Ray\'s Satellite Emporium wishes to determine the best order size for its best-s
ID: 325802 • Letter: R
Question
Ray's Satellite Emporium wishes to determine the best order size for its best-selling satellite dish.Ray has estimated that weekly demand for this model to be 25 units with a standard deviation of 5 units.His cost to carry one unit is $50 per year and the cost of placing an order with his supplier is $25.He's open 52 weeks a year.Assume weekly demand is normally distributed.
(4 pts each)
a) What is Ray’s economic order quantity in this situation? (Hint: Use average annual demand in EOQ formula)
b) The lead-time for ordering from this supplier is 3 weeks. What are the mean and standard deviation of demand during lead time?
c) Ray desires an in-stock service rate of 95%. How many units should Ray have on-hand at the time he places an order? How many units of safety stock will he carry?
d) If Ray increases his in-stock service rate to 99% how many units of safety stock will have to carry?
e)Ray is able to negotiate a lead-time of 2 weeks with the supplier. Now what safety stock will he have to carry with 95% and 99% in-stock service levels?
f) Suppose Ray is able to reduce the standard deviation of demand (through a combination of lowered prices and loyalty schemes) to 3 units. How will this impact his safety stock assuming lead time of 3 weeks with a service level of 95%?
Explanation / Answer
Annual demand = D = 25 units/ week x 52 weeks = 1300 units
Order placement cost = Co = $ 25
Annual unit carrying cost = Ch = $50
Therefore ,
Economic Order quantity ( EOQ ) = Square root ( 2 x Co x D / Ch ) = Square root ( 2 x 25 x 1300 / 50) = 36.05 ( 36 rounded to nearest whole number )
Standard deviation of demand during lead time
= Standard deviation of weekly demand x Square root ( 3 lead time )
= 5 x square root ( 3 )
= 5 x 1.732
= 8.66 units
Mean demand during lead time =Weekly demand x Lead time ( weeks ) = 25 x 3 = 75 units
Safety stock = Z value x Standard deviation of demand during lead time = 1.6448 x 8.66 = 14.24 units ( 14 units rounded to nearest whole number )
Number of units should Ray have on hand at the time he places an order ( reorder point )
= weekly demand x Lead time ( weeks ) + safety stock
= 25 x 3 + 14
= 75 + 14
= 89
Quantity of safety stock
= Z value x standard deviation of demand during lead time
= 2.3263 x 8.66
= 20.14 ( 20 rounded to nearest whole number)
= Standard deviation of weekly demand x Square root ( Lead time )
= 5 x1.414
= 7.07
Safety stock at 95% service level
= Z value x standard deviation of demand during lead time
= 1.6448 x 7.07
= 11.628 ( 12 rounded to nearest whole number )
Safety stock at 99% service level
= Zvalue x standard deviation of demand during lead time
= 2.3263 x 7.07
= 16.446 ( 16 rounded to nearest whole number )
Lead time = 3 weeks
Therefore, standard deviation of demand during lead time = 3 x square root ( 3 ) = 3 x 1.732 = 5.196
Z value for service level of 95 % = NORMSINV ( 0.95 ) = 1.6448
Revised safety stock = Z value x standard deviation of demand during lead time = 1.6448 x 5.196 = 8.546 ( 9 rounded to nearest whole number)
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