Inventory and Lead-time Service Level
Problem 1.
Regional Supermarket is open 360 days per year. Daily use of cash register tape averages 10 rolls. Usage appears normally distributed with a standard deviation of 2 rolls per day. The cost of ordering tape is $1 per order and carrying costs are 40 cents per roll a year. Lead-time is three days.
What is the EOQ?
What ROP will provide a lead-time service level of 96%?
What is the difference in expected number of units short per cycle with 96% and 98% lead-time service level? Per year? (Assuming demand is one roll at a time)
Problem 2.
Consider the following information on an inventory management system:
$10
$250
33% of item cost
25,750
515 per week
125 per week
6 weeks
a) Ignoring the uncertainty in the demand (i.e. looking only at average values), find the optimal order quantity and the reorder point. What is the annual inventory holding and ordering cost for this policy?
b) Consider now the uncertainty. The order quantity remains the same. If the target is to have a
95% leadtime service level, what should be the ROP? What is the safety stock? How much additional inventory cost is incurred due to the safety stock?
Problem 3.
CU, Inc. (CUI) produces copper contacts that it uses in switches and relays. CUI needs to determine the order quantity to meet the annual demand at the lowest cost. The price of copper depends on the quantity ordered. Here are price-break data and other information for the problem:
Price of copper:
$0.82 per pound up to 2,499 pounds
$0.81 per pound for orders between 2,500 and 4,999 pounds
$0.80 per pound for orders of 5,000 pounds or more
Annual demand: 50,000 pounds per year
Holding cost: 20% per unit per year of the price of the copper
Ordering cost: $30 per order
Regional Supermarket is open 360 days per year. Daily use of cash register tape averages 10 rolls. Usage appears normally distributed with a standard deviation of 2 rolls per day. The cost of ordering tape is $1 per order and carrying costs are 40 cents per roll a year. Lead-time is three days.
What is the EOQ?
What ROP will provide a lead-time service level of 96%?
What is the difference in expected number of units short per cycle with 96% and 98% lead-time service level? Per year? (Assuming demand is one roll at a time)
Problem 2.
Consider the following information on an inventory management system:
$10
$250
33% of item cost
25,750
515 per week
125 per week
6 weeks
a) Ignoring the uncertainty in the demand (i.e. looking only at average values), find the optimal order quantity and the reorder point. What is the annual inventory holding and ordering cost for this policy?
b) Consider now the uncertainty. The order quantity remains the same. If the target is to have a
95% leadtime service level, what should be the ROP? What is the safety stock? How much additional inventory cost is incurred due to the safety stock?
Problem 3.
CU, Inc. (CUI) produces copper contacts that it uses in switches and relays. CUI needs to determine the order quantity to meet the annual demand at the lowest cost. The price of copper depends on the quantity ordered. Here are price-break data and other information for the problem:
Price of copper:
$0.82 per pound up to 2,499 pounds
$0.81 per pound for orders between 2,500 and 4,999 pounds
$0.80 per pound for orders of 5,000 pounds or more
Annual demand: 50,000 pounds per year
Holding cost: 20% per unit per year of the price of the copper
Ordering cost: $30 per order