DCMPS HW 5.docx - IE 579 Homework 5 Answer 1 Part A Poisson demand for each of the 40 models is given as 1200/150 = 8 Applying Base Stock Model Service

DCMPS HW 5.docx - IE 579 Homework 5 Answer 1 Part A Poisson...

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IE 579 Homework 5 Answer 1 Part A Poisson demand for each of the 40 models is given as 1200/150 = 8. Applying Base Stock Model, Service Level = G ( r ¿ + 1 ) G ( x ) is the Cumulative Distribution Function of demand We have to keep Service Level as 99% Service Level ≥ 0.99 . Stock should be enough to meet this requirement. Over stocking will result in Service Level > 0.99 but that will in turn increase inventory holding cost. For the Poisson Distribution, the Cumulative Distribution Function is given by: G ( x ) = e λ k = 0 x λ k k! Therefore, to have Service Level ≥ 0.99 , e λ k = 0 r ¿ + 1 λ k k ! 0.99 For λ = 8 , we use Microsoft Excel to obtain the value for r ¿ + 1 using Trial & Error method. Forr ¿ + 1 = 14 we get the value as 0.982743 For r ¿ + 1 = 15 we get value as 0.991769 At r ¿ + 1 = 15 , for each of the 40 models , Service Level > 0.99 . Therefore, the Base Stock should be 15, and the reorder point should be 14 (i.e r ¿ = 14 ¿ . All values of r > 14 will give us a Service Level more than 0.99 . Part B For the Poisson Distribution, the Cumulative Distribution Function G ( x ) is given by: G ( x ) = e λ k = 0 x λ k k! Therefore, to have Service Level ≥ 0.99 ,
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e λ k = 0 r ¿ + 1 λ k k ! 0.99 For λ = 1200 , we use Microsoft Excel to obtain the value for r ¿ + 1 using Trial & Error. For r ¿ + 1 = 1281 we get the value as 0.990138 For r ¿ + 1 = 1280 we get the value as 0.989369. Therefore at r ¿ + 1 = 1281 , for each of the 40 models , Service Level more than 0.99 . Therefore, the Base Stock should be 1281, and the reorder point should be 1280 ( i.e r ¿ = 1280 ¿ .
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