Bill Greenis thegeneral manager for Poolco, a company that provides home pool maintenance services in the LA area. He is responsible for developing an inventory policy regarding all items that the company stocks. One item that falls under his control is a clarifying agent that is added to pool water to improve its clarity. This item costs $5 per gallon. Variable costs of storing it in inventory amount to 25% of the unit cost per year. Paperwork and shipping costs for placing an order are $10 per order. Each year the company uses an average of 500 gallons, a rate that has not changed in the past.

1. How many gallons should be ordered each time to minimize total annual costs?
2. Given your solution, what will be the order cycle under the policy? (Express the time in terms of year.)

H

K

R

Q*

T given Q*

2.Suppose that Poolco, in the above question, wants to determine the reorder point for its clarifying agent. Assume that the company operates 250 days per year and the lead time for ordering the clarifying agent is 10 days. What is the reorder point?

calculate the following :

Demand

Lead time

ROP

3.Suppose that Poolco, after some investigation, finds that in the future, the company's average demand per day is going to be normally distributed with a mean of 3.5 and a standard deviation of 2 (i.e., the demand is not at a fixed rate). What safety stock and reorder point are necessary to obtain a 90% service level? As before, assume the lead time is10 days.

calculate the following also:

Demand Mean

Demand STD

Service Level

Lead Time

z

Safety Stock

ROP