A membership function approach to lot size re-order point inventory problems in fuzzy environments

Inventory models play an important role in logistics and supply chain management for reducing cost and increasing customer satisfaction. This paper develops an approach to derive the fuzzy objective value and decision variables of the fuzzy lot size re-order point inventory problem with parameters being fuzzy numbers and the shortages are backordered with extra cost incurred. Different from the existing studies, the idea is based on Zadeh's extension principle. A pair of mixed integer nonlinear programs (MINLP) parameterised by the possibility level α is formulated to calculate the lower and upper bounds of the minimal total cost per unit time at α, through which the membership function of the minimal total cost per unit time is constructed. At the same time the membership functions of the optimal order quantity and the optimal re-order point are also provided. A numerical example studied by previous studies is solved successfully to demonstrate the validity of the proposed method. Compared with previous studies, the obtained results which precisely and completely conserve the fuzziness of the input information are more informative for finding the best inventory policy since they are expressed by membership functions rather than by crisp ones. Moreover, to provide representative crisp solutions for designing inventory systems, the Yager's ranking index method is adopted to defuzzify the obtained membership functions. The successful extension of inventory models to fuzzy environments permits inventory models to have wider applications in practice.     

A mathematical programming approach to supply chain models with fuzzy parameters

Supply chain (SC) models play an important role in supply chain management (SCM) for reducing costs and finding better ways to create and deliver value to customers. An approach to deriving the membership function of the fuzzy minimum total cost of the multi-product, multi-echelon, and multi-period SC model with fuzzy parameters is proposed in this article. On the basis of α-cut representation and the extension principle, a pair of mathematical programs are formulated to calculate the lower and upper bounds of the fuzzy minimum total cost at possibility level α. The membership function of the fuzzy minimum total cost is constructed by enumerating different values of α. To demonstrate the validity of the proposed procedure, a four-echelon five-period SC model with fuzzy parameters is solved successfully. Since the objective value is expressed by membership functions rather than by crisp values, they completely conserve the fuzziness of input information when some of the SC data are ambiguous. Thus the proposed approach can represent SCs with fuzzy parameters more accurately, and more information is provided for designing SCs in real-world applications.     

Non-linear programming for the optimization of machine repair problems in fuzzy environments

Machine repair models have wide applications in many systems such as production line systems and maintenance operations. A procedure is developed to derive the fuzzy objective value of the cost-based machine repair optimization problem, in that the cost coefficients and the machine breakdown rate are fuzzy numbers. On the basis of the extension principle, a pair of non-linear programs are formulated to calculate the lower and upper bounds of the fuzzy minimum expected total cost at the possibility level α. The membership function of the minimum expected total cost is constructed by enumerating different values of α. A numerical example is solved successfully to demonstrate the validity of the proposed method. Since the minimum expected total cost is completely expressed by a membership function rather than by a crisp value, the fuzziness of the input data is conserved, and more information is provided for decision-making. Furthermore, since the optimum repair rate obtained is fuzzy, a crisp optimum repair rate based on the Yager ranking indices is recommended for practical use.     

Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times

This paper is motivated by the performance evaluation of circulating vertical conveyor systems (CVCSs). CVCSs are bulk queues of transportation type. These material handling systems feature generally distributed inter-arrival times, which can be longer than the bulk service time. This leads to interdependencies between the number of arrivals in consecutive service intervals and the number of loads in the queue. We propose a new discrete-time approach for the steady-state analysis of such bulk service queues of transportation type with general arrival and service processes and finite server and limited queue capacities. The approach is based on a finite Markov chain that generates complete probability distributions for the key performance measures, including the queue length, waiting time and departing batch size. The proposed approach is exact in the cases of discrete-time slots, e.g. as in communication systems. We investigate the discretisation error that arises if the approach is used as an approximation for the continuous time using a numerical comparison to a discrete-event simulation. Moreover, we examine the impact of arrival stream variability on the system performance and compare the positive effects of a higher frequency of server visits with the effects arising from larger pickup capacities.     

CUSUM Statistical Monitoring of M/M/1 Queues and Extensions

Many production and service systems can be modeled as queueing systems. Their operational efficiency and performance are often measured using queueing performance metrics (QPMs), such as average cycle time, average waiting length, and throughput rate. These metrics need to be quantitatively evaluated and monitored in real time to continuously improve the system performance. However, QPMs are often highly stochastic, and hence are difficult to monitor using existing methods. In this article, we propose the cumulative sum (CUSUM) schemes to efficiently monitor the performance of typical queueing systems based on different sampling schemes. We use M/M/1 queues to illustrate how to design the CUSUM chart and compare their performance with several alternative methods. We demonstrate that the performance of CUSUM is superior, responding faster to many shift patterns through extensive numerical studies. We also briefly discuss the extensions of CUSUM charts to more general queues, such as M/G/1, G/G/1, or M/M/c queues. We use case studies to demonstrate the applications of our approach. Supplementary materials for this article are available online.     

Waste treatment: an environmental,economic and social analysis with a new group fuzzy PROMETHEE approach

Most complex decisions involve several stakeholders and therefore need to be solved using a group multi-criteria decision method. However, stakeholders or decision-makers often have divergent views, especially in the environmental sector. In order to integrate this divergence, a new group fuzzy PROMETHEE approach is introduced to combine the traditional environmental criteria of life cycle assessments with social and economic criteria. The modelling of uncertainty within the group of decision-makers using a fuzzy approach makes this method unique. The proposed fuzzy approach differs significantly from the standard one. The decision-makers express their judgments in crisp forms. In order to take into account the intrinsic dispersion of judgments within the group, a posteriori fuzzification procedure is applied. The crisp values are not simply aggregated; they are converted into a triangular fuzzy number based on the given evaluations. As a consequence, the definition of fuzzy membership functions, as required in standard fuzzy logic, is not required, which simplifies the process and makes it more reliable. The new approach is illustrated with a real case study concerning the selection of the best waste treatment solution in a natural park from among a traditional incinerator and an innovative integrated plant.     

Control charts for traffic intensity monitoring of Markovian multiserver queues

A number of recent research studies have applied queueing theory as an approximate modeling tool to mathematically describe industrial systems, which include manufacturing, distribution, and service, for instance. Among the main observable characteristics in queues, the number of users in the system can be controlled to keep waiting times as minimal as possible. The design of efficient control charts is an attempt to monitor and control such systems. Control charts are proposed to monitor infinite queues with Markovian arrivals, exponential service times, and s identical parallel servers. The proposed charts monitor traffic intensities, which are the ratio between the arrival rate and the service rate, estimated through the number of users in the queueing system at random epochs. The effectiveness and efficiency of the proposed approaches in terms of the average run lengths are established by a comprehensive set of Monte Carlo simulations.     

Non-stationary delay analysis of runway systems

This paper proposes a new approach for the estimation of aircraft delays at airports given time-varying demand and time-dependent processing times. Based on a characterization of performance models for runway systems, the analysis addresses a runway system where arrivals and departures share a common runway. It is assumed that the requests for landings and take-offs can be modeled as independent Poisson processes and that the processing times are generally distributed with operation-dependent rates. The runway is operated according to the first-come-first-serve rule. A stationary backlog-carryover (SBC) approach is developed for the approximation of time-dependent performance measures for this dynamic queueing system with mixed operations. Numerical examples demonstrate that the SBC approximation is reliable for the analysis of runway queues. Because of its simplicity, the approach is numerically stable and fast.     

模糊中心聚类的模式识别学习方法

基于一个约束条件下的非线性规划问题的优化计算思想，把模糊中心聚类中计算输入矢量与中心的距离来实现聚类作为一种优化计算问题，证明了模糊中心聚类方法，取一个适当的属函数，其聚类中心vi为模糊聚类中心价值函数的极小值，推导出了基于模糊中心聚类的模式识别的无导师递推学习方法，提出了模糊中心聚类模式分类神经网络结构，该网络可以实现并行数据处理和模式分类的软划分和硬划分。     

任意隶属度函数模糊系统的逼近特性

以四边形隶属函数作为一般的隶属函数，利用StoneWeierstrass定理对任意隶属函数的模糊系统任意逼近紧集上的任意连续实函数进行证明，是对基本模糊系统逼近任意连续非线性函数理论的推广，模糊系统对任意非线性函数的逼近性能，是模糊系统用于系统辩识的理论依据。     

Lot size optimisation under pooled and unpooled scenarios in batch production system

The lot-sizing problem in batch manufacturing systems with capacity constraints is studied using queueing relationships and optimisation techniques. In this research, the effect of lot sizes when there are parallel machines and multiple part types is considered. Furthermore, the issue of whether or not to use pooled queues, based on part types, to feed the machines is examined. Different scenarios are evaluated using GI/G/n queueing approximations to predict performance and optimise lot sizes. Optimisation is based on minimising the mean flowtimes, which include queue and lot service times. The results show that if part types are very different, there are situations in which pooling is not advantageous.     

Fuzzy-based system reliability of a labour-intensive manufacturing network with repair

This paper presents a fuzzy-based assessment model to evaluate system reliability of a labour-intensive manufacturing system with repair actions. Due to the uncertainty in human performance, labour-intensive manufacturing systems must determine the capacity of each labourer in order to accurately characterise the performance of the systems. Therefore, we model such a manufacturing system as a fuzzy multi-state network in order to characterise the labourers’ influence on workstation performance. First, the workstation reliability is defined according to the loading state by three fuzzy membership functions, namely ‘under loading’, ‘normal loading’ and ‘over loading’, respectively. The system reliability is subsequently evaluated with fuzzy intersection operations in terms of these workstation reliabilities. Thus, the system reliability is defined as a fuzzy membership function to assess whether the manufacturing system performance is sufficient to satisfy the demand reliably. A case study of a footwear manufacturing system is illustrated to explain the proposed model. Furthermore, we apply the proposed model to a non-labour-intensive manufacturing network in order to validate the applicability to this class of systems.     

A rolling horizon approach for material requirement planning under fuzzy lead times

This paper proposes a fuzzy multi-objective integer linear programming (FMOILP) approach to model a material requirement planning (MRP) problem with fuzzy lead times. The objective functions minimise the total costs, back-order quantities and idle times of productive resources. Capacity constraints are included by considering overtime resources. Into the crisp MRP multi-objective model, we incorporate the possibility of occurrence of each uncertain lead time using fuzzy numbers. Then FMOILP is transformed into an auxiliary crisp mixed-integer linear programming model by a fuzzy goal programming approach for each fuzzy lead time combination. In order to defuzzify the set of solutions associated with each fuzzy lead time combination, a solution method based on the centre of gravity concept is addressed. Model validation with a numerical example is carried out by a novel rolling horizon procedure where uncertain lead times are updated during each planning period according to the centre of gravity obtained. For illustration purposes, the proposed solution approach is satisfactorily compared to a rolling horizon approach in which lead times are allocated when the possibility of occurrence is established at one.     

Analysis of finite-buffer state-dependent bulk queues

In this paper, we consider a general state-dependent finite-buffer bulk queue in which the rates and batch sizes of arrivals and services are allowed to depend on the number of customers in queue and service batch sizes. Such queueing systems have rich applications in manufacturing, service operations, computer and telecommunication systems. Interesting examples include batch oven processes in the aircraft and semiconductor industry; serving of passengers by elevators, shuttle buses, and ferries; and congestion control mechanisms to regulate transmission rates in packet-switched communication networks. We develop a unifying method to study the performance of this general class of finite-buffer state-dependent bulk queueing systems. For this purpose, we use semi-regenerative analysis to develop a numerically stable method for calculating the limiting probability distribution of the queue length process. Based on the limiting probabilities, we present various performance measures for evaluating admission control and batch service policies, such as the loss probability for an arriving group of customers and for individual customers within a group. We demonstrate our method by means of numerical examples.     

Modelling of material handling systems for facility design in manufacturing environments with job-specific routing

Traditionally, flow times distance is used as a surrogate for cost in facility design. However, this performance measure does not fully capture the impact of facility design decisions on operational performance measures such as cycle time and work-in-progress in the system, which are often more meaningful for managers, especially in a manufacturing environment. To better measure operational performance, modelling of material handling systems using a queueing network must be integrated in the facility design process. A number of approaches are discussed in the facility design literature for modelling material flow using queueing networks. In these approaches, Poisson arrival or Markovian job routing assumptions have been used. However, for many manufacturing environments, these assumptions lead to an inaccurate estimation of the material handling system's performance and thus lead to poor facility designs. Incorporating more general queueing results for non-Markovian systems is difficult, however, because the facility design process must investigate a large number of potential solutions and thus the results from the queueing models for the material handling system must be quickly obtained. In this paper, the need for more general queueing models of material handling systems in facility design is confirmed. Then, an approach based on multi-class queueing models is adapted to capture the change in variability of the system performance caused by both different arrangements of workstations in the facility and different arrival processes to the workstations due to the job routing in a computationally efficient manner. The proposed modelling approach is shown to provide more accurate results than previous methods used in facility design based on numerical comparisons with results from discrete-event simulation.     

A new query expansion method for document retrieval based on the inference of fuzzy rules

Abstract

Automatic query expansion based on user relevance feedback techniques can improve the performance of document retrieval systems. In this paper, we present a new query expansion method based on the inference of fuzzy rules and user relevance feedback techniques to deal with document retrieval. The proposed method uses membership functions and fuzzy rules to infer relevant degrees of expansion terms and puts the expansion terms with larger relevant degrees into the original user's query. Then, the system calculates the degree of similarity of each document with respect to the expanded user's query. The proposed method gets a higher average precision rate and a higher average recall rate than the existing methods for document retrieval.     

Transfer coefficients on the shell progressive poisoning model

Abstract

The idle server first (ISF) routing strategy in a finite queueing system with multiple unequal‐rate synchronous servers is studied. This paper extends the work of [4] by considering unequal‐rate servers. The input is assumed to be a batch Poisson distribution. The state transition equations used to describe the queueing behavior of the system are successfully solved. The performance measures, including average message blocking probability, average packet delay, average message delay, and system throughput, are obtained. The results show that ISF routing can have pretty good performance, and its effective measures are almost independent of routing probabilities. Validity of the analysis has also been verified by computer simulations.     

区间数多产品多计划期生产计划问题的目标规划求解方法

针对多目标、多产品、多计划期和需求、生产费用、生产能力等参数不确定的综合生产计划问题进行了研究。引入区间数描述生产计划问题中存在的不确定性,建立了以生产成本最小和设备利用率最大为优化目标的目标规划模型。为求解模型,运用区间规划理论和基于区间序关系的可能度定义,实现了区间目标规划模型的清晰等价转换,并采用Lingo软件完成模型求解。该方法解决了传统不确定优化方法在获取概率分布和模糊隶属度函数较为困难的不足,能根据决策者的偏好以交互方式分析出不同置信水平对目标的影响,为决策者在不确定环境下进行生产计划决策提供理论依据。最后,通过算例说明方法的有效性和灵活性。     

Incorporating fuzzy weather-related outages in transmission system reliability assessment

Fuzzy models for weather-related outages of overhead lines and a combined probabilistic and fuzzy technique for transmission system reliability assessment are presented. The region-divided weather states are modelled using a probability approach. This approach and the fuzzy models of weather-related outages are combined and incorporated into a Monte Carlo simulation procedure of transmission system reliability assessment to evaluate membership functions and mean values of reliability indices. The reliability test system is used to demonstrate an application of the proposed models and method. The membership functions of reliability indices provide a wider insight into the fuzziness of weather effects, which cannot be modelled by traditional probability concepts.     

Fuzzy Reliability Analysis of the Washing System in a Paper Plant for Components with Different Membership Function

The washing system in paper plant is a complex engineering system that needs to develop effective maintenance programs for enhancing its performance via reliability analysis. The reliability analysis of these systems require precise numerical data which may be very difficult to obtain in desired crisp form due to uncertainty. In general, triangular fuzzy number are used to quantify data uncertainty and fuzzy arithmetic operations are employed which give vide range of prediction for each computed reliability index due to accumulating phenomenon of fuzziness. To reduce the range of prediction of system reliability and fasten the computation process, this paper presents \(T_\omega \) (weakest t-norm) based generalized fuzzy lambda–tau technique in which different fuzzy membership functions are used to quantify uncertainty while \(\alpha \)-cut and \(T_\omega \) based approximate fuzzy arithmetic operations are employed for computation. The advantage of this technique is that this technique uses different fuzzy numbers as input to quantify different types of uncertainties and gives fuzzy reliability indices of the system having shape preserving characteristic, fitter decision values with compressed range of prediction under vague environment which is better for strong decision making to improve system performance. To show the effectiveness of the presented approach, computed results have been compared with results obtained from four other existing approaches. Moreover, this paper uses extended Tanaka et al. (Komal in Ocean Eng 155:278–294, 2018b) approach to rank the critical components of the system. Sensitivity, long run reliability and availability analyses have also been conducted to analyse the impact of variation of different reliability indices and time respectively on system performance.