A manufacturing firm produces an item. An analyst has obtained the following est

Question

A manufacturing firm produces an item. An analyst has obtained the following estimates of characteristics of the itenm o Holding cost (h)- $0.05 per unit at each unit time o Stockout penalty (b) - S1 per unit oFixed ordering cost (A)-$30 each time o Product cost (c)- S0.5 per item o Productian Leadtime (L)- 3days Assume the production rate is much larger than D, answer the follows: A) What is the optimal order quantity B) What is the provided service level C) What is the reorder point D) What is the average cost per unit time

Explanation / Answer

A) Optimal order quantity Q = SQRT((2DA/h)*(h+b)/b) = SQRT(2*5*30/0.05)*(0.05+1)/1) = 79

B) Maximum Backorder unit, S = Q*h/(h+b) = 79*0.05/(0.05+1) = 4

Number of backorders = S2/2Q = 42/(2*79) = 0.09

C) Reorder point = D*L = 5*3 = 15

D)

Average inventory level V/2 = (Q-S)2/2Q = (79-4)2/(2*79) = 36

Average cost per unit time = (V/2)*h + (D/Q)*A + (S2/2Q)*b

= 36*0.05 + (5/79)*30 + (0.09*1

= $ 3.79  

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