Question

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.)a. Determine the order quantity Q, safety stock, and reorder point R for each type of gloves. b. According to the risk pooling strategy, 5TH decides that Is will standardize by using 61 to meet all demand for gloves. Determine the new order quantity 0, safety stock, and reorder point R for 61.

Answer 1

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