Answer to question a: Calculation for G1 : Mean annual demand og G1 gloves in ST
ID: 373148 • Letter: A
Question
Answer to question a:
Calculation for G1 :
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
Calculation for G2 :
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
ECONOMIC ORDER QUANTITY = 1291
SAFETY STOCK = 32
REORDER POINT = 513
Explanation / Answer
(6 points) STH hospital currently uses two types of surgical gloves (G1 and G2) for their healthcare workers. The annual demand for each is normally distributed. For G1 the mean is 5,000 pairs with a variance of 3,000; for G2 the mean is 8,000 pairs with a variance of 5,000. Each pair of gloves costs $3 (regardless of type), the cost to place an order is $100, and STH uses an annual holding cost of 20% of the value. Demand between G1 and G2 is independent. STH uses an (Q,R) system where Q is determined by the EOQ and a service level of 97% is used. The replenishment lead time is 5 weeks for each glove type. (You can assume each year has 52 weeks.) (4 pts) Determine the order quantity Q, safety stock, and reorder point R for each type of gloves a. b. (2 pts) According to the risk pooling strategy, STH decides that is will standardize by using G1 to meet all demand for gloves. Determine the new order quantity Q, safety stock, and reorder point R for G1.
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