Optimal production inventory policy for defective items with fuzzy time period

In this paper, an optimal production inventory model with fuzzy time period and fuzzy inventory costs for defective items is formulated and solved under fuzzy space constraint. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is linearly stock dependent. The defective rate is taken as random, the inventory holding cost and production cost are imprecise. The fuzzy parameters are converted to crisp ones using credibility measure theory. The different items have the different imprecise time periods and the minimization of cost for each item leads to a multi-objective optimization problem. The model is under the single management house and desired inventory level and product cost for each item are prescribed. The multi-objective problem is reduced to a single objective problem using Global Criteria Method (GCM) and solved with the help of Fuzzy Riemann Integral (FRI) method, Kuhn–Tucker condition and Generalised Reduced Gradient (GRG) technique. In optimum results including production functions and corresponding optimum costs for the different models are obtained and then are presented in tabular forms.     

A weighted goal programming approach for replenishment planning and space allocation in a supermarket

We propose a mixed integer non-linear goal programming model for replenishment planning and space allocation in a supermarket in which some constraints on budget, space, holding times of perishable items, and number of replenishments are considered and weighted deviations from two conflicting objectives, namely profitability and customer service level, are minimized. We apply a minimum–maximum approach to introduce demand where the maximum demand is a function of price change and allocated space. Each item is presented in the form of multiple brands, probably exposed to price changes, competing to obtain more space. In addition to inventory investment costs, replenishment costs, and inventory holding costs we also include costs related to non-productive use of space. The order quantity, the amount of allocated showroom and backroom spaces, and the cycle time of joint replenishments are key decision variables. We also propose an extended model in which price is a decision variable. Finally we solve the model using LINGO software and provide computational results.     

A survey analysis of service quality for domestic airlines

This paper presents an effective approach for evaluating service quality of domestic passenger airlines by customer surveys. To reflect the inherent subjectiveness and imprecision of the customers' perceptions to the quality levels provided by airlines with respect to multiple service attributes, crisp survey results are represented and processed as fuzzy sets. A fuzzy multicriteria analysis (MA) model is used to formulate the evaluation problem. The model is solved by an effective algorithm which incorporates the decision maker's attitude or preference for customers' assessments on criteria weights and performance ratings. An empirical study of domestic airlines on a highly competitive route in Taiwan is conducted to demonstrate the effectiveness of the approach. The evaluation outcome provides airlines with their internal and external competitive advantages, relative to competitors in terms of customer-perceived quality levels of service.     

A production–recycling–inventory system with imprecise holding costs

This paper presents an optimal control recycling production inventory system in fuzzy environment. The used items are bought back and then either put on recycling or disposal. Recycled products can be used for the new products which are sold again. Here, the rate of production, recycling and disposal are assumed to be function of time and considered as control variables. The demand inversely depends on the selling price. Again selling price is serviceable stock dependent. The holding costs (for serviceable and non-serviceable items) are fuzzy variables. At first we define the expected values of fuzzy variable, then the system is transferred to the fuzzy expected value model. In this paper, an optimal control approach is proposed to optimize the production, recycling and disposal strategy with respect so that expected value of total profit is maximum. The optimum results are presented both in tabular form and graphically.     

A hybrid method of Pareto,TOPSIS and genetic algorithm to optimize multi-product multi-constraint inventory control systems with random fuzzy replenishments

Multi-periodic inventory control problems are mainly studied employing one of two assumptions. The first is the continuous review, where depending on the inventory level, orders can be placed at any time, and the other is the periodic review, where orders can be placed only at the beginning of each period. In this paper, we relax these assumptions and assume that the time-periods between two replenishments are random fuzzy variables. While in the model of the problem at hand the decision variables are of integer type and there are space and service level constraints, for the shortages we consider a combination of back-order and lost-sales. We show the model of this problem to be an integer-nonlinear-programming type and in order to solve it, a hybrid method of Pareto, TOPSIS and Genetic Algorithm approach is used. At the end, a numerical example is given to demonstrate the applicability of the proposed methodology.     

基于双论域模糊粗糙集的应急决策模型与方法

以突发危机事件应急决策为应用背景,讨论了双论域上模糊粗糙集的基本理论,建立了基于模糊相容关系的双论域模糊粗糙集模型. 在此基础上,把突发危机事件应急决策转化为一个具有模糊决策对象的双论域决策近似空间上的粗糙近似问题,构建了基于双论域模糊粗糙集的应急决策模型.首先在双论域近似空间中计算模糊决策对象的上(下)近似,进而结合经典非确定型决策的思想给出了突发危机事件应急决策的规则.同时,给出了模型的算法.该模型给出了一种在不完全信息环境下应急决策的方法,给出了在充分考虑决策者个人偏好信息基础上的决策置信度以及最优决策规则.该方法能够比较充分地符合应急决策信息不充分、资源有限以及时间紧迫的基本特征, 进而对突发危机事件应急决策提供科学的理论基础和现实的决策方法.最后,通过应用算例说明了模型的应用过程,结果验证了本文给出模型的有效性。     

Branch and price for the vehicle routing problem with discrete split deliveries and time windows

The Discrete Split Delivery Vehicle Routing Problem with Time Windows (DSDVRPTW) consists of designing the optimal set of routes to serve, at least cost, a given set of customers while respecting constraints on vehicles’ capacity and customer time windows. Each customer can be visited by more than one vehicle since each customer’s demand, discretized in items, can be split in orders, i.e., feasible combinations of items. In this work, we model the DSDVRPTW assuming that all feasible orders are known in advance. Remarkably, service time at customer’s location depends on the delivered combination of items, which is a modeling feature rarely found in literature. We present a flow-based mixed integer program for the DSDVRPTW, we reformulate it via Dantzig-Wolfe and we apply column generation. The proposed branch-and-price algorithm largely outperforms a commercial solver, as shown by computational experiments on Solomon-based instances. A comparison in terms of complexity between constant service time vs delivery-dependent service time is presented and potential savings are discussed.     

Fuzzy variables

The purpose of this study is to explore a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed. The approach we propose is analogous to the sample space concept of probability theory. A fuzzy variable is a mapping from an abstract space (called the pattern space) onto the real line. The membership function is obtained as the extension of a special type of capacity (called a scale) from the pattern space to the real line via the fuzzy variable. In essence we are proposing an entirely new definition of a fuzzy set on the line as a mapping to the line rather than on the line. The current definition of a transformation of a fuzzy set is obtained as a derived result of our model. In addition, we derive the membership function of sums and products of fuzzy sets and present an example which reinforces the credibility of our approach.     

拟合模糊观测数据的线性回归模型

本文讨论了实验观测数据为一般模糊数的线性最优拟合问题，通过定义模糊数空间中的距离，建立了模糊数空间到模糊数空间的回归模型，证明了最小二乘问题的解与其正则方程组的解的一致性，进而由正则方程组导出了问题的显式解。本模型的计算简便，具有实用价值。     

An interactive fuzzy goal programming approach for multi-period multi-product production planning problem

This study addresses an interactive multiple fuzzy goal programming (FGP) approach to the multi-period multi-product (MPMP) production planning problem in an imprecise environment. The proposed model attempts to simultaneously minimize total production costs, rates of changes in labor levels, and maximizing machine utilization, while considering individual production routes of parts, inventory levels, labor levels, machine capacity, warehouse space, and the time value of money. Piecewise linear membership functions are utilized to represent decision maker’s (DM’s) overall satisfaction levels. A numerical example demonstrates the feasibility of applying the proposed model to the MPMP problem. Furthermore, the proposed interactive approach facilitates the DM with a systematic framework of decision making process which enables DM to modify the search direction to reach the most satisfactory results during solving process.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.     

Repair systems with exchangeable items and the longest queue mechanism

We consider a repair facility consisting of one repairman and two arrival streams of failed items, from bases 1 and 2. The arrival processes are independent Poisson processes, and the repair times are independent and identically exponentially distributed. The item types are exchangeable, and a failed item from base 1 could just as well be returned to base 2, and vice versa. The rule according to which backorders are satisfied by repaired items is the longest queue rule: At the completion of a service (repair), the repaired item is delivered to the base that has the largest number of failed items. We point out a direct relation between our model and the classical longer queue model. We obtain simple expressions for several probabilities of interest, and show how all two-dimensional queue length probabilities may be obtained. Finally, we derive the sojourn time distributions.     

A possibilistic decision model for new product supply chain design

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a possibilistic SC configuration model for new products with unreliable or unavailable SC statistical data. The supply chain is modeled as a network of stages. Each stage may have one or more options characterized by the cost and lead-time required to fulfill required functions and may hold safety stock to prevent an inventory shortage. The objective is to determine the option and inventory policy for each stage to minimize the total SC cost and maximize the possibility of fulfilling the target service level. A fuzzy SC model is developed to evaluate the performance of the entire SC and a genetic algorithm approach is applied to determine near-optimal solutions. The results obtained show that the proposed approach allows decision makers to perform trade-off analysis among customer service levels, product cost, and inventory investment depending on their risk attitude. It also provides an alternative tool to evaluate and improve SC configuration decisions in an uncertain SC environment.     

Inventory management of spare parts in an energy company

We address the problem of how to determine control parameters for the inventory of spare parts of an energy company. The prevailing policy is based on an (s, S) system subject to a fill rate constraint. The parameters are decided based mainly on the expert judgment of the planners at different plants. The company is pursuing to conform all planners to the same approach, and to be more cost efficient. Our work focuses on supporting these goals. We test seven demand models using real-world data for about 21?000 items. We find that significant differences in cost and service level may appear from using one or another model. We propose a decision rule to select an appropriate model. Our approach allows us to recommend control parameters for 97.9% of the items. We also explore the impact of pooling inventory for different demand sources and the inaccuracy arising from duplicate item codes.     

Batching deteriorating items with applications in computer communication and reverse logistics

We study two deterministic scheduling problems that combine batching and deterioration features. In both problems, there is a certain demand for identical good quality items to be produced in batches. In the first problem, each batch is assigned an individual machine that requires a cost and a time to be activated. All the machines are identical, work in parallel, and always produce good quality items. All the items are available at time zero and they deteriorate while waiting for production. Deterioration results in a linear increase of time and cost of production. In the second problem, there is a single machine that produces good quality as well as defective items in batches. Each batch is preceded by a setup time and requires a setup cost. Defective items have to be reworked on the same machine. They deteriorate while waiting for rework. At a time to be decided, the machine switches from production to rework defective items of the current batch. After rework, every defective item has the required good quality. In both problems, the objective is to find batch partitioning such that a linear combination of the production cost and production completion time is minimized. The two problems are observed at computer service providers and also reverse logistics. In computer service providers, machines and items correspond to communication service channels and information transfer tasks, respectively. We reduce both problems to minimizing a function of one variable representing the number of batches. In an optimal solution of either problem, there are at most two different batch sizes. Linear time algorithms are proposed for both problems.     

A queueing model for general group screening policies and dynamic item arrivals

Classification of items as good or bad can often be achieved more economically by examining the items in groups rather than individually. If the result of a group test is good, all items within it can be classified as good, whereas one or more items are bad in the opposite case. Whether it is necessary to identify the bad items or not, and if so, how, is described by the screening policy. In the course of time, a spectrum of group screening models has been studied, each including some policy. However, the majority ignores that items may arrive at random time epochs at the testing center in real life situations. This dynamic aspect leads to two decision variables: the minimum and maximum group size. In this paper, we analyze a discrete-time batch-service queueing model with a general dependency between the service time of a batch and the number of items within it. We deduce several important quantities, by which the decision variables can be optimized. In addition, we highlight that every possible screening policy can, in principle, be studied, by defining the dependency between the service time of a batch and the number of items within it appropriately.     

Fuzzy multi-objective programming for supplier selection and risk modeling: A possibility approach

Selection of supply chain partners is an important decision involving multiple criteria and risk factors. This paper proposes a fuzzy multi-objective programming model to decide on supplier selection taking risk factors into consideration. We model a supply chain consisting of three levels and use simulated historical quantitative and qualitative data. We propose a possibility approach to solve the fuzzy multi-objective programming model. Possibility multi-objective programming models are obtained by applying possibility measures of fuzzy events into fuzzy multi-objective programming models. Results indicate when qualitative criteria are considered in supplier selection, the probability of a certain supplier being selected is affected.     

A unified approach to fuzzy pattern recognition

Goldfarb has proposed a unified approach to pattern recognition. In Goldfarb's approach the data from a pseudometric space are isometrically embedded in a pseudo-Euclidean space. The data representation is built for every particular data set. The resulting data space will be data dependent. The aim of this paper is to extend Goldfarb's approach for fuzzy clustering. A fuzzy clustering procedure for a pseudometric data set is given. A generalisation of this algorithm to obtain the cluster substructure of a fuzzy class is also proposed.     

An approximation analysis for an assembly-like queueing system with time-constraint items

We study an assembly-like queueing system one of whose queues has items with generally distributed time-constraints, where this system has a single server providing services using each item individually. It is well-known that analysis of a queueing system which has items with time-constraint (i.e., impatient items) is difficult since the analytical model must involve all the departure times of these impatient items. We therefore propose to employ the techniques of Whitt’s approximation and show the method for obtaining the stationary distribution of the model. Through some simulation experiments, we discuss the validation of our approximation model, and show that the approximation is accurate in various kinds of situations (e.g., service time distribution and the number of queues).     

Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinement of the polynomial Lyapunov function so as to make it share the fuzzy structure of the model proves advantageous. Conditions thus obtained are tested via available SOS software.