Problem 13-21 Demand for walnut fudge ice cream at the Sweet Cream Dairy can be
ID: 425110 • Letter: P
Question
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 20 gallons per week and a standard deviation of 3.5 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 10 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 D gallons b-2. What is the probability of experiencing a stockout before this order arrives? (Do not round intermediate calculations. Round your final answer to the nearest whole percent. Omit the "%" sign in your response.) Probability 1% 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 supply of walnut fudge ice cream and finds that 2 gallons have been sold since the order was placed. Assuming the supplier's promise is valid, what is the probability that the dairy will run out of this flavor before the shipment arrives? (Do not round intermediate calculations. Round your final answer to the nearest whole percent. Omit the "%" sign in your response.) Risk probabilityExplanation / Answer
A-1) ROP = Demand*Lead Time + z*Std Dev in Demand*sqrt(Lead Time) = 20*2 + 1.28*3.5*sqrt(2) = 46.34
A-2) No. of Day of Supply Left at ROP = ROP/Average Demand = 46.34/20 = 2.317 ~ 2.32
B-1) Order Size = Demand*(Order Interval+Lead time) + z*Std Dev in Demand*sqrt(Order Interval+Lead time) - In Hand Inventory = 20*(10+2) + 1.28*3.5*(10+2) - 8 = 247.519 ~ 247.52
B-2) Probability of Stock Out = 1-Desired Service Level = 1-0.90 = 10%
C) z = (Inventory Level-Demand*Days)/(Std Dev in Lead Time*sqrt(Lead Time) = (46.34-2-20*2)/(3.5*sqrt(2)) = 0.8768
Stock In Probabilty at z = 0.8768 is 0.8076 or 80.76%
Risk Probability = 1-Stock in Probablity = 19.24%
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