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17-02-02 - UF-ESI-6321.xmcd page 1 of 2 17.2.2 You are a...

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UF-ESI-6321 17-02-02.xmcd page 1 of 2 17.2.2 You are a retailer considering your inventory system in which the sequence of events during each sales period is as follows. (1) As a retailer, you observe your inventory level i at the beginning of the period as one of the following values: i 0 4 .. := i 0 1 2 3 4 = (2) You order units from your wholesaler for immediate delivery according to this formula: o i if i 1 4 i - , 0 , ( ) := In other words, you will order and immediately receive these numbers of units depending upon these current inventory values: augment i o i , ( ) 0 4 ( ) 1 3 ( ) 2 0 ( ) 3 0 ( ) 4 0 ( ) = (3) With conditional probability p' 1 3 := retail customers will demand any one of the three discrete quantities of r 0 2 .. := d r ⟨⟩ r := d 0 1 2 ( ) = (4) You observe the inventory level at the beginning of the next period. Define a period's state to be the period's beginning inventory level i . Determine the transition matrix that could be used to model this inventory system as a Markov chain.
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