服务员多重休假的易逝品排队库存系统的稳态分析

考虑(s,S)库存策略的易逝品M/M/1排队库存系统,其中库存为空时服务员多重休假,休假时间服从指数分布.顾客的到达过程服从泊松过程,服务员的服务时间,易逝品的寿命和补货时间均服从指数分布.首先,利用拟生灭过程给出系统的稳态条件.其次,研究忽略服务时间的M/M/1休假库存系统模型,并求出了系统的稳态分布.在此基础上,进一步研究具有正服务时间的M/M/1休假排队库存系统模型,并得到了系统队长,库存水平和服务员状态的乘积形式的稳态联合分布.此外,还计算了系统的性能指标,并给出了系统单位时间的平均费用函数.最后,利用数值算例分析系统参数对一些主要性能指标的影响,并利用遗传算法计算系统最优库存策略和最优平均费用.     

具有两类需求服务的随机库存系统控制策略研究

研究具有两类顾客排队需求服务的随机库存系统.系统采取(s,Q)补货策略且当库存水平下降到安全库存s时,到达的第二类顾客以概率P得到服务.首先,建立库存水平状态转移方程并通过递推算法求解获得库存水平稳态概率分布和系统稳态指标;接下来,构建库存成本函数;最后,采用数值试验的方法研究该库存系统的最优控制策略并考察系统参数的敏感性.     

面向两类客户的双渠道采购库存控制策略

采用排队分析技术,构建基于利润最大化的库存控制模型来考察零售商面向两类客户需求的环境下,双渠道采购库存控制策略.首先,建立了库存水平状态稳态概率分布的平衡方程,并推导出其稳态概率分布以及作为构建系统利润函数的稳态性能指标.然后,建立系统利润最优化模型,并设计改进的遗传算法.最后,通过数值实验考察系统库存控制策略以及参数的敏感性.     

基于排队的库存服务系统最优控制策略

研究一个连续盘点的(s,Q)补货的库存服务系统。基于排队理论建立库存水平状态平衡方程,并推导出库存水平稳态概率分布以及作为库存控制的系统稳态性能指标。以库存成本最小化为目标,构建服务水平约束的库存控制模型。针对模型的非线性约束与整数型变量的特征,采用一种改进的遗传算法(IGA)用于决策变量的寻优。数值实验表明,当目标服务水平大于库存系统内生的服务水平时,实施服务水平约束能够降低库存控制成本。     

带有止步和中途退出的优先权排队系统

研究了一个带有止步和中途退出的优先权排队系统,其中系统中有两类顾客,第一类顾客具有优先权,而且可能中途退出,第二类顾客可能止步和中途退出.首先,建立了系统稳态概率满足的方程组.其次,采用分块矩阵的方法得到了两类顾客的稳态分布,并且得到了系统中两类顾客的的平均队长、平均中途退出率等性能指标.最后,进行了相应的性能分析与比较,为系统的优化设计提供了参考.     

具有不耐烦顾客和多重工作休假的排队库存系统

研究具有不耐烦顾客和多重工作休假的M/M/1/N排队库存系统模型,分别考虑了系统中库存为零时服务员休假和系统中顾客数为零时服务员休假两种休假方式,基于(s,S)库存策略,运用矩阵迭代方法得到了系统稳态概率分布,并给出系统相关性能指标,进而建立系统平均库存费用函数.通过数值算例对比分析了两种休假方式下的系统主要参数变化对系统重要性能指标的影响,并在最优费用的层面对两个模型的优劣进行了对比分析.     

带负顾客和强占优先权的不耐烦信元排队

考虑带有负顾客的两类信元的强占优先权M/M/1排队系统.两类信元及负顾客的到达过程均为泊松过程.两类信元到达后分别在各自有限的缓冲器内排队,第一类信元较第二类信元有强占优先权,同时第一类信元是不耐烦的.负顾客一对一抵消队尾的第一类信元(若有),若系统中无第一类信元,到达的负顾客就自动消失.负顾客不接受服务.采用矩阵分析的方法得到了两类信元各自的稳态分布,并作了相应的性能分析.     

基于两类需求分布的(s,S)库存系统研究

分析了一种基于销售损失和两类需求的(s,S)库存系统.系统拥有两种消费者,每种形式的消费者需求满足相互独立且参数不同的泊松过程,补货前置期服从指数分布.由生灭过程理论推导出稳态分布方程,并得到库存水平状态的稳态概率分布以及库存控制的系统性能指标,构建出服务水平约束下的库存控制模型.结合一种改进的遗传算法,找寻最小的库存成本.最后对系统模型中各个参数进行敏感性分析并指示其库存管理意义.     

多类顾客共享排队系统的信息理论

多类顾客的共享排队系统是排队论中一个既重要又困难的研究方向,它在计算机网络、生产制造系统与交通网络等领域中有着许多重要的实际应用.近年来,国外学者对多类顾客的共享排队系统已经开展了一些关键性的研究工作,给出了稳态联合队长的母函数,由此可以得到稳态联合队长的一阶矩和二阶矩.然而,由这个母函数反演来提供多类顾客共享排队系统的稳态联合队长的直接表达式却是一个多年来的困难问题.基于此,本文利用信息论中的最大熵原理,提供了一个高精度的近似表达式,其中这个近似表达式与它的精确表达式能够保证前三阶矩是相同的.另一方面,针对这个近似表达式,本文实现了它的有效数值计算,并通过数值算例分析了这个近似表达式中的重要因子是如何依赖于系统的原始参数.因此这个近似表达式对于推进多类顾客共享排队系统的实际应用具有重要的理论意义,同时本文的方法与结果不仅为研究多类顾客的共享排队系统提供了一条新的重要途径,而且为如何将信息理论应用于排队系统、排队网络以及更一般的随机模型研究提供了理论依据与技术支撑.     

带有转换时间和阀值的非抢占优先权排队模型

在[3]中,我们研究了在抢占规则下带有转换时间和阈值的两类顾客优先权排队系统,本文就非抢占情形对这样的系统作进一步的研究,同样求出两类顾客队长的稳态联合概率母函数。籍助这些母函数可求出诸如平均队长这样一些重要的系统性能指标。     

A hybrid tabu search based heuristic for the periodic distribution inventory problem with perishable goods

Most of the research on integrated inventory and routing problems ignores the case when products are perishable. However, considering the integrated problem with perishable goods is crucial since any discrepancy between the routing and inventory cost can double down the risk of higher obsolescence costs due to the limited shelf-life of the products. In this paper, we consider a distribution problem involving a depot, a set of customers and a homogeneous fleet of capacitated vehicles. Perishable goods are transported from the depot to customers in such a way that out-of-stock situations never occur. The objective is to simultaneously determine the inventory and routing decisions over a given time horizon such that total transportation cost is minimized. We present a new “arc-based formulation” for the problem which is deemed more suitable for our new tabu search based approach for solving the problem. We perform a thorough sensitivity analysis for each of the tabu search parameters individually and use the obtained gaps to fine-tune the parameter values that are used in solving larger sized instances of the problem. We solve different sizes of randomly generated instances and compare the results obtained using the tabu search algorithm to those obtained by solving the problem using CPLEX and a recently published column generation algorithm. Our computational experiments demonstrate that the tabu search algorithm is capable of obtaining a near-optimal solution in less computational time than the time required to solve the problem to optimality using CPLEX, and outperforms the column generation algorithm for solving the “path flow formulation” of the problem in terms of solution quality in almost all of the considered instances.     

A column generation-based heuristic algorithm for an inventory routing problem with perishable goods

An inventory routing problem is a variation of the vehicle routing problem in which inventory and routing decisions are determined simultaneously over a given time horizon. The objective is to minimize the sum of transportation and inventory costs. In this paper, we study a specific inventory routing problem in which goods are perishable (PIRP). We develop a mathematical model for PIRP and exploit its structure to develop a column generation-based solution approach. Cutting planes are added to improve the formulation. We present computational experiments to demonstrate that our methodology is effective, and that the integration of routing and inventory can yield significant cost savings.     

A Production Lot-Size Model for Perishable Items Under Two Level Trade Credit Policy for a Retailer with a Powerful Position in a Supply Chain System

This paper investigates a production lot-size inventory model for perishable items under two levels of trade credit for a retailer to reflect the supply chain management situation. We assume that the retailer maintains a powerful position and can obtain full trade credit offered by supplier yet retailer just offers the partial trade credit to customers. Under these conditions, retailer can obtain the most benefits. Then, we investigate the retailer’s inventory policy as a cost minimization problem to determine the retailer’s inventory policy. A rigorous mathematical analysis is used to prove that the annual total variable cost for the retailer is convex, that is, unique and global-optimal solution exists. Mathematical theorems are developed to efficiently determine the optimal ordering policies for the retailer. The results in this paper generalize some already published results. Finally, numerical examples are given to illustrate the theorems and obtain a lot of managerial phenomena.     

Control policies for single-stage production systems with perishable inventory and customer impatience

We consider problems of inventory and admission control for make-to-stock production systems with perishable inventory and impatient customers. Customers may balk upon arrival (refuse to place orders) and renege while waiting (withdraw delayed orders) during stockouts. Item lifetimes and customer patience times are random variables with general distributions. Processing, setup, and customer inter-arrival times are however assumed to be exponential random variables. In particular, the paper studies two models. In the first model, the system suspends its production when its stock reaches a safety level and can resume later without incurring any setup delay or cost. In the second model, the system incurs setup delays and setup costs; during stockouts, all arriving customers are informed about anticipated delays and either balk or place their orders but cannot withdraw them later. Using results from the queueing literature, we derive expressions for the system steady-state probabilities and performance measures, such as profit from sales and costs of inventory, setups, and delays in filling customer orders. We use these expressions to find optimal inventory and admission policies, and investigate the impact of product lifetimes and customer patience times on system performance.     

A model of JIT make-to-stock inventory with stochastic demand

We consider a firm that manages its internal manufacturing operations according to a just-in-time (JIT) system but maintains an inventory of finished goods as a buffer against random demands from external customers. We formulate a model in which finished goods are replenished by a small fixed quantity each time period. In the interest of schedule stability, the size of the replenishment quantity must remain fixed for a predetermined interval of time periods. We analyse the single-interval problem in depth, showing how to compute a cost-minimising value of the replenishment quantity for a given interval length, and characterising the optimal cost, inventory levels and service as functions of the interval length and initial inventory. The model displays significant cost and service penalties for schedule stability. A dynamic version of the problem is also formulated, and shown to be convex in nature with relatively easily computed optima.     

Optimal ordering policies for continuous review perishable inventory models

This paper extends the notions of perishable inventory models to the realm of continuous review inventory systems. The traditional perishable inventory costs of ordering, holding, shortage or penalty, disposal and revenue are incorporated into the continuous review framework. The type of policy that is optimal with respect to long run average expected cost is presented for both the backlogging and lost-sales models. In addition, for the lost-sales model the cost function is presented and analyzed.     

考虑客户消费行为的易逝品物流配送干扰管理模型

针对干扰事件导致易逝品物流配送难以顺利实施这一难题,运用干扰管理思想,结合行为科学中关于消费行为的研究方法对客户进行分类,将物流配送干扰管理问题分为两个阶段:第一阶段处理优先服务的客户,第二阶段处理一般服务的客户;进而构建两阶段的、多目标的干扰管理模型,并提出改进的蚁群算法进行求解。实验结果表明,本文方法虽然配送成本较高,但是却完成了较重要客户的配送任务,这有利于较大幅度提高企业的潜在效益,进而验证了在处理易逝品物流配送干扰问题上的有效性。     

考虑合同保质期的快速失效药品的二级供应链库存策略研究

医院药品对保质期和服务水平有非常高的要求,同时,药品的库存空间在医药库存中也有重要影响。首先针对快速失效的医药药品考虑了医药库存的合同保质期以及库存空间约束,同时考虑医院库存以及制造商库存,基于经济订货批量模型和经济生产批量模型建立了二级供应链的医药库存模型,然后用MATLAB软件求解了模型最优解,并对一些重要参数进行了敏感性分析。研究发现,合同保质期对医院订购批量、制造商生产批量和总库存成本有一定的影响,其中对于制造商的生产批量以及医院的库存成本影响较大。如果不考虑合同保质期的约束,将会对总库存成本带来更大损失。     

Optimal price and lot size determination for a perishable product under conditions of finite production, partial backordering and lost sale

The paper describes an EOQ model of a perishable product for the case of price dependent demand, partial backordering which depends on the length of the waiting time for the next replenishment, and lost sale. The model is solved analytically to obtain the optimal price and size of the replenishment. In the model, the customers are viewed to be impatient and a fraction of the demand is backlogged. This fraction is a function of the waiting time of the customers. In most of the inventory models developed so far, researchers considered that inventory accumulates at the early stage of the inventory and then shortage occurs. This type of inventory is called IFS (inventory followed by shortage) policy. In the present model we consider that shortage occurs before the starting of inventory. We have proved numerically that instead of taking IFS, if we consider SFI (shortage followed by inventory) policy, we would get better result, i.e., a higher profit. The model is extended to the case of non-perishable product also. The optimal solution of the model is illustrated with the help of a numerical example.     

需求依赖于服务水平的易变质品库存策略研究

本文研究需求依赖于上一周期服务水平、缺货时订单部分损失的两周期易变质品库存问题。分别考虑一次订货和多次订货两种情况,以平均利润最大化为目标构建库存模型,证明了模型解的存在性和唯一性,得到了最优库存服务水平和最优补货策略。最后,通过算例给出两个模型的应用,对重要参数进行了灵敏度分析,并且将两种模型的结果进行了对比分析。结果表明:订单损失率的增加会提高服务水平,但会使得利润降低;顾客期望服务水平的提高会降低第一阶段的服务水平,同时使利润减少;单位库存持有成本或变质率的增加会降低服务水平和平均利润。通常情况,企业通过多次订货能获得更大的利润,而只有当库存持有成本极小时,一次订购才能够获得更大的利润。同时,结果也表明:服务水平对库存策略有较大的影响,因此在进行库存决策时考虑服务水平具有重要的作用。