Dr. Jack is in charge of the Blood Bank at the local hospital. Blood is collecte

Question

Dr. Jack is in charge of the Blood Bank at the local hospital. Blood is collected in the regional blood center 200 miles away and is delivered to the hospital by airplane. Dr. Jack reviews the inventory and places order every Monday morning for delivery the following Monday morning. If demand begins to exceed supply, surgeons postpone non-urgent procedures, in which case blood is back ordered. The demand for blood in every given week is normal with mean 100 pints and standard deviation 34 pints. The demands are independent across weeks.

a. (3 points) On Monday morning Dr. Jack reviews his reserves and observes 200 pints in on-hand inventory, no back orders, and 73 pints in pipeline inventory. Suppose the order up-to level is 285. How many pints will he order?

b. (3 points) Dr. Jack targets a 99% expected fill rate. What order up-to level should he choose?

c. (3 points) Dr. Jack targets a 99% service level. What order up-to level should he choose? d. (3 points) Dr. Jack is planning to implement a computer system that will allow daily ordering, seven days per week, and that the lead time will also be reduced to one day. What will be the average order quantity?

Explanation / Answer

a. Given,

Inventory level = 200 pints

Pipeline = 73 pints

Order up to level = 285 pints

Inventory position= 200 + 73 = 273 pints

Pints that can be ordered = 285-273 = 12 pints

b. Expected fill rate = 99% = 0.99

As we know, Fill rate = 1 – (Expected Back orders / Expected demand in 1 period)

Given, expected demand in 1 period = 100

0.99 = 1- (EBO/100)

(EBO/100) = 1-0.99 = 0.01

EBO= 0.01 * 100 = 1

EBO= L(z) * standard deviation---------------- A

Standard deviation for (Lead time plus 1 period) = 34* (2^0.5) = 48.083

Putting values in A,

1= L(z) * 48.083

So, L(z) = 1/48.083 = 0.0207

Check for z value in normal loss table corresponding to 0.0207 entry

So, z= 1.65

S = Dt+1 + z * sdt+1

    = 200 + 1.65 * 48.083 = 279.33 = 280 pints

c. Given, N = 7 days / week

L = 1 day

Average order quantity = Average demand in the order period = D/N = 100/7 = 14.285 pints = 15 pints

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