numerical example under fuzzy and neutrosophic fuzzy demand. KEYWORDS: Inventory, Fuzzy and Neutrosophic Fuzzy Price dependent Demand.

Two-Phase Fuzzy Real-Time Approach for Fuzzy Demand Electric Vehicle Routing Problem with Soft Time Windows

Environmental concerns have called for several measures to be taken within the logistics and transportation fields. Among these measures is the adoption of electric vehicles instead of diesel-operated vehicles for personal and commercial-delivery use. The optimized routing of electric vehicles for the commercial delivery of products is the focus of this paper. We study the effect of several practical challenges that are faced when routing electric vehicles. Electric vehicle routing faces the additional challenge of the potential need for recharging while en route, leading to more travel time, and hence cost. Therefore, in this work, we address the issue of electric vehicle routing problem, allowing for partial recharging while en route. In addition, the practical mandate of the time windows set by customers is also considered, where electric vehicle routing problems with soft time windows are studied. Real-life experience shows that the delivery of customers’ demands might be uncertain. In addition, real-time traffic conditions are usually uncertain due to congestion. Therefore, in this work, uncertainties in customers’ demands and traffic conditions are modeled and solved using fuzzy methods. The problems of fuzzy real-time, fuzzy demand, and electric vehicle routing problems with soft time windows are addressed. A mixed-integer programming mathematical model to represent the problem is developed. A novel two-phase solution approach is proposed to solve the problem. In phase I, the classical genetic algorithm (GA) is utilized to obtain an optimum/near-optimum solution for the fuzzy demand electric vehicle routing problem with soft time windows (FD-EVRPSTW). In phase II, a novel fuzzy real-time-adaptive optimizer (FRTAO) is developed to overcome the challenges of recharging and real-time traffic conditions facing FD-EVRPSTW. The proposed solution approach is tested on several modified benchmark instances, and the results show the significance of recharging and congestion challenges for routing costs. In addition, the results show the efficiency of the proposed two-phase approach in overcoming the challenges and reducing the total costs.

A Smart Manufacturing Process for Textile Industry Automation under Uncertainties

Most textile manufacturing companies in the world heavily rely on manual labor, particularly in the fabric inspection section, especially for cotton fabric. Establishing smart manufacturing systems like industrial automation in the textile industry for cotton fabric inspection is important for error-free inspection. The proposed make-to-order (MTO) inventory model focuses on the strategic development of a supply chain network under fuzzy uncertainty. The distinctiveness of this research lies in integrating a methodology that involves human and machine interaction, along with allocating resources to investment in smart manufacturing. This article presents a case study of the Jagatjit Cotton Textiles (JCT) manufacturing company in Punjab, India, as an example to validate the model and check the performance of SMT in the fabric inspection process in cotton TC mills. This paper contributes by developing four distinct textile supply chain models with industrial automation under triangular and trapezoidal fuzzy demand. A numerical analysis is conducted to verify the effectiveness of installing automated fabric inspection machines in the cotton plant. This article proposes an iterative solution algorithm (KDPMG) to obtain the global optimum for the proposed model. A comparative study of the proposed algorithm, KDPMG, and the genetic algorithm (GA) is presented in this study to verify the credibility of the obtained results. It is observed that KDPMG provides more appropriate solutions to the problem compared to the GA. Moreover, the computational time of KDPMG is significantly less than that of the GA. The rigorous analysis reveals that maximum profit can be achieved under trapezoidal fuzzy demand with fully automated fabric inspection technology. Using a triangular fuzzy demand pattern, the model with fully automated smart manufacturing achieves an 8.62% higher profit compared to a traditional system. Similarly, in the case of a trapezoidal fuzzy demand pattern, the adoption of automation in cotton plants can achieve an 8.69% higher profit. Hence, the implementation of smart manufacturing systems in the mending section of the cotton textile industry proves to be more profitable compared to the traditional inspection process.

Enhancing Inventory Management through Advanced Technologies and Mathematical Methods: Utilizing Neutrosophic Fuzzy Logic

Optimal inventory management is one of the most critical components for companies to thrive in the competitive market while meeting their customers’ demands, reducing costs, and developing their operations. In this paper, the utilization of different technologies and instruments ranging from the most modern ones to mathematical ones was analyzed to demonstrate how the system can function successfully. It is expected that Neutrosophic fuzzy logic is one of the most complicated approaches that allow for proper uncertainty management, forecasting, and inventory control improvements. Fundamentally, the process could be that much more insightful due to the availability of mathematical modelling and on-the-go support systems. Through the use of dynamic programming with the help of Python tools to process these models, Full optimization under fuzzy demand is possible to achieve. Therefore, one could conclude that companies have many opportunities to develop their operations, reduce costs, and keep their customers happy even in a highly dynamic and uncertain business environment.

Optimizing Inventory Management: A Comprehensive Analysis of Models Integrating Diverse Fuzzy Demand Functions

This review study provides a comprehensive analysis of the classification of inventory models, with a focus on incorporating various fuzzy demand functions. The incorporation of fuzzy sets theory within inventory models is highlighted as a significant advancement in the field. The study emphasizes the importance of efficiently locating pertinent publications on this topic, rendering it a valuable resource for individuals interested in exploring inventory models that incorporate fuzzy demand functions. There was a need for a systematic and complete examination of recent breakthroughs in fuzzy inventory management. Our objective was to provide an illuminating overview of the significant developments in this field and offer insights into the probable future directions of research. Our evaluation of various model components has unveiled new and underexplored territories that may warrant further exploration. Perhaps it would be prudent to consider the possibility of establishing simpler models or incorporating qualitative methods into existing models and initiating a discourse on this topic.

Module division method of complex products for responding to user’s requirements

With the gradual diversification of personalized usage scenarios, user requirements play a direct role in product design decisions. Due to the problem of fuzzy demand caused by user cognitive bias, traditional design methods usually focus on realizing product functions and cannot effectively match user requirements. Therefore, this paper proposes a complex product module division method for user requirements. The method constitutes of three tasks, requirement analysis of module division, design mapping of module division and scheme implementation of module division. Firstly, based on the progressive architecture from initial requirements to precise requirements, the effective user requirements are obtained through similarity recommendation. Secondly, according to the four types of knowledge of function, geometry, physics and design, the design structure matrix is constructed to complete the Requirement-Function-Structure mapping. The improved Fuzzy C-means Algorithm is used to solve the mapping model, and finally a module division scheme that meets the user requirements is obtained. Taking the chip removal machine as an example, the rationality and effectiveness of the method are verified. The results show that the product modules divided by this method can effectively meet the multiple user requirements.

Sparrow search algorithm with adaptive t distribution for multi-objective low-carbon multimodal transportation planning problem with fuzzy demand and fuzzy time

In this paper, we present a multi-objective low-carbon multimodal transportation planning problem with fuzzy demand and fuzzy time (MOLCMTPP-FDFT) that minimizes both cost and time while incorporating mandatory carbon emission, carbon tax, carbon trading, and carbon offset policies. Chance constrained programming and interval programming are introduced to formulate the fuzzy demand chance constrained programming model and the fuzzy time interval programming model, respectively. Then, the mathematical model of uncertain MOLCMTPP-FDFT is transformed into a deterministic model. Based on the sparrow search algorithm, t distribution and the concept of Pareto optimality for multi-objective optimization, we also propose a solution strategy for the proposed model. In this algorithm, the number of iterations is used as the degree of freedom of - to update the sparrow location, which strikes a balance between the capabilities of global search and local search. Finally, the proposed algorithm and MOLCMTPP-FDFT are applied to a real case, resulting in a minimum cost of 260730.48 and a time duration of 13.044, which outperform the minimum cost of 268874.88 and minimum time of 18.32 obtained using single-mode transportation. The carbon emissions resulting from the lowest-cost solution obtained using single-mode transportation are 3,198.48, which are significantly more than the allowed emissions. Therefore, the proposed algorithm and mathematical model of MOLCMTPP-FDFT are valuable tools for optimizing multimodal transportation route. Additionally, the experimental results not only validate the superior efficiency and energy-saving benefits of the proposed multimodal transportation routes in comparison to the actual single-modal transportation, but also demonstrate the applicability of different low-carbon policies.

Possibilistic Aggregate Production Planning Considering Dynamic Workforce with Fuzzy Demand

This Aggregate Production Planning (APP) is a combination of Possibilistic Linear Programming (PLP), Fuzzy Goal Programming (FGP), and the Perfume Accounting System (PAS) to maximize profit. APP involves strategic decisions on Production levels, Inventory management, and Resource allocation to meet client demand while maximizing profit. Traditional planning models face significant challenges due to the uncertainties and complexities inherent in real world production environments. In this paper, there is an integration of PLP, Fuzzy Goal Programing, and throughput accounting system to overcome these challenges. At the very end of the paper, based on the data received from the company, the derived findings were by using Lingo Version 18 software. The model includes possibility distributions of the input parameters. Decision-makers can take into account the uncertainty and imprecision in demand forecasts and dynamic workforce in maximizing profit while taking into account risk tolerance.

Green Distribution Route Optimization of Medical Relief Supplies Based on Improved NSGA-II Algorithm under Dual-Uncertainty

With growing concerns about environmental issues, sustainable transport schemes are receiving more attention than ever before. Reducing pollutant emissions during vehicle driving is an essential way of achieving sustainable transport plans. To achieve sustainable transport and reduce carbon emissions, on the premise of ensuring rescue timeliness, this research proposes a multi-objective distribution route optimization model considering the minimization of transportation cost and transportation risk under dual-uncertainty constraints, providing a practical framework for determining the optimal location of rescue centers and distribution routes in emergencies using fuzzy theory. First, this paper proposes objective functions that innovatively take into account the congestion risk and accident risk during the distribution of medical supplies while introducing the carbon emission cost into the transportation cost and using the fuzzy demand for supplies and the fuzzy traffic flow on the roads as uncertainty constraints. Then, this paper designs a multi-strategy hybrid nondominated sorting genetic algorithm (MHNSGA-II) based on the original form to solve the model. MHNSGA-II adapts a two-stage real number coding method for chromosomes and optimizes the population initialization, crowding distances selection, and crossover and mutation probability calculation methods. The relevant case analysis demonstrates that, compared with the original NSGA-II, MHNSGA-II can decrease the transportation cost and transportation risk by 42.55% and 5.73%, respectively. The sensitivity analysis verifies the validity and rationality of the proposed model. The proposed framework can assist decision makers in emergency logistics rescue.

An inventory analysis in a multi-echelon supply chain system under asymmetry fuzzy demand: a fmincon optimization

In this article, the three-echelon supply chain model is developed with a single supplier, a single vendor and a single buyer in a fuzzy environment. The three-stage inspection technique is considered at the end of the vendor's process to supply high-quality products to the buyer. Moreover, the demand rate of the product in the market is often assumed to be uncertain, and accordingly, in this paper, the uncertainty is handled using fuzzy numbers. The primary goal of this model is to minimize the overall inventory cost relative to the asymmetry hexagonal fuzzy demand. Additionally, a backorder strategy is incorporated to gain customer satisfaction and reduce lost sales. To validate this model, numerical examples are tested and constrained non-linear optimization (i.e. fmincon solver) is performed to derive the optimal solution for the decision variables. Finally, conclusions with potential future directions are provided.

Optimization of Closed-loop Supply Chain Network for Vegetable and Fruit Agricultural Products Considering Fuzzy Demand and Purchasing Price

Due to the seasonal and perishable nature of vegetable and fruit agricultural products, which can easily cause sudden changes in demand and prices in a short period of time, a decision model framework was established to address the uncertainty issues related to vegetable and fruit agricultural products. The framework consists of triangular fuzzy numbers, a closed-loop supply chain network model for vegetable and fruit agricultural products, and an optimization model based on chance constrained programming, while considering demand, return rate,utilization rate. And with the goal of minimizing the sum of fixed costs, transportation costs, purchasing costs, packaging costs, storage costs, processing cost and disposal costs in the supply chain network, the model is validated through two scenarios: fuzzy demand and deterministic demand. The model calculation results indicate that under certain other conditions, the return rate is positively correlated with the total cost; The relationship between utilization rate and total cost may be either positive or negative, influenced by the combined effects of transportation costs and disposal costs in reverse logistics activities; The cost increase and facility selection corresponding to adjacent demand proportion nodes are different. Proved the effectiveness and feasibility of the model.

Multi-modal and multi-product hierarchical hub location problem with fuzzy demands

The hub location is a major problem in the systems with high dependence on the transportation of goods, information, and passengers between the constituent parts. The present study is aimed to introduce a multi-commodity multi-model hierarchical hub location problem with uncertain demand. Thus, it is estimated by intuitionistic fuzzy variables. The objective function in the present problem is to minimize the total transportation costs in the network to determine the optimal hub location, allocate non-hub nodes to the hubs and the ground hubs to the air hubs, and identify the type of vehicles required in each route. The model has a hierarchical structure consisting of a three-echelon network (i.e., central hubs, non-central hubs, and demand nodes) connected in the star-tour-star form. A four-index mathematical model was presented and solved by GAMS optimization software. The results indicated that the objective function (cost) has a descending trend with increasing the number of hubs which can be assigned to the decline in the transportation costs. The costs increased by a decrease in the maximum delivery time which could be due to the selection method of the transportation mode. In the multi-product case, the costs declined by increasing the number of hubs as these hubs decremented the network complexity. Regarding the NP-Hard nature of the hub problems, a genetic meta-heuristic algorithm was proposed in the MATLAB software to solve the large-scale problem. According to the results, this algorithm offered close-optimal solutions. Noteworthy, this study employed known AP datasets.

Optimal Procurement of COVID-19 Vaccine with Time-Dependent Holding Cost and Shortages under Cloud Fuzzy Demand Rate

COVID-19 vaccine has emerged as the most powerful weapon against the spread of the coronavirus. Therefore, the management of the vaccine inventory is undoubtedly the most influential and important task for the global distribution of the vaccine. This paper is an attempt to model the vaccine inventory system having time-varying holding costs and partially backlogged shortages. The concept of fuzzy set and cloud pentagonal fuzzy number has been incorporated to make the models more realistic and applicable. Models are solved and validated through numerical examples and graphical representation. Further, sensitivity analysis has been done to identify the most sensitive parameters of all. Finally, managerial insights and conclusions have been drawn to make the vaccine inventory system more robust.

Data-Driven Empty Container Repositioning for Large Scale Railway Network With Fuzzy Demands

The Chinese rail network has a fast-growing number of containers in service to promote intermodal transport service and to attract more freight demand to the railway for a sustainable transport system. The repositioning of empty containers induces a significant problem for the large-scale rail network, due to the spatial imbalance between freight supply and demand. Traditionally, the empty container repositioning (ECR) problem is solved with the estimated parameters of a given demand distribution, which may difficult known to decision maker. This article develops a data-driven framework for the ECR problem based on the large datasets available. This framework employs machine-learning algorithms to forecast the supply/demand of empty containers, and to draw parameters identifying the factors that can be hardly integrated into optimization models. Based on those parameters, two optimization models for different ECR modes are then proposed to explore the optimal ECR plan. An integrated weight coefficient is introduced into the objective functions, which minimizes the total kilometers that empty containers transported. The models are solved by CPLEX after constraints conversion based on triangular fuzzy supply/demand. The numerical results based on a real-world case show that the proposed solution method can yield the optimal empty container repositioning plan. The total container-kilometer may increase after data-driven parameters are introduced, as some of the empty container repositioning may no longer follow the shortest path, while the final plan becomes more practicable and executable.