A class of (Q,R) inventory models with partial backorders, Poisson demands, and Erlang-distributed lead times.
Item
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Title
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A class of (Q,R) inventory models with partial backorders, Poisson demands, and Erlang-distributed lead times.
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Identifier
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AAI9119691
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identifier
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9119691
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Creator
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Woo, York Y.
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Contributor
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Adviser: Georghios P. Sphicas
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Date
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1991
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Language
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English
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Publisher
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City University of New York.
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Subject
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Business Administration, Management
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Abstract
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The framework of analysis in this study is the stochastic (Q,R) model for a single inventory item. The inventory position, which is the level of inventory on hand plus on order minus backorders, is continuously monitored. Customers demand single units according to a Poisson process. When the position reaches the prespecified reorder level R, an order is placed with suppliers for a lot of size Q units. The lead time, defined as the time from placing the order until the shipment arrives, is a random variable with an Erlangian type of distribution.;We first consider such an inventory system with exponentially distributed lead times, which is a special case of Erlangian distributions. When a stockout occurs, some customers are willing to wait for backorders but the rest will take their business elsewhere. After a certain number of outstanding orders have been placed by the system, however, all new demands will be lost because the expected waiting time for backlogging will then be longer than customers' tolerance limits. An analytical model exactly representing this system is derived by solving a truncated stochastic process. Under a special case, the model also represents another inventory system where the interarrival time between two successive customers has an Erlang distribution and an order is placed by the system whenever a unit is demanded. Some properties of the net inventory probability distribution are then presented with proof. Since solutions of the optimal inventory policy cannot be explicitly obtained, some experimentation is designed and performed in order to investigate the nature of this system. Numerical results of the sensitivity analysis are also reported with some discussion.;We then consider a continuous review inventory system with Erlang-distributed lead times where all customers will wait to be backlogged when the system is out of stock. Another analytical model which closely approximates this system is built by conditioning the probabilities of net inventory first on the inventory position and then on the lead time. Several properties of this model are then established. Closed-form expressions of both the net inventory probability and the average inventory cost function are also obtained. Sensitivity analysis is designed and conducted by using numerical examples to examine the effect of lead time variability on the optimal solution. Exponential lead time is studied as a special case, and then compared with the previous exact model when all unsatisfied demands can be backordered. Finally, we provide some suggestions for future research.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
