Extend (r, Q) Inventory Model Under Lead Time and Ordering Cost Reductions When the Receiving Quantity is Different from the Ordered Quantity

This paper investigates the continuous review inventory model involving variable lead time with partial backorders, where the amount received is uncertain. The options of investing in ordering cost reduction is included, and lead time can be shortened at an extra crashing cost. The objective of this article is to simultaneously optimize the order quantity, reorder point, ordering cost and lead time. We first assume that the lead time demand follows a normal distribution and develop an algorithm to find the optimal solution. Then, we relax the assumption of normality to consider a distribution free case where only the mean and standard deviation of lead time demand are known. We apply the minimax distribution free procedure to solve this problem. For both cases, we also show that the objective cost function to be minimized is jointly convex in the decision variables. Furthermore, two numerical examples are given to illustrate the results.     

A Note on EOQ Model for Items with Mixtures of Exponential Distribution Deterioration,Shortages and Time-varying Demand

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. In this paper, we derive the EOQ model for inventory of items that deteriorates at a mixtures of exponential distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal reorder time Further, we also find that the optimal procedure is independent of the form of the demand rate. Finally, we also assume that the holding cost is a continuous, nonnegative and non-decreasing function of time in order to generalize EOQ model. Moreover, four numerical examples and sensitivity analyses are provided to assess the solution procedure.     

Inventory control in environments with seasonal demand

In the traditional reorder point model no consideration is taken to variations in demand. The purpose of this paper is to present an extended reorder point model based on an assumption of stationary demand suitable for ERP systems and capable of taking such considerations. The purpose is also to assess potential benefits of using the model by means of simulation and to provide some rough heuristic guidelines for the practitioner regarding when to use this model rather than the traditional one. The result from the assessment indicates that even in cases with a low degree of seasonality it is of significant importance to consider seasonal variations when calculating the demand during the lead time part of the reorder point to be able to achieve targeted service levels. Considering seasonal demand when calculating safety stocks and order quantities is basically only of significant importance in cases when the degree of seasonality is high.     

Optimal structure of joint inventory-pricing management with dual suppliers and different lead times

We consider a joint inventory-pricing control problem in a single-product, periodic-review, dual-supplier inventory system. The two suppliers have different lead times. One expedited supplier offers instantaneous replenishment, and one regular supplier requires an L-period lead time for delivery. The supply quantity is stochastic and the demand is price-dependent. For the expedited inventory replenishment, we characterize the optimal policy as a state-dependent almost-threshold policy by extending the stochastically linear in mid-point to a multidimensional setting. To investigate the optimal regular inventory replenishment and pricing policy, we propose the notions of partially stochastic translation (PST) and increasing partially stochastic translation (IPST), which help in obtaining the antimultimodularity preservation in dynamic programming problems. We provide properties, sufficient conditions, and examples for PST and IPST functions. By applying PST and IPST, we obtain the antimultimodularity of the profit functions. The antimultimodular profit functions ensure that the optimal regular ordering quantity and the optimal price are monotone in the current inventory level and outstanding order quantities. Moreover, we reveal that as the time interval increases, the effects of previous outstanding orders on the optimal regular ordering and pricing decisions are decreasing and increasing, respectively. PST and IPST also enable us to further characterize the optimal expedited ordering quantity as decreasing in the inventory level. However, the optimal expedited ordering quantity can be non-monotone with respect to the outstanding order quantities, as shown in the example.     

Valuing lead time

When do short lead times warrant a cost premium? Decision makers generally agree that short lead times enhance competitiveness, but have struggled to quantify their benefits. Blackburn (2012) argued that the marginal value of time is low when demand is predictable and salvage values are high. de Treville et al. (2014) used real-options theory to quantify the relationship between mismatch cost and demand volatility, demonstrating that the marginal value of time increases with demand volatility, and with the volatility of demand volatility. We use the de Treville et al. model to explore the marginal value of time in three industrial supply chains facing relatively low demand volatility, extending the model to incorporate factors such as tender-loss risk, demand clustering in an order-up-to model, and use of a target fill rate that exceeded the newsvendor profit-maximizing order quantity. Each of these factors substantially increases the marginal value of time. In all of the companies under study, managers had underestimated the mismatch costs arising from lead time, so had underinvested in cutting lead times.     

Mixture representations for discrete Linnik laws

In this paper we give mixture representations for the discrete Mittag–Leffler and Linnik laws. Our results form the discrete analogues of the mixture representations for the generalized symmetric Linnik distribution obtained by P AKES (1998). As an application, we derive the infinite divisibility of mixtures of Mittag–Leffler distributions. Alternative mixture representations in terms of discrete stable distributions are also presented.     

The interchangeability of safety stocks and safety lead time

Due to the uncertainty in estimating both the demand for end products and the supply of components from lower levels, buffering techniques should be included before the loading of a material requirement planning (MRP) system. Safety stocks and safety lead time are two techniques of providing buffering for loading. There have been many studies made concerning the determination of the amount of safety stocks and safety lead time. Some guidelines for choosing between safety stocks and safety lead time for dealing with uncertainty in both demand and supply also have been established. Although these two different methods have been used successfully, it has not been documented that using these two methods in a given situation will yield essentially the same results; that is, the interchangeability of these two buffering techniques has not been explored quantitatively.Since the net influence of safety stocks and safety lead time and their quantitative interchangeability are of major interest, an analytical model is proposed for this study. The lead-time offset procedure for components loading are represented by a matrix model that is based on a lot-for-lot lot-sizing technique. This lead-time offset matrix model is the product of the precedence matrix and the fixed-duration matrix. The precedence matrix is formed according to the total requirement factor matrix and the duration matrix is formed by each component process time. Thus, the lead-time offset matrix will generate the starting period of each component.When the lead-time offset procedure is modeled, the net influence of buffering quantity can be analyzed. The planned safety stock that is normally used to accommodate unexpected demand, shortage in supply, and defects from the operation at each process can be combined with demand to form the master production schedule. The revised lead time due to the integration of the safety stocks can be calculated through the lead-time offset model. The safety lead time may extend the component process time as well as overall production lead time if the designated safety lead time is longer than the available slack time in a fixed lead-time loading system.When the proposed lead-time offset model is further examined, it is found that planned safety stocks at the higher level can buffer the fluctuations of lower level components quantity as well as the fluctuations of same level components quantity. Safety stocks can also buffer shortages that are caused by the delay of raw material and manufacturing processes. Thus, safety stocks can be used to buffer unexpected delay time up to certain limits. A planned safety lead time at higher level component process can buffer the fluctuations of lower level components process time, as well as the same level component process time. The safety lead time can be used to produce additional products to meet unexpected excessive demand up to certain limits under the following conditions: 1. The excessive demand is known before the actual processing of the components in the lowest level. 2. The raw material at the lowest level is available.Although safety stocks and safety lead time are interchangeable in terms of the ability to buffer variations in quantity, the conditions for safety lead time are seldom met in actual practices. Thus, the slack time in a fixed lead-time loading system cannot be considered as an effective measure to substitute safety stocks. However, all or part of the delay in manufacturing processes or the supply from the lower level components can be buffered by the safety stock and the MPS will still be met. From this study, it is obvious that the slack time can be reduced when safety stocks are planned for an MRP system. The reduction of fixed lead-time duration will be beneficial to the overall planning and scheduling in MRP systems.     

基于战时物资应急调度的库存控制方法

战时军用物资需求的不可预测性极大地影响了物资订货判断决策。为了更有效地对战时物资应急调度的物资库存进行管理．在对平时和应急调度时的物资不同的需求特性分析基础上,提出了一种新的动态订货法,该方法旨在根据物资不同时期的需求变化动态地确定再订货点和订货批量,以实现对库存更高效的控制,并通过仿真表明采用这种新的库存管理方法可以有效地提高保障效率和降低库存成本,为应急调度行动提供了有力的保障。     

生鲜食品的二级补货系统优化研究

针对连锁超市的配送网络。建立一个两级的库存系统模型，其中包括一个中心仓库和若干门店，每个门店面对的是随机的相互独立的需求，该需求服从正态分布。该库存系统是采用基于连续检测的再订货点方法管理。本文针对超市的生鲜食品补货的特征，增加对于过剩成本的考虑，采用分散库存控制权的方法，按照从门店到配送中心的思路。优化总库存成本，从而得出最佳的订购批量，同时也得出最佳的产品供给水平、再订货点等。     

Stochastic volatility with leverage: Fast and efficient likelihood inference

This paper is concerned with the Bayesian analysis of stochastic volatility (SV) models with leverage. Specifically, the paper shows how the often used Kim et al. [1998. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65, 361–393] method that was developed for SV models without leverage can be extended to models with leverage. The approach relies on the novel idea of approximating the joint distribution of the outcome and volatility innovations by a suitably constructed ten-component mixture of bivariate normal distributions. The resulting posterior distribution is summarized by MCMC methods and the small approximation error in working with the mixture approximation is corrected by a reweighting procedure. The overall procedure is fast and highly efficient. We illustrate the ideas on daily returns of the Tokyo Stock Price Index. Finally, extensions of the method are described for superposition models (where the log-volatility is made up of a linear combination of heterogenous and independent autoregressions) and heavy-tailed error distributions (student and log-normal).     

Het bepalen van bestelniveaus wanneer afname en levertijd gamma-verdeeld resp. normaal-verdeeld zijn

In studies of inventory control problems in industry it is often supposed that there is a variable demand and a constant delivery time.
This assumption is rarely tenable. In this paper rules are developed for determining the reorder level when the demand has a gamma distribution and the delivery time is normally distributed.     

A Bayesian learning procedure for the.(s, Q) inventory policy

We present an asymptotically optimal Bayesian learning procedure for the ( s, Q ) inventory policy, for the case when the probability distribution of lead time demand is unknown. This distribution is not required to be a member of a certain family, and the maximal lead time demand is also allowed to be unknown. The algorithm developed for this purpose Is an extension of a standard iterative procedure, which in its original form -in spite of claims to the contrary-might produce solution values that are arbitrarily far away from the optimal one.     

Finite sample multivariate structural change tests with application to energy demand models

This paper considers finite sample motivated structural change tests in the multivariate linear regression model with application to energy demand models, in which case commonly used structural change tests remain asymptotic. As in Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68], we account for intervening nuisance parameters through a two-stage maximized Monte Carlo test procedure. Our contributions can be classified into five categories: (i) we extend tests for which a finite-sample theory has been supplied for Gaussian distributions to the non-Gaussian context; (ii) we show that Bai et al. [1998. Testing and dating common breaks in multi-variate time series. The Review of Economic Studies 65 (3), 395–432] test severely over-rejects and propose exact variants of this test; (iii) we consider predictive break test approaches which generalize tests in Dufour [1980. Dummy variables and predictive tests for structural change. Economics Letters 6, 241–247] and Dufour and Kiviet [1996. Exact tests for structural change in first-order dynamic models. Journal of Econometrics 70, 39–68]; (iv) we propose exact (non-Bonferonni based) extensions of the multivariate outliers test from Wilks [1963. Multivariate statistical outliers. Sankhya Series A 25, 407–426] to models with covariates; (v) we apply these tests to the energy demand system analyzed by Arsenault et al. [1995. A total energy demand model of Québec: forecasting properties. Energy Economics 17 (2), 163–171]. For two out of the six industrial sectors analyzed over the 1962–2000 period, break and further goodness-of-fit and diagnostic tests allow to identify (and correct) specification problems arising from historical regulatory changes or (possibly random) industry-specific effects. The procedures we propose have potential useful applications in statistics, econometrics and finance (e.g. event studies).     

Joint and marginal specification tests for conditional mean and variance models

This article proposes a class of joint and marginal spectral diagnostic tests for parametric conditional means and variances of linear and nonlinear time series models. The use of joint and marginal tests is motivated from the fact that marginal tests for the conditional variance may lead to misleading conclusions when the conditional mean is misspecified. The new tests are based on a generalized spectral approach and do not need to choose a lag order depending on the sample size or to smooth the data. Moreover, the proposed tests are robust to higher order dependence of unknown form, in particular to conditional skewness and kurtosis. It turns out that the asymptotic null distributions of the new tests depend on the data generating process. Hence, we implement the tests with the assistance of a wild bootstrap procedure. A simulation study compares the finite sample performance of the proposed and competing tests, and shows that our tests can play a valuable role in time series modeling. Finally, an application to the S&P 500 highlights the merits of our approach.     

Research issues for multi-level lot sizing in MRP systems

What lot size model(s) to use in a Material Requirements Planning (MRP) system is an unresolved and often debated issue. The concept of dependent demand, the complex network defined by the product structure, the dynamics of an operating MRP-based system, and the subsequent use of the planned order release schedule by other company subsystems represent a totally new environment for making and managing lot size decisions.The purpose of this paper is to identify and briefly examine ten research issues related to lot sizing in a dependent demand product structure. These ten issues expand the solution space for lot sizing in an MRP-based system compared to a reorder point based system. Areas for further research are suggested.     

基于工作过程导向的《城市污水处理系统营运》学习领域开发研究

对"基于工作过程导向"的《城市污水处理系统营运》学习领域的开发进行了讨论和探索。针对企业需求选择教学内容,并按照企业实际工作过程将教学内容重新排序,构建了"基于工作过程导向"的知识、理论和实践一体化、教学做一体化的职业教育学习领域。     

Constrained mixture distributions

The problem of estimating the weights associated with mixture distributions subject to several constraints, such as the percentile and/or moment constraints, is analyzed using the general theory of polyhedral convex cones and systems of inequalities. We address three problems associated with constrained mixture distributions: (a) Compatibility: a set of inequalities is obtained to check whether or not any given set of constraints lead to a feasible solution for the weights, (b) Feasible solutions: a general expression for building feasible solutions for the weights associated with the given constraints is obtained, and (c) Equivalence: the set of all feasible weights is obtained. In addition, the problem is shown to lead to a new mixture distribution, without extra constraints. This new mixture distribution can then be easily used for the statistical analysis (e.g. estimation and hypotheses testing) instead of the original mixture distribution with extra constraints. The proposed methods are illustrated by numerical examples.     

Numerical and analytical results for the transportation problem of Monge-Kantorovich

The Monge-Kantorovich transportation problem has a long and interesting history and has found a great variety of applications (see Rachev and Rüschendorf (1998a,b)). Some interesting characterizations of optimal solutions to the transportation problem (resp. coupling problems) have been found recently. For the squared distance and discrete distributions they relate optimal solutions to generalized Voronoi diagrams. Numerically we investigate the dependence of optimal couplings on variations of the coupling function. Numerical results confirm also a conjecture on optimal couplings in the one-dimensional case for nonconvex coupling functions. A proof of this conjecture is given under some technical conditions. Received: November 1999     

A flexible parametric approach for estimating switching regime models and treatment effect parameters

In this paper, we propose a flexible, parametric class of switching regime models allowing for both skewed and fat-tailed outcome and selection errors. Specifically, we model the joint distribution of each outcome error and the selection error via a newly constructed class of multivariate distributions which we call generalized normal mean–variance mixture distributions. We extend Heckman’s two-step estimation procedure for the Gaussian switching regime model to the new class of models. When the distributions of the outcome errors are asymmetric, we show that an additional correction term accounting for skewness in the outcome error distribution (besides the analogue of the well known inverse mill’s ratio) needs to be included in the second step regression. We use the two-step estimators of parameters in the model to construct simple estimators of average treatment effects and establish their asymptotic properties. Simulation results confirm the importance of accounting for skewness in the outcome errors in estimating both model parameters and the average treatment effect and the treatment effect for the treated.