Problem 1
A souvenir shop in downtown San Francisco is open 350 days a year and sells an average of 48 Golden Gate Bridge T-shirts a day. The ordering costs are $35 per order. The annual holding cost per shirt is $2.25. After careful review, it was determined that the Lead Time Demand (LTD) was normally distributed at 185 T-shirts with a std. deviation of 30 shirts.
a) Assume that management has specified that no more than 1% risk of a stock out is acceptable. What should the safety stock be?
b) What should the reorder point (ROP) be?
c) What is the annual additional holding cost of maintaining the level of safety stock needed to support the 1% stock out risk?
d) If management specified that a 2% risk of stock out during lead time would be acceptable, would the safety stock holding costs decrease or increase?
Problem 2
The Hard Rock Hotel in Chicago needs bath towels for its guests. They have determined that the mean usage is 1,350 towels per day with a daily standard deviation of 125 towels. The towel service has a 4-day lead time to provide towels to the Hotel.
a) What is the lead time demand (LTD)?
b) What is the standard deviation of the LTD (σLTD)?
c) For a 97% service level, what should be the safety stock?
d) For the 97% service level, what is the ReOrder Point (ROP)?
Problem 3
A mail-order firm has three regional warehouses. Demand at each warehouse is normally distributed with a mean of 10,500 per week and a standard deviation of 1,100. Annual holding cost is 35%, and each unit of product costs the company $10. Each order incurs an ordering cost of $2,000 and lead time is 2 weeks. The company wants the probability of stocking out in a flow to be no more than 10%. Assume 50 working weeks in a year.
a) Assuming that each warehouse operates independently, what should be the ordering policy at each warehouse?
a. How much should be ordered?
b. What should be the ROP?
i. LTD and Safety Stock
c. What is the annual ordering costs?
d. What is the annual holding costs (include the safety stock)?
e. On average, how long does a unit of product spend in the warehouse?
b) Assume that all five of the warehouses are centralized into a single facility, what should the ordering policy be for the centralized warehouse?
a. How much should be ordered?
b. What should be the ROP?
i. LTD and Safety Stock
c. What is the annual ordering costs?
d. What is the annual holding costs (include the safety stock)?
e. On average, how long does a unit of product spend in the warehouse?
Based on cost, which system would you recommend and why?