PROBLEMS
VU DINH NGHIEM HUNG
SCHOOL OF ECONOMICS AND MANAGEMENT
PROBLEM 1
• Suppose that the demand for a product is 30 units per month and the
items are withdrawn at a constant rate. The setup cost each time a
production run is undertaken to replenish inven- tory is $15. The
production cost is $1 per item, and the inventory holding cost is $0.30
per item per month.
• (a) Assuming shortages are not allowed, determine how often to
make a production run and what size it should be.
• (b) If shortages are allowed but cost $3 per item per month, determine how often to make a production run and what size it should
be.
PROBLEM 2
• The demand for a product is 600 units per week, and the items are
withdrawn at a constant rate. The setup cost for plac- ing an order to
replenish inventory is $25. The unit cost of each item is $3, and the
inventory holding cost is $0.05 per item per week.
• (a) Assuming shortages are not allowed, determine how often to
order and what size the order should be.
• (b) If shortages are allowed but cost $2 per item per week, determine how often to order and what size the order should be.
PROBLEM 3
• Kris Lee, the owner and manager of the Quality Hard- ware Store, is reassessing his inventory policy for
hammers. He sells an average of 50 hammers per month, so he has been placing an order to purchase 50
hammers from a wholesaler at a cost of $20 per hammer at the end of each month. However, Kris does all
the ordering for the store himself and finds that this is taking a great deal of his time. He estimates that the
value of his time spent in placing each order for hammers is $75.
• (a) What would the unit holding cost for hammers need to be for Kris’ current inventory policy to be optimal
according to the basic EOQ model? What is this unit holding cost as a per- centage of the unit acquisition
cost?
• (b)
• What is the optimal order quantity if the unit holding cost ac- tually is 20 percent of the unit acquisition
cost? What is the corresponding value of TVC total variable inventory cost per year (holding costs plus the
administrative costs for plac- ing orders)? What is TVC for the current inventory policy?
• (c) If the wholesaler typically delivers an order of hammers in 5 working days (out of 25 working days in an
average month), what should the reorder point be (according to the basic EOQ model)?
• (d) Kris doesn’t like to incur inventory shortages of important items. Therefore, he has decided to add a
safety stock of 5 hammers to safeguard against late deliveries and larger-than- usual sales. What is his new
reorder point? How much does this safety stock add to TVC?
PROBLEM 4
• Cindy Stewart and Misty Whitworth graduated from busi- ness school
together. They now are inventory managers for compet- ing wholesale
distributors, making use of the scientific inventory management
techniques they learned in school. Both of them are purchasing 85horsepower speedboat engines for their inventories from the same
manufacturer. Cindy has found that the setup cost for initiating each
order is $200 and the unit holding cost is $400.
• Cindy has learned that Misty is ordering 10 engines each time. Cindy
assumes that Misty is using the basic EOQ model and has the same
setup cost and unit holding cost as Cindy. Show how Cindy can use
this information to deduce what the annual demand rate must be for
Misty’s company for these engines.
PROBLEM 5
• You have been hired as an operations research consultant by a company to
reevaluate the inventory policy for one of its prod- ucts. The company
currently uses the basic EOQ model. Under this model, the optimal order
quantity for this product is 1,000 units, so the maximum inventory level
also is 1,000 units and the maxi- mum shortage is 0.
• You have decided to recommend that the company switch to using the EOQ
model with planned shortages instead after determining how large the unit
shortage cost ( p) is compared to the unit holding cost (h). Prepare a table
for management that shows what the optimal order quantity, maximum
inventory level, and maximum shortage would be under this model for
each of the following ratios of p to h: 1 ,1,2,3,5,10.