Question

An EOQ Problem

Suppose we must secure 8000 of some SKU annually, at a cost of $10 a unit. There are 250 working days inthe year and costs us $30 to place an order, regardless of its size. We estimate our inventory holding cost to be 30% annually.

* Should we order 8000 immediately?

* Should we order these one at a time?

* Generally speaking, what is the annual cost of a particular order size “Q”?

* So, how do we identify the “best” order size?

* Suppose we make this optimal order size our policy. What is the annual cost of this policy?

* How many times a year will we order?

* How much time will pass between placing one order and placing the next? (Or, what is the length of the “order cycle”?)

* What is the most we would ever have in inventory?

* On average, how much would we have in inventory?

* Suppose it takes 10 days for an order to arrive. When should we place the order?

Answer 1

EOQ = [ 2 x demand x cost of ordering / cost of holing a unit per annum]^1/2

= [ 2 x8000x30/0.3]^1/2 = 1264 units

EOQ is the quantity that minimises the total cost of ordering and holding the inventory.

Ordering 8000 units would save the company in ordering cost, but will also cause the company to hold the entire consignment for a year, that will offset all savingss. At EOQ the total cost of both heads is minimised, hence it is advisable to order that number of units (1264)

Annual cost = ordering cost + holding cost + purchase cost

In this case, if Q units are ordered then the total cost

= Purchase price per unitx8000+ Q/2 x cost of holding one unit + (Annual demand / Q) x ordering cost

= 10x8000+Q/2 x 0.3+(8000/Q)x30

Annual cost = 80000+189+190 = 80379

Number of orders = 8000/Q = 8000/1264 =6.329 per year

Length of order cycle = Q / demand per day = 1264 / 8000/250 = 39.5 days

Max inventory wll be equal to the order size Q, whereas the avg inventory will be equal to Q/2.

The order should be placed when we have 10 days of stock with us i.e. 10 x (8000/250) =320

Hence the order needs to be placed when the stock reaches 320.