A machine produces items to stock according to the following base-stock policy: a production run is started as soon as the number of items on stock drops below level 5, and the production run is stopped as soon as the number of items on stock reaches level 5 again. Demands for the items occur as a Poisson process with a rate of 8 items per day (= 24 hours). The production times of items are exponentially distributed with a mean of 2 hours. Demands are satisfied in order of arrival, and demands that cannot be satisfied directly from stock are back-ordered (i.e., they are delivered as soon as possible later on). a) Determine the long-term fraction of demands that has to be backordered. b) What is the expected amount of time a demand that has to be backordered will be in the system? c) Calculate the Laplace-Stieltjes transform of the amount of time for an arbitrary demand to be delivered (either directly from stock or backordered). d) How long does a period take on average during which there are, uninterruptedly, no items on stock? And how long does a period take on average during which there are, uninterruptedly, items on stock
A machine produces items to stock according to the following base-stock policy: a production run is started as soon as the number of items on stock drops below level 5, and the production run is stopped as soon as the number of items on stock reaches level 5 again. Demands for the items occur as a Poisson process with a rate of 8 items per day (= 24 hours). The production times of items are exponentially distributed with a mean of 2 hours. Demands are satisfied in order of arrival, and demands that cannot be satisfied directly from stock are back-ordered (i.e., they are delivered as soon as possible later on). a) Determine the long-term fraction of demands that has to be backordered. b) What is the expected amount of time a demand that has to be backordered will be in the system? c) Calculate the Laplace-Stieltjes transform of the amount of time for an arbitrary demand to be delivered (either directly from stock or backordered). d) How long does a period take on average during which there are, uninterruptedly, no items on stock? And how long does a period take on average during which there are, uninterruptedly, items on stock
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A machine produces items to stock according to the following base-stock policy: a
production run is started as soon as the number of items on stock drops below level
5, and the production run is stopped as soon as the number of items on stock
reaches level 5 again. Demands for the items occur as a Poisson process with a rate
of 8 items per day (= 24 hours). The production times of items are exponentially
distributed with a mean of 2 hours. Demands are satisfied in order of arrival, and
demands that cannot be satisfied directly from stock are back-ordered (i.e., they are
delivered as soon as possible later on).
a) Determine the long-term fraction of demands that has to be backordered.
b) What is the expected amount of time a demand that has to be backordered
will be in the system?
c) Calculate the Laplace-Stieltjes transform of the amount of time for an
arbitrary demand to be delivered (either directly from stock or backordered).
d) How long does a period take on average during which there are,
uninterruptedly, no items on stock? And how long does a period take on
average during which there are, uninterruptedly, items on stock
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VIEWStep 2: Determine the long-term fraction of demands that must be backordered
VIEWStep 3: Determine the expected amount of time a demand that has to be backordered will be in the system
VIEWStep 4: Calculate the Laplace-Stieltjes transform of the time amount for an arbitrary demand to be delivered
VIEWStep 5: Calculate the mean length of period taken during no item on stock
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