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(Q,r) Model
The (Q,r) model is a class of models in inventory theory. T. Whitin, G. Hadley, Analysis of Inventory Systems, Prentice Hall 1963 A general (Q,r) model can be extended from both the EOQ model and the base stock modelW.H. Hopp, M. L. Spearman, Factory Physics, Waveland Press 2008 Overview Assumptions # Products can be analyzed individually # Demands occur one at a time (no batch orders) # Unfilled demand is back-ordered (no lost sales) # Replenishment lead times are fixed and known # Replenishments are ordered one at a time # Demand is modeled by a continuous probability distribution # There is a fixed cost associated with a replenishment order # There is a constraint on the number of replenishment orders per year Variables *D = Expected demand per year *\ell = Replenishment lead time *X = Demand during replenishment lead time *g(x) = probability density function of demand during lead time *G(x) = cumulative distribution function of demand during lead time *\theta = mean demand ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inventory Theory
Material theory (or more formally the mathematical theory of inventory and production) is the sub-specialty within operations research and operations management that is concerned with the design of production/ inventory systems to minimize costs: it studies the decisions faced by firms and the military in connection with manufacturing, warehousing, supply chains, spare part allocation and so on and provides the mathematical foundation for logistics. The inventory control problem is the problem faced by a firm that must decide how much to order in each time period to meet demand for its products. The problem can be modeled using mathematical techniques of optimal control, dynamic programming and network optimization. The study of such models is part of inventory theory. Issues One issue is infrequent large orders vs. frequent small orders. Large orders will increase the amount of inventory on hand, which is costly, but may benefit from volume discounts. Frequent orders are co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dynamic Lot Size Model
The dynamic lot-size model in inventory theory, is a generalization of the economic order quantity model that takes into account that demand for the product varies over time. The model was introduced by Harvey M. Wagner and Thomson M. Whitin in 1958. Harvey M. Wagner and Thomson M. Whitin, "Dynamic version of the economic lot size model," Management Science, Vol. 5, pp. 89–96, 1958 Problem setup We have available a forecast of product demand over a relevant time horizon t=1,2,...,N (for example we might know how many widgets will be needed each week for the next 52 weeks). There is a setup cost incurred for each order and there is an inventory holding cost per item per period ( and can also vary with time if desired). The problem is how many units to order now to minimize the sum of setup cost and inventory cost. Let us denote inventory: I=I_+\sum_^x_-\sum_^d_\geq0 The functional equation representing minimal cost policy is: f_(I)=\underset\left i_I+H(x_)s_+f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Base Stock Model
The base stock model is a statistical model in inventory theory.W.H. Hopp, M. L. Spearman, Factory Physics, Waveland Press 2008 In this model inventory is refilled one unit at a time and demand is random. If there is only one replenishment, then the problem can be solved with the newsvendor model. Overview Assumptions # Products can be analyzed individually # Demands occur one at a time (no batch orders) # Unfilled demand is back-ordered (no lost sales) # Replenishment lead times are fixed and known # Replenishments are ordered one at a time # Demand is modeled by a continuous probability distribution Variables *L = Replenishment lead time *X = Demand during replenishment lead time *g(x) = probability density function of demand during lead time *G(x) = cumulative distribution function of demand during lead time *\theta = mean demand during lead time *h = cost to carry one unit of inventory for 1 year *b = cost to carry one unit of back-order for 1 year *r = reorder point *SS=r-\t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newsvendor Model
The newsvendor (or newsboy or single-periodWilliam J. Stevenson, Operations Management. 10th edition, 2009; page 581 or salvageable) model is a mathematical model in operations management and applied economics used to determine optimal inventory levels. It is (typically) characterized by fixed prices and uncertain demand for a perishable product. If the inventory level is q, each unit of demand above q is lost in potential sales. This model is also known as the ''newsvendor problem'' or ''newsboy problem'' by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be worthless at the end of the day. History The mathematical problem appears to date from 1888 where Edgeworth used the central limit theorem to determine the optimal cash reserves to satisfy random withdrawals from depositors. According to Chen, Cheng, Choi and Wang (2016), the term "newsb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Production Quantity
The economic production quantity model (also known as the EPQ model) determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost. The EPQ model was developed by E.W. Taft in 1918. This method is an extension of the economic order quantity model (also known as the EOQ model). The difference between these two methods is that the EPQ model assumes the company will produce its own quantity or the parts are going to be shipped to the company while they are being produced, therefore the orders are available or received in an incremental manner while the products are being produced. While the EOQ model assumes the order quantity arrives complete and immediately after ordering, meaning that the parts are produced by another company and are ready to be shipped when the order is placed. In some literature, "economic manufacturing quantity" model (EMQ) is used for "economic productio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Distributed
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event. It is named after French mathematician Siméon Denis Poisson (; ). The Poisson distribution can also be used for the number of events in other specified interval types such as distance, area, or volume. For instance, a call center receives an average of 180 calls per hour, 24 hours a day. The calls are independent; receiving one does not change the probability of when the next one will arrive. The number of calls received during any minute has a Poisson probability distribution with mean 3: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very small probability it could be 10. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of a popu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Derivatives
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for z=f(x, y, \ldots), the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: :f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomson M
Thomson may refer to: Names * Thomson (surname), a list of people with this name and a description of its origin * Thomson baronets, four baronetcies created for persons with the surname Thomson Businesses and organizations * SGS-Thomson Microelectronics, a electronics manufacturer * Various travel subsidiaries of TUI Group: ** Thomson Airways (now TUI Airways), a UK-based airline ** Thomson Cruises (now Marella Cruises), a UK-based cruise line ** Thomson Holidays (now TUI UK), a UK-based travel company ** Thomsonfly, a former UK airline, formerly Britannia Airways *Thomson Directories, local business search company and publisher of: **Thomson Local, the UK business directory *Thomson Multimedia, former name of Technicolor SA, a French multinational corporation * Thomson Reuters, Canadian media and information services company ** Thomson Corporation, former name of the company prior to its 2008 merger with Reuters ** Thomson Financial, former business division of Thomson ** T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Safety Stock
Safety stock is a term used by logistics, logisticians to describe a level of extra stock that is maintained to mitigate risk of stockouts (shortfall in raw material or packaging) caused by uncertainties in supply and demand. Adequate safety stock levels permit business operations to proceed according to their plans.Monk, Ellen and Bret Wagner. Concepts in Enterprise Resource Planning. 3rd Edition. Boston: Course Technology Cengage Learning, 2009. Safety stock is held when uncertainty exists in demand, supply, or manufacturing yield, and serves as an insurance against stockouts. Safety stock is an additional quantity of an item held in the inventory to reduce the risk that the item will be out of stock. It acts as a buffer stock in case sales are greater than planned and/or the supplier is unable to deliver the additional units at the expected time. With a new product, safety stock can be used as a strategic tool until the company can judge how accurate its forecast is after the fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reorder Point
The reorder point (ROP) is the level of inventory which triggers an action to replenish that particular inventory stock. It is a minimum amount of an item which a firm holds in stock, such that, when stock falls to this amount, the item must be reordered. It is normally calculated as the forecast usage during the replenishment lead time plus safety stock. In the EOQ (Economic Order Quantity) model, it was assumed that there is no time lag between ordering and procuring of materials. Continuous Review System The reorder point for replenishment of stock occurs when the level of inventory drops down to zero. In view of instantaneous replenishment of stock the level of inventory jumps to the original level from zero level. In real life situations one never encounters a zero lead time. There is always a time lag from the date of placing an order for material and the date on which materials are received. As a result the reorder point is always higher than zero, and if the firm place ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
