Question

7. A shop has a demand for water is approximated by a normal distribution with a mean of 31 gallons per week and a standard deviation of 4 gallons per week. The manager desires a service level of 90 percent. The lead time is three days, and the shop opens seven days a week. (9 marks) a. If an ROP model is used, what ROP would be consistent with the desired service level? b. If a fixed-interval model is used, how much should be ordered for the 90 percent service level with an order interval of 7 days and a supply of 10 gallons on hand at the order time? c. Suppose the manager is using the ROP model described in part a. One day after placing an order with the supplier, the manager receives a call from the supplier that the order will be delayed because of problems at the supplier's plant. The supplier promises to have the order there in two days. After hanging up, the manager checks the water and finds that 7 gallons have been used since the order was placed. Assuming the supplier's promise is valid, what is the probability that water will run out before the shipment arrives? (calculate to 2 decimal places I

Answer 1

Weekly Demand d = 31 gallon

SD pf Weekly Demand = 4

Service Level = 90%

Z = 1.28

Lead Time LT = 3 days = 3/7 week

a.

ROP = d*LT + Z*Sd of Demand*(LT)^(1/2)

ROP = 31*(3/7) + 1.28*4*(3/7)^(1/2)

ROP = 16.64 gallons

ROP = 17 gallons

b.

Order Interval P = 7 days = 1 week

On Hand Inventory I = 10

Order Quantity Q = d*(LT+P) + Z*Sd of Demand*(LT+P)^(1/2) - I

LT +P = 3/7 + 1 = 10/7 weeks

Q = 31*(10/7) + 1.28*4*(10/7)^(1/2) - 10

Q = 50.41 - 10

Q = 40.41

Q = 40 gallons

c.

Stock on Hand = ROP - Used Stock = 17 - 7 = 10 galoon

Expected Receiving day = 2 days = 2/7 weeks

Now, we will treat 10 gallon as ROP with 2 days lead time and we will find the value of Z. After that we will find the service level basiz Z value and after that wwe will find the stock out probabiity bu subtractting service level from 1.

10 = 31*(2/7) + Z*4*(2/7)^(1/2)

10 = 8.8571 + Z*2.1381

Z = (10-8.8571)/2.1381

Z = 0.5345

Service Level = 0.7035

Stock out Probability = 1 - Service Level

Stock out Probabiity = 1 - 0.7035

Stock out Probability = 0.2965

Stock out Probability = 0.30