Study of parameters is necessary for regulating inventories. Suppose a manufacture wishes to purchase 24,000 units of raw material, the following would be the alternatives:
A.   Purchase all 24,000 units at a time during the year.
B.    Purchase the quantity in two instalments of 12,000 units during the year.
C.    Purchase 2,000 units every month during the year.
In this case, procurement cost changes from policy to policy. Here the question arises to find out the economic order quantity, where per unit cost should be minimum. The size of an order that minimise the total inventory cost is known as the Economic Order Quantity (EOQ).

(Inventory pattern of instantaneous replenishment and constant demand)

It indicates instantaneous receipt of an order size Q. A constant usage rate represented by the sloping lines takes the inventory level down to zero during the interval between the order time and instantaneous replenishment. The average number of items in storage is Q/2.

Cost-Order size relationship

The figure shows the relationship between cost per period (unit cost) and order quantity Q in case of inventory carrying cost order and cost for the inventory. The total cost is obtained by adding inventory carrying cost and the order cost. Total Cost per period is minimum at point ‘M’. Hence, OM represents the Economic Order Quantity (EOQ).
Economic Order Quantity (EOQ)

Q = 2 x N x A / C x I
Q = Economic order quantity (Size)
N = Annual consumption of raw material (Unit per year)
A = Procurement cost (per ‘Q’ Quantity)
C = Unit Cost (Cost of Unit material)
I = Inventory carrying rate.

Ex. ABC and Company gets an order for the supply of 24,000 units of its product for a year. The supply should be instantaneous. The customer does not maintain any buffer stock, so he will not tolerate any shortages in supply. The inventory holding cost is 10% and the set of cost of machine, fixture etc. is Rs. 350 per run. Find out :
1.      Optimum size of production lot for minimum cost.
2.    How many runs will be required for this ?
3.    Duration of each run.
4.    What is cycle time ?
Assume the capacity of the equipment as 3000 units per month. Each unit costs Rs. 5/-
Sol.

Where
Q = Economic lot size
N = Yearly requirement
N = 24,000
A = Set up cost per Q. = Rs. 350/-
C = Unit cost = Rs. 5/-
I = Inventory holding cost (10%)
I = 0.1 of unit cost C.
Substituting these values for the above relation for Q.

Q = 5800 units …..(i) (Ans)
Number of runs = 24000/5800 = 4.1…..(ii) (Ans)
That is 5 runs of which 4 runs will be 5800 units and fifth run will be of 800 units.
Duration of each run = Q/Production rate = 5800/3000 = 1.93 months…(iii)  (Ans)
The length of cycle time =( 5800/24000 ) * 12 = 2.9 month ….(iv) (Ans)

Ex.2 A company has an order of supplying 50,000 units of its product per year, the cost of the set-up is Rs. 1,000/- There are ten workers engaged with the wage rate of Rs. 15/- per day. The overhead cost is Rs. 100/- per day. The daily production capacity is 200 units. The material cost of each unit is Rs. 10/-. The annual rate of depreciation, insurance, taxes and storage cost etc. is 20% of unit cost. The supply should be instantaneous and no shortage are permitted.
Find out:
a.     The economic lot size.
b.    The number of runs.
c.     Duration of each run.
Sol. Use the relation – 

Where,
N = Annual requirement = 50,000 items
A = set up cost = Rs. 1,000
I = Inventory holding cost (20% of unit cost) = 0.2
C = Unit cost
C = Material cost + Labour cost + Overhead cost
C = 10 + (10 * 15 / 200) + (100/200)
C = 11.25

Q = 6666     ….(i)   (Ans)
Number of runs = 50000/6666 = 8
Number of runs = 8    ……(i) (Ans)
(7 runs of 6666 each and the eighth is 3334)
Duration of each run = 6666/200 = 33.33 days …..(iii) (Ans)