Question

Question 1: The local convenience store wants to place a beverage on a continuous review inventory replenishment policy. The demand on average is 15 cases per month. It costs 5 dollars to place an order. The cost per case of the beverage is 12 dollars. The interest rate per week is 0.5% per week per case. The lead time for every order is 2 weeks. Demand is 15 cases per month and standard deviation is 2.7 a) ( Use EOQ to calculate the order quantity. b) Using the order quantity from part (a), calculate the reorder point that will make the fill rate at least 90%. Compute the resulting average inventory cost. c) Using the order quantity from part (a), calculate the reorder point that makes the type-I approximation of fill rate to be at least 90%. Compute the true fill rate and inventory level resulting from the reorder point and compare to the values in part (b). What does this say about the accuracy of the type I service approximation?

Answer 1

average demand, d	15	cases/month
annual demand, D	180	cases
ordering cost, Co	$          5.00
cost/ case, p	$        12.00
carrying cost, Cc	0.50%	per week/case
=	$          0.06	per week/case
=	$          0.24	per month/case
=	$          2.88	per year/case
lead time, L	2	weeks
demand standard deviation, ?d	2.7	cases
a. EOQ = sqrt(2*Co*D/Cc)
Q	25	cases
b. Reorder Point, R = Normal consumption during lead-time + Safety Stock
fill rate	90%
z	1.2815516
weekly demand	3.75
R = dL+z*?d*sqrt(L)
R=	12	cases
Average inventory cost = product cost+ ordering cost+ holding cost
average inventory cost = pD+(Q/2)*Cc+(D/Q)*Co
	$        2,232
R=?z+ expected demand during lead time
fill rate	90%
z	1.2815516
R	11	cases
True Fill rate = 1 – E(z)*?/ dL
For 90% service level E(z) = 0.048 from probability tables
True fill rate =	98.27%
The true fill rate is higher than the expected fill rate, thus the approximation is slightly off the target, and we should have slightly less inventory on hand than calculated before.

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