A machine produces items to stock according to the following base-stock policy: aproduction run is started as soon as the number of items on stock drops below level5, and the production run is stopped as soon as the number of items on stockreaches level 5 again. Demands for the items occur as a Poisson process with a rateof 8 items per day (= 24 hours). The production times of items are exponentiallydistributed with a mean of 2 hours. Demands are satisfied in order of arrival, anddemands that cannot be satisfied directly from stock are back-ordered (i.e., they aredelivered 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 backorderedwill be in the system?c) Calculate the Laplace-Stieltjes transform of the amount of time for anarbitrary 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 onaverage during which there are, uninterruptedly, items on stock

As per the base-stock policy, when the no. of items on stock drops below level the production…

Answered: A machine produces items to stock…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 36E

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