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%?

Answer 1

1. Given are following data :

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 )

1. Given, Lead time = 3 weeks

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

1. Z value for in stock service rate = NORMSINV ( 0.95 ) = 1.6448

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

1. Z value of service level of 99 percent = NORMSINV ( 0.99) = 2.3263

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)

1. Standard deviation of demand during Lead time of 2 weeks

= 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 )

1. Revised standard deviation of weekly demand = 3 weeks

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)