OPM 352 Operations Management Homework- Widener University
Problem I
A souvenir shop in downtown San Francisco is open 300 days a year and sells an average of 37 Golden Gate Bridge T-shirts a day. The ordering costs are $15 per order. The annual holding cost per shirt is $0.65. After careful review, it was determined that the Lead Time Demand (LTD) was normally distributed at 370 T-shirts with a std. deviation of 23 shirts.
1) Assume that management has specified that no more than 1% risk of a stock out is acceptable. What should the safety stock be?
2) What should the reorder point (ROP) be?
3) What is the annual additional holding cost of maintaining the level of safety stock needed to support the 1% stock out risk?
4) 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 II
The Hard Rock Hotel in Chicago needs bath towels for its guests. They have determined that the mean usage is 3250 towels per day with a daily standard deviation of 260 towels. The towel service has an expected 4-day lead time with a standard deviation of 2 days to provide towels to the Hotel.
1) What is the lead time demand (LTD)?
2) What is the standard deviation of the LTD (σLTD)?
3) For a 98% service level, what should be the safety stock?
4) For the 98% service level, what is the ReOrder Point (ROP)?
Problem III
Every year the Novelty Gift Shop sells Valentine Hearts with the year inscribed on them. They make a single purchase and do not reorder. Each Heart costs them $3.50, but they can sell them before Valentine's Day for $15. After Valentine's Day, they put them in the discount bin and are sold for $1.50 each. Assuming that the cost the hold the hearts is negligible, what should be an appropriate service level?
Problem IV
A mail-order firm has four regional warehouses. Demand at each warehouse is normally distributed with a mean of 1,800 per month and a standard deviation of 250. Annual holding cost is 35%, and each unit of product costs the company $20. Each order incurs an ordering cost of $1,450 and lead time is 2 months. The company wants the probability of stocking out in a flow to be no more than 5%.
1) Assuming that each warehouse operates independently, what should be the ordering policy at each warehouse?
i. How much should be ordered?
ii. What should be the ROP?
a. LTD and Safety Stock
iii. What is the annual ordering costs for one warehouse?
iv. What is the annual holding costs (include the safety stock) for one warehouse?
v. On average, how long does a unit of product spend in the warehouse?
2) Assume that all five warehouses are now merged into a single centralized facility, what should be the ordering policy for the centralized warehouse?
i. How much should be ordered?
ii. What should be the ROP?
a. LTD and Safety Stock
iii. What is the annual ordering costs for one warehouse?
iv. What is the annual holding costs (include the safety stock) for one warehouse?
v. On average, how long does a unit of product spend in the warehouse?
3) Based on cost, should you have five regional warehouses or a single centralized warehouse? Why?
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