Created By: Rushabh Shah
Deterministic Inventory Control Model Formulas
1.
Model I(a) EOQ model with constant rate of demand
2 DCo
Ch
Q* 
Q*
t 
D
TVC 
*
2 DCo Ch
TC *  TVC  DC
2.
Model I(b) EOQ model with different rates of demand
2 DCo
TCh
Q* 
t
*
Q*

D
2 DCo Ch
T
 TVC  DC
TVC 
TC *
3.
Model I(c) Economic Production Quantity Model when Supply
(Replenishment) is gradual
2 DCo 
p 


Ch  p  d 
Q* 
Q*
t 
D
*
TVC 
 pd 
2 DCo Ch 

p 

TC *  TVC  DC
N* 
D
Q*
Here N=Optimal Number of production cycles
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Created By: Rushabh Shah
4.
p=rate of receipt of inventory
d=rate of usage of inventory
Model II(a) EOQ model with Constant Rate of Demand and Variable Order
Cycle Time
Q* 
M* 
2 DCo  Ch  Cs 


Ch  C s


2 DCo  Cs


Ch  Ch  C s 
Q*
t 
D
*
TVC 
 Cs

2 DCo Ch 

 Ch  C s 
R*  Q*  M *
5.
Where R=maximum Shortage Units
M=Optimal Stock Level
Q=Economic Order Quantity
Cs=Cost of shortage
Model II(b) EOQ Model With Constant rate of Demand and Fixed Reorder
Cycle Time
 Cs
M 
 Ch  C s

* D *t

 C * Cs 
TVC   h
* D *t
C

C
s 
 h
6.
Model II(c) EOQ Model with gradual supply and shortage allowed
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Created By: Rushabh Shah
2 DCo
Ch
Q* 
 Ch  C s

 Cs
 pd
Q2*  Q* 
 p
 p 


 p  d 
  Ch 


C

C
 h
s 
 pd
TVC  2 DC0Ch 
 p
C0  p  d   Cs 



Ch  p   Ch  C s 
Q1*  2 D
7.
Model III(a) EOQ model with Warehouse Space Constraint
n
 fQ
W
Qi * 
2 Di Coi
Chi  2 f i
i 1
8.
  Cs 


C

C
 h
s 
i
i
Model III(b) EOQ model with Investment Constraint
n
C Q
i 1
i
Qi * 
i
F
2 Di Coi
Chi  2 Ci
where
Chi  r * Ci
9.
Model III(c) EOQ model with average Inventory level Constraint
n
1
Qi  M

2 i 1
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Created By: Rushabh Shah
10.
Model III(d) EOQ model with Number of orders Constraint
Number of Orders per year = N *
DC
 DC
where
N= specified number of orders
DC= Demand in rupees
11.
Model IV EOQ model with all units discounts available
(i)
Model with one price break
(ii)
Model with two price break
Sums of Deterministic Inventory Control Model
1.
I(a)
2.
I(c)
3.
I(c)
The production department for a company requires 3600 K.g of raw
material for manufacturing a particular item per year. It has been
estimated that the cost of placing an order is Rs. 36 and the cost of
carrying inventory is 25 percent of the investment in the inventories. The
price is Rs. 10 per K.g. The purchase manager wishes to determine an
ordering policy for raw material.
A contractor has to supply 10,000 bearings per day to an automobile
manufacturer. He find that when he starts production run he can produce
25,000 bearing per day. The cost of holding a bearing in stock for a year
is Rs 2 and the set up cost of a production run is Rs. 180. How frequently
should production run be made.
A product is sold at the rate of 50 pieces per day and is manufactured at a
rate of 250 pieces per day. The set up cost of the machines is Rs. 1000
and the storage cost is found to be Rs. 0.0015 per piece per day. With
labour charges of Rs. 3.20 per piece, material cost at Rs 2.10 per piece
and overhead cost of Rs. 4.10 per piece, find the minimum cost batch size
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4.
II(a)
5.
II(c)
6.
III(a)
7.
III(b)
Created By: Rushabh Shah
if the interest charges are 8 percent (assume 300 working days in a year).
Compute the optimal number of cycles required in a year for the
manufacturing of this product.
A commodity is to be supplied at a constant rate of 200 units per day.
Supplies of any amount can be obtained at any required time, but each
ordering cost Rs 50, cost of holding the commodity in inventory is Rs
2.00 per unit per day while the delay in the supply of the item induces a
penalty of Rs 10 per unit per day. Find the optimal policy (Q,t) where t is
the reorder cycle period and Q is the inventory after reorder.
The demand for an item in a company is 18,000 units per year and the
company can produce the item at a rate of 3,000 per month. The cost of
one set up is Rs 500 and the holding cost of one unit per month is 15
paise. The shortage cost of one unit is Rs. 240 per year. Determine the
optimum manufacturing quantity and the number of shortages. Also
determine the manufacturing time and the time between set-ups.
A small shop produces three machine parts 1,2,3 in lots. The shop
has only 650 sq. m of storage space. The appropriate data for the
three items are presented in the following table.
Item
1
2
3
Demand(units per year) 5000
2000
10000
Set up Cost (Rs)
100
200
75
Cost per unit(Rs)
10
15
5
Floor space required (sq
0.70
0.80
0.40
ft/unit)
The shop uses an inventory carrying charge of 20 percent of average
inventory valuation per annum. If no stock outs are allowed,
determine the optimal lot size of each item under given storage
constraint.
A shop produces three items in lots. The demand rate for each item is
constant and can be assumed to be deterministic. No back orders are
to be allowed. The pertinent data for the items is given in the
following table.
Item
Carrying Cost(Rs. Per
unit per year)
Set up Cost (Rs per
setup)
Cost per unit(Rs)
Yearly Demand (units)
8.
III(c)
9.
III(d)
1
20
2
20
3
20
50
40
60
6
10,000
7
12,000
5
7,500
Determine approximately the economic order quantities for three
items subject to the condition that the total value of average
inventory levels of these items does not exceed Rs. 1,000.
Consider the data of above example no 6. with a constraint of limited
storage space sufficient only for 560 units of all types of items instead
of 650 sq. ft. of storage space. Determine the optimal number of
units of each item separately so as to satisfy the given constraint.
A company has to purchase four items A,B,C and D for the next year.
The projected demand and the unit price in Rs are as follows
Item
Demand(units)
Unit Price (Rs)
A
60,000
3
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Created By: Rushabh Shah
B
C
D
10.
IV
(one
price
break)
11.
IV
(two
price
break)
40,000
1,200
5,000
2
24
4
If the company wants to restrict the total number of orders to 40 for
all the four items, how many orders should be placed for each item.
The annual demand of a product is 10,000 units. Each unit cost Rs
100 if orders placed in quantities below 200 units but for orders of
200 or above the price is Rs. 95. The annual inventory holding cost is
10 percent of the value of the item and the ordering cost is Rs 5 per
order. Find the economic lot size.
A shopkeeper estimates annual requirement of an item as 2000 units.
He buys from supplier at a cost of Rs 10 per item and the cost of
ordering is Rs 50 each time. If the stock holding costs are 25 percent
per year of stock value, how frequently should he replenish his
stocks? Further suppose the supplier offers a 10 per cent discount on
orders between 100 and 499 items, and a 20 percent discount on
orders exceeding or equal to 500. Can the shop keeper reduce his
costs by taking advantage of either of these discounts.
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