7Deterministic_Models.ppt

ppt on deterministic model ch-7 production and operation mgt

1. INVENTORY
CONTROL

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?

3. Models of Inventory
Deterministic Model
Probabilistic Model

4. Deterministic
Models

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 sizeare 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
C
o= Ordering cost/order
C
c= 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 C
o
Cost of carrying per year = Q/2 X C
c
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
C
o= cost per set up
C
c=carrying Cost/unit/year
P= cost of production/unit
t
1= period of consumption & production
t
2 = period of consumption
t = cycle time = t
1+ t
2

12. Economic batch quantity (EBQ or Q*) =
√2C
or / C
c[1-(r/k)]
t
1* = Q*/k
t
2* = (k-r)t1/r
Cycle time = t
1* + t
2*
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
C
o= Rs. 500 per set up
C
c= 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
C
c= Carrying Cost/unit/period
C
o= ordering cost
C
s= shortage cost/unit/period
Q= order size
Q
1= maximum Inventory
Q
2= Maximum stock out
T
1= period of positive stock
T
2= period of shortage
T= t
1+t
2= cycle time

16. Q*= √2C
oD x Cs+Cc
Cc Cs
Q
1* = √2C
oDX Cs
Cc C
s+C
c
Q
2* = Q* -Q
1*
T* = Q*/ D
T
1* = Q
1*/ d
T
2* = Q
2*/ 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
C
o= cost per set up
C
c=carrying Cost/unit/year
P= cost of production/unit
t
1= period of production & consumption of the item satisfying
periods requirement.
t
2 = period of consumption
t
3= period of shortage
t
4= period of production as well as consumption of the item
satisfying back order

19. EBQ = √2C
okrC
c+ C
s
C
ck-r C
s
Q
1* = √2C
or(k-r)C
s
C
ck C
c +C
s