一类系数为梯形模糊数的整数规划

介绍了模糊数学和整数规划的背景、现状、以及发展趋势,并以模糊结构元理论定义了梯形模糊加权序,进一步证明了模糊整数规划模型的最优解等价于整数规划模型的最优解,再利用整数规划模型的最优解的求解方法求解模糊整数规划模型的最优解,最后,通过算例验证方法的可行性.     

提前期需求为模糊随机条件下的连续库存补货策略

考虑提前期内需求为模糊随机变量且提前期为可缩短情形下,建立由购买商和供应商所组成的简单供应链连续库存补货策略优化模型,其中订单量、再订货点和提前期为决策变量.首先推导出模糊随机需求条件下购买商和供应链的成本函数,然后,进一步考虑总需求为三角模糊数,推导出供应商、购买商和供应链的模糊成本函数.在此基础上分别从购买商成本最小和供应链成本最小角度对模型进行求解,结合具体算例对模型进行应用分析和比较分析,结果表明模型具有有效性和实用性,并得出如下结论:从购买商本身角度考虑订购策略所产生的供应链成本总是大于从供应链整体角度考虑订货策略所产生的供应链成本,同时从购买商本身角度考虑订货策略所产生的最优订购量、购买商成本低于从供应链整体角度考虑订货策略所产生的最优订购量、购买商成本.     

模糊连续需求下供应链收益共享契约机制研究

研究一个由供应商和零售商组成的两级供应链系统在模糊连续需求环境下的运作过程。将市场需求视为三角模糊数,利用模糊截集理论分析模糊连续需求下的分散决策和集中决策过程,并给出收益共享契约机制下的决策模型。研究结果表明：在模糊连续需求环境下,零售商的订购量存在唯一最优解;供应链系统的“双重边际化”效应同样存在;收益共享契约机制可以实现供应链中成员问的协调。最后,通过数值例子对模型进行了比较分析。     

求解上层含约束条件的模糊二层线性规划的结构元方法

讨论了一类上层含约束条件的模糊二层线性规划模型,利用结构元方法,证明了模型最优解等价于二层线性规划模型最优解,并通过Kuhn-Tucker方法得到了模型最优解,最后通过数值算例验证了方法的可行性.     

模糊数据的线性回归模型

研究观测数据为模糊数据的统计线性回归模型 ,由该模型所得回归系数非模糊 ,易于应用。对于对称三角模糊数据一元线性回归给出最优解的解析表达式 ;将对称三角模糊数多元线性回归问题给出转化为一类二次规划问题的方法 ;证明了最优解的存在性和估计量的无偏性。     

制造商在模糊需求环境下的定价决策研究

提出制造商在模糊需求环境下定价决策的最优解问题.引入采用LR型模糊数均值的求解的方法.提出LR型模糊数形式运算的计算方法,并指出在所论问题中LR型模糊数对形式运算的封闭性,提出最优解求解的步骤并编制计算机程序以用于实际计算.举出实例,得出最优价格为122元的结论.     

模糊随机需求的连续盘点存储策略研究

考虑到需求的模糊随机性,建立模糊随机需求情况下连续盘点存储策略的模糊随机成本模型。利用模糊随机变量的期望值理论,推导出了其成本期望值模型的解析表达式,进而给出了最优再订货点所属区间的判别条件以及最优再订货点和经济订货量的计算式;基于此,设计了一模糊随机需求的连续盘点最优存储策略算法。最后结合数值算例,分析了模糊随机需求概率分布及缺货成本对最优存储策略的影响。     

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。     

制造商零售商系统在模糊需求环境下的订货决策研究

提出制造商零售商系统在模糊需求环境下订货量、批发价在合作与非合作情况下的最优解问题.引入采用LR型模糊数符号距离的求解的方法.提出LR型模糊数形式运算的计算方法,并指出在所论问题中LR型模糊数对形式运算的封闭性,提出最优解求解的步骤并编制计算机程序以用于实际计算.举出实例,得出最优订货量为634件的结论.     

带权值的模糊多目标线性规划

本文提出了求解一般多目标性规划问题 (MOL P)的带权值的模糊多目标线性规划方法 .证明了在权值都大于零的条件下 ,与 (MOLP)原问题对应的带权值的模糊多目标线性规划问题的最优解为模糊有效解 ,从而为原问题的有效解 ,并作了实例验证 .     

考虑随机模糊缺陷率且允许缺货的EOQ模型

针对实际库存管理中的产品缺陷问题,研究了含随机模糊缺陷率且允许缺货的经济订购批量(EOQ)模型,并运用随机模糊理论将其转化为确定模型,设计了随机模糊模拟仿真算法进而确定了其最优订购策略.数值算例分析了缺陷率对最优订货量和最优利润的影响.     

Improving service rate for a tree-type three-echelon supply chain system with backorders at retailer's level

This research deals with a distributive or tree-type three-echelon production-distribution supply chain system with allowable backorder. Allowing backorder could reduce the total of a production-distribution system by reducing holding cost due to the lower average inventory, even though backorders carry some cost and lower a company's goodwill. The main purpose of this research is to develop replenishment policies for a tree-type three-echelon supply chain system with allowable backorder. The supply chain network is composed of a producer, multiple distributors, and multiple retailers. This research attempts to improve service rate by reducing the backorder at the retailer level. The distributors are allowed to ship product to retailer quicker in order to reduce backorder. The total cost function of the proposed model is developed. Since the total cost function contains some integer variables, differentiating the function with respect to the variables could not be used as a basis to solve for the optimal solutions. A branching search process was utilized to find the integer solutions. A numerical example is used to demonstrate improvement in service rate and total cost using the model.     

客户耐烦期相同的生产——库存系统最优模型

在常数需求率以及有限生产率条件下研究了订货客户耐烦期相同的一类新的生产——库存模型 ,在每一个周期内考虑了延期交货时间超过耐烦期的短缺费用和销售机会损失等因素 ,给出了相应的最优生产时间和周期的确定方法 ,利用数学软件 Matlab及计算机为工具给出了数字例子进行说明 ,其方法和结果为库存系统的管理决策提供了理论依据     

A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

This paper develops a single wholesaler and multi retailers mixture inventory distribution model for a single item involving controllable lead-time with backorder and lost sales. The retailers purchase their items from the wholesaler in lots at some intervals throughout the year to meet the customers’ demand. Not to loose the demands, the retailers offer a price discount to the customers on the stock-out items. Here, it is assumed that the lead-time demands of retailers are uncertain in both stochastic and fuzzy sense, i.e., these are simultaneously random and imprecise. To implement this behavior of the lead-time demands, at first, these demands are assumed to be random, say following a normal distribution. With these random demands, the expected total cost for each retailer is obtained. Now, the mean lead-time demands (which are crisp ones) of the retailers are fuzzified. This fuzzy nature of the lead-time demands implies that the annual average demands of the retailers must be fuzzy numbers, suppose these are triangular fuzzy numbers. Using signed distance technique for defuzzification, the estimate of total costs for each retailer is derived. Therefore, the problem is reduced to optimize the crisp annual costs of wholesaler and retailers separately. The multi-objective model is solved using Global Criteria method. Numerical illustrations have been made with the help of an example taking two retailers into consideration. Mathematical analyses have been made for global pareto-optimal solutions of the multi-objective optimization problem. Sensitivity analyses have been made on backorder ratio and pareto-optimal solutions for wholesaler and different retailers are compared graphically.     

Optimal ordering policies for periodic-review systems with replenishment cycles

In this paper, we consider inventory models for periodic-review systems with replenishment cycles, which consist of a number of periods. By replenishment cycles, we mean that an order is always placed at the beginning of a cycle. We use dynamic programming to formulate both the backorder and lost-sales models, and propose to charge the holding and shortage costs based on the ending inventory of periods (rather than only on the ending inventory of cycles). Since periods can be made any time units to suit the needs of an application, this approach in fact computes the holding cost based on the average inventory of a cycle and the shortage cost in proportion to the duration of shortage (for the backorder model), and remedies the shortcomings of the heuristic or approximate treatment of such systems (Hadley and Whitin, Analysis of Inventory Systems, Prentice-Hall, Englewood Cliffs, NJ, 1963). We show that a base-stock policy is optimal for the backorder model, while the optimal order quantity is a function of the on-hand inventory for the lost-sales model. Moreover, for the backorder model, we develop a simple expression for computing the optimal base-stock level; for the lost-sales model, we derive convergence conditions for obtaining the optimal operational parameters.     

Intuitionistic fuzzy optimization technique for Pareto optimal solution of manufacturing inventory models with shortages

This paper discusses a manufacturing inventory model with shortages where carrying cost, shortage cost, setup cost and demand quantity are considered as fuzzy numbers. The fuzzy parameters are transformed into corresponding interval numbers and then the interval objective function has been transformed into a classical multi-objective EPQ (economic production quantity) problem. To minimize the interval objective function, the order relation that represents the decision maker’s preference between interval objective functions has been defined by the right limit, left limit, center and half width of an interval. Finally, the transformed problem has been solved by intuitionistic fuzzy programming technique. The proposed method is illustrated with a numerical example and Pareto optimality test has been applied as well.     

A stochastic periodic review integrated inventory model involving defective items, backorder price discount, and variable lead time

The purpose of this article is to investigate a stochastic integrated supplier-retailer inventory problem. The model analyzed in this article explores the problem of the protection interval, the backorder price discount, the lead time, and the numbers of shipments from the supplier to the retailer in one production run as control variables to widen applications for an integrated periodic review inventory model. We consider the situation in which the supplier and the retailer establish a long-term strategic partnership and contract to jointly determine the best strategy. We assume that the protection interval demand follows a normal distribution. Our objective is to determine the optimal review period, the optimal backorder price discount, the optimal lead time, and the optimal number of shipments from the supplier to the retailer in one production run, so that the joint expected annual total cost incurred has the minimum value. Furthermore, an algorithm of finding the optimal solution is developed. Also, the sensitivity analysis included and a numerical example is given to illustrate the results of the proposed model.     

模糊需求下订购批量问题的研究

库存管理模型在现实生活中有着广泛的运用,它为管理决策者有效地确定最佳订购批量提供帮助.然而,由于历史数据的缺乏,需求量在很多情况下往往被主观地确定,因而带有一定的模糊性.本文针对两种不同类型的模糊需求:离散型与连续型,运用模糊理论分别建立了相应的模糊库存模型.该模型不同于已有的模糊库存模型如下:在现有的模糊库存的文献中,大多采用的是利用模糊集的知识对确定EOQ模型加以研究,而本文从模糊理论的角度对报童问题进行研究.     

An inventory model with backorders with fuzzy parameters and decision variables

The paper considers an inventory model with backorders in a fuzzy situation by employing two types of fuzzy numbers, which are trapezoidal and triangular. A full-fuzzy model is developed where the input parameters and the decision variables are fuzzified. The optimal policy for the developed model is determined using the Kuhn-Tucker conditions after the defuzzification of the cost function with the graded mean integration (GMI) method. Numerical examples and a sensitivity analysis study are provided to highlight the differences between crisp and the fuzzy cases.