A company’s warehouse can store up to 4 units of agood. Each month, an average of 10 orders for the good arereceived. The times between the receipt of successive ordersare exponentially distributed. When an item is used to fillan order, a replacement item is immediately ordered, and ittakes an average of one month for a replacement item toarrive. If no items are on hand when an order is received,the order is lost. What fraction of all orders will be lost dueto shortages?

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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A company’s warehouse can store up to 4 units of a
good. Each month, an average of 10 orders for the good are
received. The times between the receipt of successive orders
are exponentially distributed. When an item is used to fill
an order, a replacement item is immediately ordered, and it
takes an average of one month for a replacement item to
arrive. If no items are on hand when an order is received,
the order is lost. What fraction of all orders will be lost due
to shortages?

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