2. Inventory decisions
When to replenish the inventory of an item?
How much of an item to order when the
inventory of that item is to be replenished?
5. Different models
Purchase model with instantaneous
replenishment & without shortages;
Manufacturing model without shortages;
Purchase model with instantaneous
replenishment & with shortages;
Manufacturing model with shortages.
6. Purchase model with instantaneous
replenishment & without shortages
In this
Orders of equal size are placed at periodical intervals
The item against an order are replenished immediately and
items are consumed at a constant rate.
The price per unit is same irrespective of order size.
Let
D = Annual demand in units
Co = Ordering cost/order
Cc= carrying cost/unit/year
P = purchase price per unit
Q = Order size
7. No. of orders / yr = D/Q
Average inventory = Q/2
Cost of Ordering/ yr = D/Q X Co
Cost of carrying per year = Q/2 X Cc
Purchase cost per year = Dp
8. Total inventory cost/ yr = Cost of Ordering/
yr + Cost of carrying per year + Purchase
cost per year
Optimal order size = EOQ = Q* =
√2CoD/Cc
Total no of orders per yr = D/Q*
Time between orders = Q*/D
9. Ques
Ram industry needs 5400 units /yr of a
bought out components which will be used
in its main product. The ordering cost is Rs.
250 per order and the carrying cost per unit
per year is Rs. 30.Find:
Economic Order Quantity
Numbers of orders per year
Time between successive orders.
10. Manufacturing model without
shortages
Manufacturing model - If company manufactures
an item which is required for its main product
In this model- shortages are not permitted
Rate of consumption of the item is assumed to be
uniform throughout the year.
Production & consumption takes place
simultaneously for the cycle time.
During the remaining cycle time, only
consumption of item takes place & cost of
production per unit is same irrespective of
production lot size.
11. r = annual demand
k = production rate of item
Co= cost per set up
Cc =carrying Cost/unit/year
P= cost of production/unit
t1 = period of consumption & production
t2 = period of consumption
t = cycle time = t1 + t2
12. Economic batch quantity (EBQ or Q*) =
√2Cor / Cc[1-(r/k)]
t1* = Q*/k
t2* = (k-r)t1/r
Cycle time = t1* + t2*
No. of set ups per year = r/Q*
13. Ques:
An automobile factory manufactures a particular
type of gear within the factory. This gear is used in
the final assembly. The particulars of this gear
are:
r= 14000units/yr
k=35000/unit
Co= Rs. 500 per set up
Cc= Rs. 15/unit/yr
Find EBQ and cycle time
14. Purchase model with instantaneous
replenishment & with shortages
In this an item will be received
instantaneously & it is consumed at a
constant rate.
The purchase price per unit is same
irrespective of order size.
If there is no stock at the time of receiving a
request for the item, it is assumed it will be
satisfied at a later date with penalty. This is
called as backordering.
15. D = demand/period
Cc= Carrying Cost/unit/period
Co= ordering cost
Cs= shortage cost/unit/period
Q= order size
Q1= maximum Inventory
Q2= Maximum stock out
T1= period of positive stock
T2= period of shortage
T= t1 +t2 = cycle time
16. Q*= √2CoD x Cs+Cc
Cc Cs
Q1* = √2CoD X Cs
Cc Cs+Cc
Q2* = Q* - Q1*
T* = Q*/ D
T1* = Q1*/ d
T2* = Q2*/ D
No. of orders/ period = D/ Q*
17. Manufacturing model with shortages.
Items is produced and consumed
simultaneously for a portion of the cycle
time.
During the remaining cycle time only the
consumption of item take place
Cost of consumption is same irrespective of
the production size
Stock out is permitted in this model
18. r = annual demand
k = production rate of item
Co= cost per set up
Cc =carrying Cost/unit/year
P= cost of production/unit
t1 = period of production & consumption of the item satisfying
periods requirement.
t2 = period of consumption
t3= period of shortage
t4= period of production as well as consumption of the item
satisfying back order
19. EBQ = √2Co kr Cc+ Cs
Cc k-r Cs
Q1* = √2Co r(k-r) Cs
Cc k Cc +Cs