A class of distributions generated from distributions of exponential type

A class of exponential type distributions with special exponential parameters is defined. It is assumed that the exponential parameters vary according to some (known) probability law. It has been shown in this paper that the compound distribution can be easily represented in form involving moment generating function of the mixing distribution. The results obtained in this paper provide an efficient and simple method of obtaining compound failure time distribution with known mixing distributions (uniform, exponential, gamma).     

Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

In this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797–809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log‐concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log‐concavity properties of compound distributions. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 345–356, 2015     

Explicit formulas for the order size and reorder point in certain inventory problems

This study concentrates on distributions of leadtime demand that permit explicit solution to the lot-size, reorder point model. The optimal order size for the general case is first expressed as a function of the economic order quantity and a quantity known as the “residual mean life” in reliability theory. The concept of “no aging” is then utilized to identify a broad class of distributions for which the optimal order size can be determined explicitly, independent of the reorder point.     

Estimating negative binomial demand for retail inventory management with unobservable lost sales

The importance of effective inventory management has greatly increased for many major retailers because of more intense competition. Retail inventory management methods often use assumptions and demand distributions that were developed for application areas other than retailing. For example, it is often assumed that unmet demand is backordered and that demand is Poisson or normally distributed. In retailing, unmet demand is often lost and unobserved. Using sales data from a major retailing chain, our analysis found that the negative binomial fit significantly better than the Poisson or the normal distribution. A parameter estimation methodology that compensates for unobserved lost sales is developed for the negative binomial distribution. The method's effectiveness is demonstrated by comparing parameter estimates from the complete data set to estimates obtained by artificially truncating the data to simulate lost sales. © 1996 John Wiley & Sons, Inc.     

Optimal inventory policies in contagious demand models

In the past, contagious distributions have been successfully applied in bacteriology, entomology, and accident statistics. This paper applies the notion of contagious distributions in the inventory control of new products and seasonal or style goods, which have an lying “true contagion” for their demands, namely, the influence of past demands on occurrence of demands. A contagious distribution is derived by assuming a nonstationary Poisson process where the demand rate at any instant depends on the past demands to that instant. Using this contagious distribution, an inventory model is developed seasonal goods and new product lines. Optimal order policies as a function of the initial level and the review period are derived.     

Discriminating between the Weibull and log‐normal distributions

Log‐normal and Weibull distributions are the most popular distributions for modeling skewed data. In this paper, we consider the ratio of the maximized likelihood in choosing between the two distributions. The asymptotic distribution of the logarithm of the maximized likelihood ratio has been obtained. It is observed that the asymptotic distribution is independent of the unknown parameters. The asymptotic distribution has been used to determine the minimum sample size required to discriminate between two families of distributions for a user specified probability of correct selection. We perform some numerical experiments to observe how the asymptotic methods work for different sample sizes. It is observed that the asymptotic results work quite well even for small samples also. Two real data sets have been analyzed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

基于行为复合机制的结构化图形动画技术的研究与实践

在各类计算机动画中 ,角色动画可满足实时性及交互性的需要 ,其核心技术在于角色的建模技术。该文主要介绍了作者所研制的角色动画制作系统———“网动王 98” (简称Net_Anim系统 )中所采用的角色建模机制及其相关技术 ,内容包括 :角色的对象模型及其运行机制 ;角色复合行为的实现算法及相关的关键问题 ;应用示例 :Net_Anim系统的特色和有待进一步研究和解决的相关问题。     

Bayesian strategies for dynamic pricing in e‐commerce

E‐commerce platforms afford retailers unprecedented visibility into customer purchase behavior and provide an environment in which prices can be updated quickly and cheaply in response to changing market conditions. This study investigates dynamic pricing strategies for maximizing revenue in an Internet retail channel by actively learning customers' demand response to price. A general methodology is proposed for dynamically pricing information goods, as well as other nonperishable products for which inventory levels are not an essential consideration in pricing. A Bayesian model of demand uncertainty involving the Dirichlet distribution or a mixture of such distributions as a prior captures a wide range of beliefs about customer demand. We provide both analytic formulas and efficient approximation methods for updating these prior distributions after sales data have been observed. We then investigate several strategies for sequential pricing based on index functions that consider both the potential revenue and the information value of selecting prices. These strategies require a manageable amount of computation, are robust to many types of prior misspecification, and yield high revenues compared to static pricing and passive learning approaches. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Sensitivity of the (Q,R) inventory model to penalty cost parameter

This paper treats an approximate continuous review inventory model with backlogging of excess demand and stochastic leadtime. The major result derived is that the behavior of the optimal order size with respect to the shortage cost parameter is determined solely by the “conditional mean residual life” function corresponding to the leadtime demand distribution. Some minor results and illustrative examples are also included.     

A time dependent continuous review inventory model with compound poisson demand

We discuss a time dependent optimal ordering policy for a finite horizon inventory system for which the provision of service is essential and thus no stockout is allowed. It is assumed that the system can place an order at any point in time during the horizon when it cannot meet the customer's demand and that lead time is negligible. The demand is considered to be distributed as a compound Poisson process with known parameters and the functional equation approach of dynamic programming is used to formulate the objective function. An algorithm has been developed to obtain the solution for all the cases. In addition, analytical solutions of the basic equation under two limiting conditions are presented.     

Yield randomness,cost tradeoffs,and diversification in the EOQ model

Existing production/inventory models with random (variable) yield take the yield distribution as given. This work takes a step towards selecting the optimal yield randomness, jointly with lot sizing decisions. First, we analyze an EOQ model where yield variance and lot size are to be selected simultaneously. Two different cost structures are considered. Secondly, we consider source diversification (‘second sourcing’) as a means of reducing effective yield randomness, and trade its benefits against its costs. Conditions for the superiority of diversification between two sources with distinct yield distributions over a single source are derived. The optimal number of identical sources is also analyzed. Some comments on the congruence of the results with recent JIT practices are provided.     

Performance evaluation of a production/inventory system with periodic review and endogenous lead times

This paper considers a discrete time, single item production/inventory system with random period demands. Inventory levels are reviewed periodically and managed using a base‐stock policy. Replenishment orders are placed with the production system which is capacitated in the sense that there is a single server that sequentially processes the items one at a time with stochastic unit processing times. In this setting the variability in demand determines the arrival pattern of production orders at the queue, influencing supply lead times. In addition, the inventory behavior is impacted by the correlation between demand and lead times: a large demand size corresponds to a long lead time, depleting the inventory longer. The contribution of this paper is threefold. First, we present an exact procedure based on matrix‐analytic techniques for computing the replenishment lead time distribution given an arbitrary discrete demand distribution. Second, we numerically characterize the distribution of inventory levels, and various other performance measures such as fill rate, base‐stock levels and optimal safety stocks, taking the correlation between demand and lead times into account. Third, we develop an algorithm to fit the first two moments of the demand and service time distribution to a discrete phase‐type distribution with a minimal number of phases. This provides a practical tool to analyze the effect of demand variability, as measured by its coefficient of variation, on system performance. We also show that our model is more appropriate than some existing models of capacitated systems in discrete time. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

A single-period,multi-echelon stochastic model under a mix of assemble to order and assemble in advance policies

This article presents a stochastic model for a single-period production system composed of several assembly/processing and storage facilities in series. The production system operates under a composite strategy of the assemble to order and assemble in advance policies. The developed mathematical model is simpler and more compact than the ones provided in earlier articles. Moreover, the formulation allows the optimal inventory levels at the start of the period to be determined from the solution to the well-known newsboy problem. We also analyze the problem under the free distribution approach which only assumes the knowledge of the first two moments of the demand distribution. The robustness of this approach is tested by carrying an extensive experimental comparison using different demand distributions. Finally, the composite model is extended by considering the effects of some budgetary constraints. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 599–614, 1998     

Power series expansions for the distribution and mean value function of a geometric process with Weibull interarrival times

The geometric process is considered when the distribution of the first interarrival time is assumed to be Weibull. Its one‐dimensional probability distribution is derived as a power series expansion of the convolution of the Weibull distributions. Further, the mean value function is expanded into a power series using an integral equation. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 599–603, 2014     

A continuous-review inventory system with lost sales and variable lead time

Using a system-point (SP) method of level crossings, we derive the stationary distribution of the inventory level (stock on hand) in a continuous-review inventory system with compound Poisson demand, Erlang as well as hyperexponentially distributed lead times, and lost sales. This distribution is then used to formulate long-run average cost functions with/without a service level constraint. Some numerical results are also presented, and compared with the Hadley and Whitin heuristic. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 259–278, 1998     

On a shape estimator of weiss

The problem of estimating the shape-parameter of a distribution is considered. We introduce a class of estimators the distributions of which are independent of location and scale. An estimator proposed by Weiss [1] is a member of this class. We find the asymptotically most efficient estimator in this class which differs from that proposed by Weiss.     

Queues with stochastic service rates

The purpose of this paper is to explore an extension of the output discipline for the Poisson input, general output, single channel, first-come, first-served queueing system. The service time parameter, μ, is instead considered a random variable, M. In other words, the service time random variable, T, is to be conditioned by a parameter random variable, M. Therefore, if the distribution function of M is denoted by F_M(μ) and the known conditional service time distribution as B(t |_μ), then the unconditional service distribution is given by B(t) = Pr {T ≤ t}. = ∫_-∞^∞ B(t |_μ) dF_M(μ). Results are obtained that characterize queue size and waiting time using the imbedded Markov chain approach. Expressions are derived for the expected queue length and Laplace-Stieltjes transforms of the steady-state waiting time when conditional service times are exponential. More specific results are found for three special distributions of M: (1) uniform on [1.2]; (2) two-point; and (3) gamma.     

Some test functions for the parameters of the weibull distributions

Test functions, based on various types of censored and noncensored data, for testing several hypotheses about the location, the scale, and the shape parameters of the Weibull distributions are proposed. The exact sampling distributions of these test statistics are derived and their properties in special cases are discussed. A numerical example is considered to illustrate the application of the test functions. The results of this paper possess good possibility of wide application in view of the fact that hosts of real data arising from diverse fields of human endeavor are adequately described by the Weibull distribution.     

Optimal advertising and inventory control of perishable goods

The primary goal of this article is to extend the results of a previous article to the case where the effect of advertisement on sales lasts more than one period. Monotonicity of the optimal advertising and inventory policies in the various factors is investigated. Also, attention will be focused on the relationship between the fluctuations over time of the optimal policies and the variations over time of the factors involved, such as demand distributions and holding costs. For example, if over a finite interval the demand decreases from one period to the next, reaches a minimum, and then increases, then the optimal advertising policy will produce the opposite effect. The period of minimum demand never precedes that of maximum goodwill; moreover, the optimal inventory level decreases while the demand decreases. Finally, when demand distributions are just translates of one another, the results of this article can be extended to nonperishable goods.     

Designing acceptance sampling schemes for life testing with mixed censoring

Mixed censoring is useful extension of Type I and Type II censoring and combines some advantages of both types of censoring. This paper proposes a general Bayesian framework for designing a variable acceptance sampling scheme with mixed censoring. A general loss function which includes the sampling cost, the time‐consuming cost, the salvage value, and the decision loss is employed to determine the Bayes risk and the corresponding optimal sampling plan. An explicit expression of the Bayes risk is derived. The new model can easily be adapted to create life testing models for different distributions. Specifically, two commonly used distributions including the exponential distribution and the Weibull distribution are considered with a special decision loss function. We demonstrate that the proposed model is superior to models with Type I or Type II censoring. Numerical examples are reported to illustrate the effectiveness of the method proposed. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004