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How much inventory to be added when the

inventory is replenished?

order quantity problems (eg.RM, prod. Run)

task of the firm to determine the optimum

quantity (or economic lot size)

Graphical Approach

EOQ= 2qty required ordering cost/Carrying cost

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Cost of the item= D x P

where D=Annual Demand

P=price per unit

If quantity discounts are given then,

Cost of the item= D x P x quantity discount

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Ordering costs/acquisition costs/replenishingcosts/set-up costs:

includes the entire cost of acquiring the rawmaterials

Includes making requisition, purchase ordering,transporting,receiving,inspecting and storing.

OC increase in proportion to the number of ordersplaced and the frequency of order

OC = O X n= O X D/Q(EOQ)

Where O= ordering cost per order

D/Q= n

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Carrying Cost: incurred for maintaining a given

level of inventory

Includes: warehousing, handling,clerical and

staff, insurance, deterioration and obsolescene = C X Q/2

where C = carrying cost per unit,

Q/2= average quantity to carry

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Therefore, TC= DP+ OD/Q +CQ/2

Or, TC= CC+OC

T= OD/Q + QC/2

The total cost function is a trade off between thecarrying cost and the ordering cost for

determining the EOQ.

To obtain the formula for EOQ above equation is

differentiated with respect to Q and setting thederivative equal to zero, we obtain the EOQ

EOQ(Q)= 2qty required(D) orderingcost(O)/Carrying cost(C)

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Mehta Company is a well known manufacturer of consumer

goods. The companys product line has various types ofproducts for the consumers at a cheap and reasonablerate. The estimated annual requirement of the company isis 1200 units. The purchasing cost per unit (P) is Rs 50.

The ordering cost (O)of the company for each order comesto Rs 37.50. And to hold this stock of inventory the

company incurs a carrying costs per unit of Rs 1.A numberof alternatives are available for the firm. It may purchaseits entire requirement of 1200 units in the beginning ofthe year in one single lot or in 12 monthly lots of 100 unitseach and so on. If only one order of 1200 units is placed,the firm will have a starting inventory of 1200 units. With

constant consumption, the inventory size will reduce in asystematic way and will reach zero level at the end of theyear. As the firm will hold 1200 units in the beginning andzero unit at the end of the year find out the averageinventory held during the year and the average value?

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If monthly purchases are made,12 orders of 100

units each will be placed during the year.Thusthe firm will have 100 units at the start of the

month and zero units at the end of the month.

Find out the average inventory held during the

month and the av. Value? The firm can work out

many possibilities in the same manner to

minimise the cost on inventory management. If

the firms objective is to minimize the the

Inventory investment then monthly orders or

even less than that may be favoured. However,this may not be the most economical .The firm

should therefore study the implication of both

the CC and the OC.

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Annual requirement (D):1200 units, CC per unit :Re1,OC per order:Rs 37.50

Order size(Q)

1200 600 400 300 240 200 150 120 100

Av.inventory

(Q/2)

600 300 200 150 120 100 75 60 50

No. oforders(n/Q)

1 2 3 4 5 6 8 10 12

Annual

CC(CQ/2)

600 300 200 150 120 100 75 60 50

Annual

OC(OA/Q)

37.5 75 112.5 150 187.5 225 300 375 450

Total Annual

costs (rs)

637.5 375 312.5 300 307.5 325 375 435 500

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Also calculate EOQ using the formula approach.

Let us assume that the company receives a

quantity discount of 0.5 % (0.005) per unit. Cal

the discount savings.

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That point where the order should be placed

to replenish the inventory

To determine the reorder point we should

know the lead time and the average usageReorder point = lead X average usage

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Safety Stock: reorder point is assumed under

the point of uncertainty. It is difficult to

predict the usage and the lead time

accurately. The demand may fluctuate fromweek to week and day to day.The actual

delivery time may be different form the lead

time.If actual usage increases or the delivery

of inventory is delayed then the firm mayface the problem of stock out which can

prove costly for the firm.

Reorder point= lead x av.usage x safety stock