Questions for MS1 - Inventory Models
Question 1
The XYZ Company purchases a component used in making automobile generators, directly from the supplier. XYZ’s generator production operation, which is operated at a constant rate, will need 1000 components per month. Assume that ordering costs are £25 per order, the unit purchasing cost is £2.50 per component, and that the annual holding costs are charged at 20% of the unit purchase cost per component. There are 250 working days per year and the lead time is 5 days. Answer the following inventory policy questions for XYZ.
a) What is the EOQ for this component?
b) What is the reorder point?
c) What are the total holding and ordering costs associated with your recommended EOQ?
Question 2
Suppose that XYZ’s management in Question 1 likes the operational efficiency of ordering once each month and in quantities of 1000 units. How much more expensive would this be than your EOQ recommendation? Would you recommend in favour of the 1000 unit order quantity? Explain. What would the reorder point be if the 1000 unit quantity were acceptable?
Question 3
Apply the EOQ model to the following quantity discount situation where D = 500 units per year, S = £40 per order and H = 20% of unit purchase price per year.
|
Discount Category
|
Order Size
|
Discount (%)
|
Unit Cost
|
|
1
|
0-99
|
0
|
£10.00
|
|
2
|
100 or more
|
3
|
£9.70
|
What order quantity do you recommend?
Question 4
An item of inventory has constant demand of 2500 units a year. It costs £500 to set up each production run and the variable cost is £30 per unit. Holding costs are 20% of value per year and the production rate is 10000 units per year. There is a lead time of 2 months from receiving a production requisition until finished units begin to come from the production line. Find the optimal batch size and reorder level (assuming shortages are not allowed).
Wilson Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7200 copies. The cost of one copy of the book is £14.50. The holding cost is based on an 18% annual rate, and production setup costs are £150 per setup. The equipment on which the book is produced has an annual production volume of 25000 copies. Wilson has 250 working days per year, and the lead time for a production run is 15 days. Use the production lot size model to compute the following values:
i. Minimum cost production lot size
ii. Number of production runs per year
iii. Cycle time
iv. Length of a production run
v. Maximum inventory
vi. Total annual cost
vii. Reorder point.
Question 6
i. For the basic EOQ model, what are the two types of costs included in the total variable cost that impact on the optimal value of Q? What is the relationship between these two costs at the point where the order quantity equals its optimal value?
ii. Does the optimal order quantity increase or decrease if the demand rate is increased? If the order cost is increased? If the unit holding cost is increased? In each case, what is the intuitive explanation?
iii. Can the optimal order quantity change fairly significantly if a fairly small (say 10%) change is made in either the order cost or the unit holding cost? How about if the change is made in both costs in opposite directions?
iv. What happens to the optimal order quantity if both the order cost and unit holding cost are changed by the same percentage amount in the same direction?