Answer:
Answer to question a:
<u>Calculation for G1 : </u>
Mean annual demand og G1 gloves in STH Hospital = 5000
Variance of annual demand = 3000
Therefore, Variance of demand during lead time of 5 weeks =3000 x 5/52 = 15000/52
Hence standard deviation of demand during lead time of 5 weeks
= Square root ( 15000/ 52)
= 16.984
Service level = 97%
Corresponding Z value = NORMSINV ( 0.97) = 1.8807
Therefore, Safety stock = Zvalue x Standard deviation of demand during lead time
= 1.8807 x 16.984
= 31.94 ( 32 rounded to nearest whole number )
Reorder point
= Average weekly demand x Lead time ( weeks ) + safety stock
= 5000/52 x 5 + 32
= 480.77 + 32
= 512.77 ( 513 rounded to next higher whole number )
= 513
Calculation of Economic Order quantity:
Annual demand = D = 5000
Co = Ordering cost = $100
Ch = 20% of $3 = $0.6
Therefore, economic order quantity ( EOQ)
= Square root ( 2 x 100 x 5000/0.6)
= 1291
ECONOMIC ORDER QUANTITY = 1291
SAFETY STOCK = 32
REORDER POINT = 513
<u>Calculation for G2 : </u>
Mean annual demand = 8000
Variance of annual demand = 5000
Therefore, Variance of demand during lead time of 5 weeks =5000 x 5/52 = 25000/52
Hence standard deviation of demand during lead time of 5 weeks
= Square root ( 25000/52)
= 21.92
Service level = 97%
Corresponding Z value = NORMSINV ( 0.97) = 1.8807
Therefore, Safety stock = Zvalue x Standard deviation of demand during lead time
= 1.8807 x 21.92
= 41.22 ( 42 rounded to next higher whole number)
Reorder point
= Average weekly demand x Lead time ( weeks ) + safety stock
= 8000/52 x 5 + 32
= 769.23 + 32
= 801.23 ( 802 rounding to next higher whole number )
Calculation of Economic Order quantity:
Annual demand = D = 8000
Co = Ordering cost = $100
Ch = 20% of $3 = $0.6
Therefore, economic order quantity ( EOQ)
= Square root ( 2 x 100 x 8000/0.6)
= 1632.99 ( 1633 rounded to nearest whole number)
ECONOMIC ORDER QUANTITY = 1633
SAFETY STOCK = 42
REORDER POINT = 802
Answer to question b :
When demand for both gloves are pooled together ,
Mean demand of the combined types = 5000 + 8000 = 13,000
Variance of the annual demand for the combined types
= Variance of G1 + Variance of G2
= 3000 + 5000
= 8000
Hence, standard deviation of annual demand( 52 weeks ) for the combined types
= Square root ( 3000 + 5000)
= Square root ( 8,000)
= 89.44
Standard deviation of demand during lead time of 5 weeks for the combined type
= 89.44 x Square root ( 5/52) = 89.44 x 0.31 = 27.726
Service level = 97%
Hence corresponding Z value for above service level = NORMSINV ( 0.97) =1.8807
Hence , Safety stock
= Z value x Standard deviation of demand for the combined type
= 1.8807 x 27.726
= 52.14
= 53 ( by rounding to next higher whole number )
Reorder point
= Average weekly demand x Lead time ( weeks ) + safety stock
= ( 13000/52) x 5 + 53
= 250 x 5 + 53
= 1250 + 53
= 1303
Calculation of Economic Order quantity:
Annual demand = D = 13000
Co = Ordering cost = $100
Ch = 20% of $3 = $0.6
Therefore, economic order quantity ( EOQ)
= Square root ( 2 x Co x D / Ch)
= Square root ( 2 x 100 x 13000/0.6)
= 2081.66 ( 2082 rounded to next higher whole number )
ECONOMIC ORDER QUANTITY = 2082
SAFETY STOCK = 53
REORDER POINT = 1303