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Economic order Quantity (EOQ) Homework Help, Tutoring
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Economic order Quantity (EOQ) Assignment / Homework Help
Economic order Quantity (EOQ)

      The Economic order quantity refers to that order quantity, which minimizes total cost per annum & thus average cost per unit for the purchased items, within the range of possible order quantities. This total cost consists of two parts- (1) Ordering costs & (2) Carrying costs.
Ordering cost is independent of the quantity ordered; on the other hand, with the increase in the quantity ordered, carrying cost increases. Carrying cost includes storage cost, handling cost, insurance charges, cost of obsolescence etc. & the opportunity cost of the capital blocked. Thus, with the increase in size of purchase (because in that case the number of purchase decreases), there is a decrease in the ordering cost but as the size of purchase increases, the carrying cost increases. Therefore, a balance between ordering cost & carrying cost is necessary to find out so that it becomes possible to find the most favorable quantity.

We can have an idea on this matter, by a tabular presentation in respect of a particular item:
Estimated usage per annum is 24000 units & price per unit charged by the supplier is $ 6, ordering cost per order is $ 50, carrying cost of stock as % of average stock value is 10%
Bases on the above information, economic order quantity can be determined by preparing a schedule as under:

No. of orders per                           1          2          4          6          8          10        12           16             20
Annum

Order Size                              24000    12000     6000    4000    3000    2400    2000     1500       1200

(Total requirement)
(No. of orders)

Average Stock                      12000       6000    3000    2000    1500    1200    1000       750        600

(Order size/2) 

Avg. Stock Value                   72000      36000  18000  12000  9000    7200    6000     4500      3600

(Avg. stock*unit cost)

Stock carrying                          7200      3600      1800     1200    900   720       600    450          360

Costs (10% of average

stock value)
Ordering costs                            50       100         200      300     400    500      600      800        1000

(No. of orders*order
Cost per order) 

Total cost per annum             7250    3700    2000    1500   1300   1220  1200   1250   1360  

(Carrying cost+
Ordering cost)

     It can be seen from the above table that, with the increase in quantity ordered, stock carrying costs also increases & with the decrease in quantity ordered, the stock carrying costs decreases; while with the increase in quantity ordered, ordering cost decreases & with the decrease in quantity ordered, ordering cost increases. Thus when the ordered quantity is 2000 units, the total costs are the lowest at $ 1200. Thus economic order quantity is 2000 units.
Costs of materials are not included in the total cost. Where the price per unit is fixed, this is not required. Where, for higher quantity, discount is available progressively, cost of materials at each level has to be considered.

      EOQ can be determined on the basis of graphical form & also by applying mathematical formula.  But, EOQ determination in graphical or tabular form is lengthy & also accurate solution may not be provided. It is possible to find out EOQ mathematically by applying the following formula:

EOQ=√ (2CoO)/Cc

Where Co = Consumption per annum (i.e. usage in units)

              O = Ordering cost for placing a order

Cc = Carrying cost (including interest) of one unit for one year (usually     expressed as % of the cost per unit)

    Thus, we may obtain EOQ mathematically, by taking the information previously used in the table.

     EOQ = √ (2*24000*50)/10% of 6 = √ 2400000/0.60 = √4000000 = 2000 units = 6 orders per annum.

An alternative mathematical calculation is as follows:

EOQ shall lie at the point where the total ordering cost shall be equal to the total carrying cost. Let the number of orders (each of economic quantity) per annum be represented by ‘N’.  The average stock is 24000/N*2, carrying cost is 10% of $ 6 or $ 0.60 & total ordering cost is N* $ 50.

Now, $ 0.60*24000 = N* $ 50           or, $ 0.60*24000 = N*N
                        N*2                                         2*50

Now, N2 = 0.60*24000 = 144 or, N= 120 times
                        2*50

EOQ = Annual usage = 24000 = 2000 units.
            No. of orders        12 

For determining, the EOQ as mentioned above, some problems or limitations are involved in the use of table, graph, or mathematical formula which is mentioned below:

  1. The assumption that all costs i.e. ordering costs, unit costs etc. are known & constant may not prove correct.

  2. Determination of carrying cost is a subjective matter & the estimates of interest rates on which it is based may vary.

  3. The assumption that rate of consumption or usage throughout the year will remain constant may not come true & also seasonal variations may be there.

  4. The assumption may not hold that for an individual component an economic order quantity can be set, having no regard to the manufacture of the other components entering either into it or into further assemblies, of which it forms a part. In order that completed component stocks can be held in waiting stores, it is possible that every component can be made in an economic order quantity yet out of phase with other components.

Example:

Particulars relating to an inventory are as below:

Annual consumption -6000 units (in 360 days)

Cost per unit - $ 1

Ordering cost - $ 6 per order

Inventory carrying charge – 50%

Normal lead time = 30 days

Safety stock – 60 days consumption

Find out-(a) each time, how much should be ordered, (b) when the order should be placed, (c) what should be the ideal inventory level immediately before the delivery of material ordered is received, (d) each many times orders for EOQ should be placed in a year.

Solution:

  1. EOQ = √ (2CoO)/Cc

Where Co = 6000 units, O = $ 6 per order, Cc = 50% of $1 = $ 0.50

EOQ = √ (2*6000*6)/0.40

= 1200 units.

Hence each time 1200 units should be ordered.

  1. Re-ordering level= Safety stock+ Lead time consumption

 = (60+30) or 90 day’s consumption

= 90*(6000/360) = 1500 units

Hence, an order should be placed when the stock reaches 1500 units

  1. The ideal inventory level, immediately before the delivery of material ordered is received is the safety stock level, which represents 60 days consumption i.e.

60*(6000/360) = 1000 units.

  1. No of times orders for EOQ to be placed in a year = 6000/1200 = 5 times

Example:

Calculate (a) Re-ordering level, (b) Maximum level, (c) Minimum level & (d) Danger level, from the given below details:

Re-ordering quantity is to be calculated on the basis of the following information:

Cost of placing a purchase order is $ 40

No of units purchased during the year are 10000 units

Purchase price per unit inclusive of transportation cost is $ 100

Annual cost of storage is $ 5

Details of lead time: Average 20 days, Maximum 30 days, Minimum 12 days. For emergency purchases 8 days.

Rate of consumption: Average 30 units per day, maximum 40 units per day.

Solution:

  (a) Re-order level = Maximum usage per period * Maximum delivery period
= 40 units per day * 30 days = 1200 units

(b) Maximum level = Re-order level + Re-order quantity-(Minimum Usage*Minimum delivery period) [Working notes 1 & 2]

=1200 units+ 400 units- (20 units per day*12days)

= 1360 units

(c) Minimum level = Re-order level-(Average usage*Average delivery period)

= 1200 units – (30 units*20days)

= 600 units

(d) Danger level = Average usage*Lead time for emergency purchase

=30 units* 8 days

=240 units

Working Notes: (1) Re-ordering quantity = EOQ = √ (2CoO)/Cc

= √ (2*10000*40)/5 = 400 units

(2) Minimum Usage: - Average usage is 30 units per day. Total of minimum & maximum usage is (30 units *2) or 60 units per day. Since maximum usage is 40 units per day, minimum usage is (60-40) units or 20 units per day.

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