模糊随机需求下多产品报童问题的均衡策略

针对模糊随机需求下单制造商多零售商的分布控制型多产品报童问题, 建立了含资金约束的期望利润最大化两层规划模型.结合模糊随机模拟技术与遗传算法, 设计了求解模型的混合智能算法.该算法不仅可获得上层制造商的最优折扣批发价及下层零售商的最优订购量,亦可求得该折扣形式的起始折扣点(折扣区间).算例分析表明,当制造商采取最优数量折扣策略时:1)促使零售商订货量增加至资金约束上限;2)部分产品订货量可达模糊随机市场需求的最大可能值:3)零售商和制造商的利润均增加.     

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。     

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.     

离散模糊需求报童问题的可信性模型研究

基于可信性理论,建立了确定离散模糊需求报童问题订货量的期望成本与利润模型,并与基于可能性理论的质心特征值分析模型进行了比较.数值研究结果表明:1)对应每一模型的最小模糊成本和最大利润的订货量不一致,且模糊期望模型与质心特征值模型确定的订货量不同;2)对应不同订货量,模糊可能性成本、利润之和及期望成本、利润之和均不为固定常数.由于在模糊环境下,与概率测度对应的模糊量描述是可信性测度,所以,相比而言,离散模糊需求报童问题的模糊期望值模型较模糊可能性模型好.     

需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.     

模糊随机需求报童问题的Stackelberg-Nash均衡策略

针对模糊随机需求下的分布控制型报童问题,建立了无数量折扣和有数量折扣情况下的利润最大化两层规划模型,并结合模糊随机模拟技术和遗传算法设计了模型求解的混合智能算法.解决了上层制造商制定包括折扣区间和折扣价格的最优数量折扣策略,以及下层多零售商确定各自的最优订货量的Stackelberg-Nash均衡策略问题.     

离散模糊需求报童问题的可能性模型研究

基于可能性分布函数质心特征值,本文建立了确定离散模糊需求报童问题订货量的利润模型,并分析了成本模型和利润模型的关系。研究结果表明:1)基于可能性分布函数质心的模糊可能性成本和利润模型确定的订货量不一致;2)对应不同订货量,模糊可能性成本与利润之和不为固定常数。数值计算表明:该方法不可取。     

带有随机订货点的两阶段报童模型

销售商可通过二次订货以达到降低风险、增加利润的目的,然而在实际中由于生厂商供货能力不足等不可控因素,销售商往往无法确定何时能进行第二次订货。针对这种现象,本文研究二次订货时间不确定的报童问题,假设随机订货时间点和需求率均服从均匀分布,建立了带有随机订货点的两阶段报童模型,给出了两阶段最优期望总订货量,使得零售商在整个销售期内的期望利润达到最大值。最后通过数值算例,对比分析了本文的二次订购模型与传统一次订购模型,研究结果指出在整个销售期内二次订货可以提高零售商的期望利润。     

服务水平约束下动态定价与库存管理

本文研究服务水平约束下的动态定价与库存管理问题。企业在有限期内销售某种产品,产品的需求为随机需求,且期望需求依赖于产品价格。在每一期期初,企业需要在满足服务水平约束的条件下同时决定订货量和产品价格。本文首先构建了动态定价和订购联合决策的随机动态规划模型,并证明了最优解的存在性。进一步,通过对最优解的结构进行刻画,将原问题的求解转化为若干子问题的求解,降低了问题求解的难度。通过对最优解的分析发现,当期初库存增大时,产品最优价格降低。通过分析目标服务水平对利润的影响,证明了服务水平与利润之间存在权衡,实现高的服务水平需要承受利润损失。数值模拟表明,相对于传统的静态定价策略,采用动态定价策略可以降低追求服务水平所带来的利润损失,验证了动态定价策略的有效性。     

随机需求下有产能约束的技术创新策略研究

在随机需求和技术变革的环境下,基于有产能约束的单供应商-单零售商的供应链结构,研究供应商分销价格决策和技术创新策略以及零售商订货决策。建立了三阶段Stackelberg博弈模型,通过逆推方法求得了供应商最优分销价格和技术创新策略以及零售商最优订货量,深入探讨了供应商产能、新技术出现概率以及市场需求期望与波动分别对供应商、零售商和供应链整体利润的影响。结果表明当供应商产能不足时进行技术创新会提高供应商和供应链的利润,但零售商因间接承担供应商技术创新的投资成本而利润下降;当供应商产能过剩时进行技术创新则会降低供应商及供应链的利润,而零售商的利润增加。新技术出现概率增加会提高供应链各成员的利润;提高市场需求期望并减小市场波动对供应商及供应链有利,但可能会降低零售商的利润。     

A Multi-Objective Production Inventory Model with Backorder for Fuzzy Random Demand Under Flexibility and Reliability

In this paper, an Economic Production Quantity (EPQ) model is developed with flexibility and reliability consideration of production process in an imprecise and uncertain mixed environment. The model has incorporated fuzzy random demand, an imprecise production preparation time and shortage. Here, the setup cost and the reliability of the production process along with the backorder replenishment time and production run period are the decision variables. Due to fuzzy-randomness of the demand, expected average demand is a fuzzy quantity and also imprecise preparation time is represented by fuzzy number. Therefore, both are first transformed to a corresponding interval number and then using the interval arithmetic, the single objective function for expected profit over the time cycle is changed to respective multi-objective functions. Due to highly nonlinearity of the expected profit functions it is optimized using a multi-objective genetic algorithm (MOGA). The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.     

Random fuzzy EOQ model with imperfect quality items

This paper investigates an economic order quantity (EOQ) problem with imperfect quality items, where the percentage of imperfect quality items in each lot is characterized as a random fuzzy variable while the setup cost per lot, the holding cost of each unit item per day, and the inspection cost of each unit item are characterized as fuzzy variables, respectively. In order to maximize the expected long-run average profit, a random fuzzy EOQ model is constructed. Since it is almost impossible to find an analytic method to solve the proposed model, a particle swarm optimization (PSO) algorithm based on the random fuzzy simulation is designed. Finally, the effectiveness of the designed algorithm is illustrated by a numerical example.     

Dynamic pricing model and algorithm for perishable products with fuzzy demand

This paper studies the dynamic pricing problem of selling fixed stock of perishable items over a finite horizon, where the decision maker does not have the necessary historic data to estimate the distribution of uncertain demand, but has imprecise information about the quantity demand. We model this uncertainty using fuzzy variables. The dynamic pricing problem based on credibility theory is formulated using three fuzzy programming models, viz.: the fuzzy expected revenue maximization model, α‐optimistic revenue maximization model, and credibility maximization model. Fuzzy simulations for functions with fuzzy parameters are given and embedded into a genetic algorithm to design a hybrid intelligent algorithm to solve these three models. Finally, a real‐world example is presented to highlight the effectiveness of the developed model and algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Two storage inventory model with fuzzy deterioration over a random planning horizon

An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α₁ and α₂ are also presented.     

Project scheduling problem with mixed uncertainty of randomness and fuzziness

Project scheduling problem is to determine the schedule of allocating resources so as to balance the total cost and the completion time. This paper considers project scheduling problem with mixed uncertainty of randomness and fuzziness, where activity duration times are assumed to be random fuzzy variables. Three types of random fuzzy models as expected cost minimization model, (α, β)-cost minimization model and chance maximization model are built to meet different management requirements. Random fuzzy simulations for some uncertain functions are given and embedded into genetic algorithm to design a hybrid intelligent algorithm. Finally, some numerical experiments are given for the sake of illustration of the effectiveness of the algorithm.     

An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon

An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

不确定同时取送货车辆路径问题及粒子群算法研究

研究了不确定同时取送货车辆路径问题(VRPSPD),考虑运行环境的不确定性,顾客时间窗口要求和对顾客同时进行取货和送货服务的情况,以运作成本最低和顾客满意度最高为决策目标,构建不确定VRPSPD数学模型。模型中,引入模糊随机理论来描述决策环境中的双重不确定性,假定顾客需求量(送货量)和取货量是模糊随机变量。随后,提出基于模糊随机算子的改进粒子群算法对模型进行求解。为了适应模型特点和提高算法效率,设计合理的编码和解码过程,制定多个适应度函数方案处理多目标问题,并应用更加科学的更新策略。最后在应用案例中,通过参数测试获取合理的算法参数取值,采用计算结果分析和求解算法测评验证模型和算法的有效性。