7. 15.00 points value: Problem 13-21 Demand for walnut fudge ice cream at the Sw

Question

7. 15.00 points value: Problem 13-21 Demand for walnut fudge ice cream at the Sweet Cream Dairy can be approximated by a normal distribution with a mean of 18 gallons per week and a standard deviation of 6.7 gallons per week. The new manager desires a service level of 90 percent. Lead time is two days, and the dairy is open seven days a week. (Hint: Work in terms of weeks.) Use Table B and Table B1. a-1. If an ROP model is used, what ROP would be consistent with the desired service level? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) ROP gallons a-2. How many days of supply are on hand at the ROP, assuming average demand? (Do not round intermediate calculations. Round your final answer to 2 decimal places.) Days b-1. If a fixed-interval model is used instead of an ROP model, what order size would be needed for the 90 percent service level with an order interval of 7 days and a supply of 8 gallons on hand at the order time? (Do not round intermediate calculations. Round your final answer to the nearest whole number.) Order size gallons

Explanation / Answer

Mean Demand= 18 per week = 2.57 per day

Demand Std Dev = 6.7 per week = 0.957 per day

Expected Service Level = 90% (Z = 1.282)

Lead TIme = 2 days

A1) ROP = Mean Demand *Lead Time + Z* Demand Std Dev * sqrt(Lead time) = 2.57*2 + 1.282*0.957*sqrt(2) = 6.875 gallons

A2) Number of days of inventory available at ROP = ROP/Mean Demand = 6.875/2.57 = 2.67 days

B1) Order Interval = 7 days

Amount in hand = 8

Order Size = Demand Mean*(Order Interval + Lead Time) + Z* Demand Std Dev*sqrt(Lead Time+Order Interval) - Amount in hand

Order Size = 2.57*(7+2) + 1.282*0.957*sqrt(2+7) - 8 = 18.81 ~ 19 gallons

B2) We know, ROP = Demand Mean*Lead Time + Z*Demand Std Dev*sqrt(Lead Time)

For first instance our ROP is Amount in hand, thus putting respective values we get,

8 = 2.57*2 + Z*0.957*sqrt(2)

Therefore Z = (8-2.57*2)/(0.957*sqrt(2)) = 2.1131

Therefore, at Z= 2.1131, we have 1.74% of Stock Out probability.

C) Amount in Hand = ROP - Amount already Sold = 6.875 - 2 = 4.875

We know, ROP = Demand Mean*Lead Time + Z*Demand Std Dev*sqrt(Lead Time)

For first instance our ROP is Amount in hand, thus putting respective values we get,

4.875 = 2.57*2 + Z*0.957*sqrt(2)

Therefore Z = (4.875-2.57*2)/(0.957*sqrt(2)) = -0.1958

At Z= -0.1958, we have 45.22% of Stock In probability & 54.78% of Stock Out Probability.

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