Question

15 pts (3 pts for each answer 1 through 5)

Nissan Motors has been producing a particular ignition box for its car engines. The Fabrication Department of the company has a monthly demand of 500 ignition boxes (Part #37822) with a weekly standard deviation of 80. The leadtime for this part is two weeks. For the purposes of this problem, you may assume that each month is exactly 4 weeks long. Nissan requires a 97% service level for this item.

In the Fabrication Department, 20 hours (with labor costs of $30 per hour) is allowed for each setup of Part #37822. The Accounting department has determined the variable cost per box of Part #37822 is $100, while the Finance Department requires a carrying cost of 25% per year of the value of any item in inventory. Order cost is $125/order.

The Fabrication Department is using a Fixed Quantity/Variable Interval inventory management system.
3 pts 1) Determine how much they should order each time an order is placed.
4 pts 2) Assume Nissan wanted a 99.9% service level for this item. Based on this managerial decision, what should the reorder point be? What does this information tell you?
4 pts 3) What happens to the order quantity when the setup cost is reduced to 15 hours? What is the new EOQ? What can you determine about the relationship between EOQ and item cost?
4 pts 4) Using original parameters, what happens to the order quantity when the order cost increases to $150/order? What is the new EOQ? What is the relationship between order costs and EOQ?

Answer 1

1)

The quantity the company should order each time an order is placed is called Economin order quantity (EOQ).

Suppose A= Demand for the year

Cp = Cost to place a single unit order

Ch = Cost to hold/carry one unit inventory for a year

> From the data, demand for the year is 500. Hence A=500

> Total cost for a unit = total setup cost + variable cost.

From fabrication department,
Setup time for a unit =			20 hours
labour cost per unit =			$30 per hour
Total setup cost for a unit =			$30*20=$600

Variable cost per box =

$100

Hence total cost = $600+$100

= $700 per unit.

Carrying cost per unit per year (Ch)= 25% per year of the value of any item in inventory

= 25% * $700

= $175

Order cost (Cp) = $125 per unit

> EOQ formula is as follows

Hence they should order 26 units each time an order is placed.

2)

Reorder point= Normal consumption during lead time.

where, d is demand rate per period and Lt is lead time

Now, Assuming that Nissan wants 99% service level.

where, d = average weekly demand = 500/4 = 125
S = standard deviation of weekly demand = 80
z = number of standard deviations corresponding to the service level probability
Lt = 2 weeks

From normal standard distribution table, for service level 99%, the corresponding z value is: z = +2.33

This tells that the reorder point is at 276.36 units, approximately 276 units.

3)

When setup cost is reduced to 15 hours.

Setup time for a unit =			15 hours
labour cost per unit =			$30 per hour
Total setup cost for a unit =			$30*15=$450

Variable cost per box =

$100

Hence total cost = $450+$100

= $550 per unit.

Carrying cost per unit per year (Ch)= 25% per year of the value of any item in inventory

= 25% * $550

= $137.5

Order cost (Cp) = $125 per unit

> EOQ formula is as follows

Hence they should order 30 units each time an order is placed.

Hence, EOQ and item cost are inversely proportional. As the item cost decreases, the EOQ increases.

4)

Order cost increases to $150 per order.

Setup time for a unit =			20 hours
labour cost per unit =			$30 per hour
Total setup cost for a unit =			$30*20=$600

Variable cost per box =

$100

Hence total cost = $600+$100

= $700 per unit.

Carrying cost per unit per year (Ch)= 25% per year of the value of any item in inventory

= 25% * $700

= $175

Order cost (Cp) = $150 per unit

> EOQ formula is as follows

Hence they should order 29 units each time an order is placed.

Order cost is directly proportional to EOQ. That means as order cost increases, the EOQ also increases.