Download - 3.Inventory Mgt
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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