7Deterministic_Models.ppt

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?

Models of Inventory
 Deterministic Model
 Probabilistic Model

Different models
 Purchase model with instantaneous
replenishment & without shortages;
 Manufacturing model without shortages;
 Purchase model with instantaneous
replenishment & with shortages;
 Manufacturing model with shortages.

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

 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

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

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.

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.

 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

 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*

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

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.

 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

 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*

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

 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

 EBQ = √2Co kr Cc+ Cs
Cc k-r Cs
Q1* = √2Co r(k-r) Cs
Cc k Cc +Cs

7Deterministic_Models.ppt

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7Deterministic_Models.ppt