Inventory management with log-normal demand per unit time

This paper examines optimal policies in a continuous review inventory management system when demand in each time period follows a log-normal distribution. In this scenario, the distribution for demand during the entire lead time period has no known form. The proposed procedure uses the Fenton-Wilkinson method to estimate the parameters for a single log-normal distribution that approximates the probability density function (PDF) for lead time demand, conditional on a specific lead time. Once these parameters are determined, a mixture of truncated exponentials (MTE) function that approximates the lead time demand distribution is constructed. The objective is to include the log-normal distribution in a robust decision support system where the PDF that best fits the historical period demand data is used to construct the lead time demand distribution. Experimental results indicate that when the log-normal distribution is the best fit, the model presented in this paper reduces expected inventory costs by improving optimal policies, as compared to other potential approximations.     

Inventory control for lognormal demand

This paper develops an explicit but approximate solution to the reorder point inventory model for lognormal lead time demand. Solution to the same model under a constraint on fraction of demands backordered is also obtained. Both solutions are extended to cover the three- and four-parameter lognormal families, and the methods are illustrated with hypothetical data.     

Inventory models with back-order discounts and variable lead time

For inventory problems with stock-out under probabilistic demands, most of the published data assumes that the average shortages are very small and thus are neglected. However, some of the stock-out in practice might be significant and is back ordered and filled as soon as an adequate size of replenishment arrives. Typically, a supplier will institute an emergency expediting order to obtain the item when a shortage occurs and a price discount can always be offered on the stock-out item in order to secure more back orders. In this article, an inventory model with negotiable back orders is first proposed, then another model where lead time is also subject to change is discussed. Numerical examples are included to illustrate the procedures of the solution.     

Adaptive lead time quotation in a pull production system with lead time responsive demand

In this paper, a single-stage single-class kanban controlled manufacturing system is considered, where the problem is quoting accurate lead times for orders that are generated by an MRP system. Order release mechanism as in classical MRP is sensitive to the changes in the lead time according to the concept of lead time syndrome. The objective is to establish a cost effective lead time quoting procedure. The problem is modeled as a two-dimensional Markov chain, and it is solved explicitly by using matrix geometric techniques. Comparative analysis is done between static and dynamic lead time quoting procedures, and significant cost benefits of the dynamic procedure are shown under various scenarios. Guidelines for setting design parameters such as the number of kanbans and the frequency of updating the lead time are provided through numerical tests.     

A discrete-time round-robin queue with bernoulli input and general arithmetic service time distributions

Summary We present a discrete-time round-robin queue with a last-in-first-served rule: a newly arriving job receives a quantum of service immediately and only thereafter joins the tail of the queue. For Bernoulli input and general arithmetic service times we compute steady-state probabilities and mean response times.     

Design of production-inventory control systems incorporating fast-sampling control policies with implementation lead time

In this paper, singular perturbation methods are used to synthesize fast-sampling error-actuated control policies for two production-inventory system models in which there is a finite time delay of several sampling periods between the formulation and the implementation of the control policies. In the first model it is assumed that the demand for the product cannot be influenced by the management of the production-inventory system, and in the second model it is assumed that the demand for the product can be influenced by advertising and that the desired instantaneous demand rate is specified by management. In both cases, it is shown that the system will exhibit good transient and steady-state behaviour when controlled by such control policies. Furthermore, it is also shown that non-interacting control can be achieved when effective expenditure on advertising is introduced in order to influence the demand for the product, and that the provision of this extra flexibility thus leads to improved transient behaviour.     

Mixture inventory model with back orders and lost sales for variable lead time demand with the mixtures of normal distribution

In recent papers by Ben-Daya and Raouf and by Ouyang et al. a continuous review inventory model is presented in which they considered both the lead time and the order quantity as decision variables. When the demands of the different customers do not have identical lead times, then we cannot use only a distribution (such as Ouyang et al. who used a normal distribution) to describe the demand of the lead time. Hence, we have extended the model of Ouyang et al. by considering the mixtures of normal distribution (see the book by Everitt and Hand). In addition, we also still assume that shortages are allowed. Moreover, the total amount of stock-out is considered as a mixture of back orders and lost sales during the stock-out period. Moreover, we also develop an algorithmic procedure to find the optimal order quantity and optimal lead time; the effects of parameters are also studied.     

An ordering policy with lead time

An ordering policy in which a working item can be replaced by an item supplied by order with load time is considered. We discuss the optimum ordering policy minimizing the expected cost per unit time for an infinite time span. It is shown in n, theorem that there exists a finite and unique optimum policy under suitable conditions. A sub-optimum policy is also presented.     

Inventory model for seasonal demand with option to change the market

In real life, when bulk purchase becomes convenient or even mandatory, it is a common practice for distributors to explore an alternative market in order to maximize the revenue earned. In this paper, we consider an inventory model for a product having seasonal demand with two potential markets, say, primary and alternate. The distributor has a single opportunity of procurement prior to multiple demand seasons in the primary and the alternate market. Both the markets have similar demand patterns, with time lag between their demand seasons. The demand is a price and time dependent function with increasing, constant and declining phases within each demand season. The scale parameter of demand rate depends upon the market. In each market, successive seasons are separated by random time. In one replenishment cycle, the distributor has a single option to exit the primary market by transferring the inventory, with or without change in selling price. This option can be exercised at the end of any complete season at the primary market. Our investigations indicate that it will be beneficial for the distributor to shift to the alternate market even at a slightly lower selling price if demand rate in the alternate market is higher. Optimal number of seasons at the primary market before change of price or market is obtained. Optimal policy is obtained for jointly determining the order quantity and price. Concavity of the profit function is discussed. Solution procedure, numerical examples and sensitivity analysis are presented.     

Single-machine scheduling with general costs under compound-type distributions

We investigate the problem of scheduling n jobs on a single machine with the following features. The cost functions are general stochastic processes, which can be used to model the effects of stochastic price fluctuations, stochastic due times, etc., and the stochastic processing times follow a class of distributions, which includes exponential, geometric, and other families of distributions. Such a class of distributions is characterized by its characteristic functions. The optimal policies for these scheduling problems, both without precedence constraints, or with precedence in the form of nonpreemptive chains, are discussed, respectively. This research was partially supported by the Research Grants Council of Hong Kong under Earmarked Grant No. CUHK4170/03E, PolyU5251/03E, and N_CUHK442/05, and NSFC Research Funds No. 70329001, and 70518002.     

需求依赖广告费用和销售价格的newsboy型产品库存模型

在假定随机需求是关于销售价格和广告费用的一般函数的前提下,提出一个新的ｎｅｗｓｂｏｙ模型,给出了寻求最优广告费用、销售价格及订货量的分析方法,并且还分析了需求的不确定性对最优销售价格和广告策略的影响．最后,通过数值实例验证了模型的求解过程并得到相关管理启示．     

Integrated inventory control and inspection policies with deterministic demand

In this paper, we develop integrated inventory inspection models with and without replacement of nonconforming items. Inspection policies include no inspection, sampling inspection, and 100% inspection. We consider a buyer who places an order from a supplier. When a lot is received, the buyer uses some type of inspection policy. The fraction nonconforming is assumed to be a random variable following a beta distribution. Both the order quantity and the inspection policy are decision variables. In the inspection policy involving determining sampling plan parameters, constraints on the buyer and manufacturer risks are set in order to obtain a fair plan for both parties. A solution procedure for determining the operating policies for inventory and inspection consisting of order quantity, sample size, and acceptance number is proposed. Numerical examples are presented to conduct a sensitivity analysis for important model parameters and to illustrate important issues about the developed models.     

An optimal inventory solution for Weibull demand distributions

The problem considered here is an infinite stage inventory decision process in which the penalty cost for failing to have in stock sufficient items to satisfy demand at the next stage includes a fixed administrative cost (red tape) and a cost proportional to the deficiency in stock. It is shown here that when the demand follows a Weibull distribution, optimal constant stock level solution exists. A simple computer program is given to calculate this optimal solution.     

Analysis of the problem of continuous-product inventory control under deterministic lead time

Consideration was given to the control of the continuous-product inventory in the storage system delivering to the end consumers. In the system, the product is replenished at a deterministic lead time of duration obeying the volume of order. The system behavior is described by a regenerative random or deterministic process. The general task of control lies in determining the optimal time to place the replenishment order. Functionals of the mean specific income and mean specific costs were constructed, and a theorem of solution existence and uniqueness was given. For several variants of the model, explicit solutions of the problem of control under different inter-parameters relations were obtained. A number of examples of particular economic systems obeying the model under study were discussed. A procedure for seeking numerical parameters of the optimal control was analyzed in detail.     

Perturbation analysis of closed queueing networks with generalservice time distributions

Perturbation analysis of closed queuing networks with nonexponential service time distributions is studied. Perturbation analysis formulas using realization probabilities are extended to these networks. A perturbation generation function, which generalizes the perturbation generation rule, is defined. equations for realization probability and formulas for sensitivity of the system throughput with respect to service time distribution parameters are presented. The formulas provide an analytical method of calculating throughput sensitivity and an explanation of the application of perturbation analysis algorithms for networks with general service time distributions. The author focuses on the extension of concepts and intuitive explanations of the formulas rather than on mathematical derivations     

Guaranteed cost control for multi-inventory systems with uncertain demand

In this paper we consider the problem of controlling a multi-inventory system in the presence of uncertain demand. The demand is unknown but bounded in an assigned compact set. The control input is assumed to be also constrained in a compact set. We consider an integral cost function of the buffer levels and we face the problem of minimizing the worst-case cost. We show that the optimal cost of a suitable auxiliary problem with no uncertainties is always an upper bound for the original problem. In the special case of minimum-time control, this upper bound is tight, namely its optimal cost is equal to the worst-case cost for the original system. Furthermore, the result is constructive, since the optimal control law can be explicitly computed.     

Adaptive neural dynamic surface control for a general class of stochastic nonlinear systems with time delays and input dead-zone

International Journal of Control, Automation and Systems - This paper investigates adaptive tracking control for a more general class of stochastic nonlinear time-delay systems with unknown input...     

Dynamic pricing of durable products with heterogeneous customers and demand interactions over time

In this study, we analyze a dynamic pricing problem in which the demand is interdependent over time and the customers are heterogeneous in their purchasing decisions. The customers are grouped into different classes depending on their purchase probabilities and the customer classes evolve over time depending on the demand realizations at every period, which are a function of the prices set by the company. To decide on the optimal prices at every period, we model this problem using a stochastic dynamic program (SDP) and we develop several approximation algorithms to solve this SDP since the size of the state space of the SDP makes the optimal solution almost impossible to find. We present the efficiencies of the heuristics and provide managerial insights through a computational study in which we compare the revenues obtained with each heuristic with an upper bound value that we find on the optimal revenues.