Breakeven analysis.pdf

12/6/2021
Hamed.Ali.Mohamed2@gmail.com 2

There are two basic types of costs a company incurs.
• Variable Costs
• Fixed Costs
Variable costs are costs that change with changes in production levels or sales.
Examples include: Costs of materials used in the production of the goods.
Fixed costs remain roughly the same regardless of sales/output levels.
Examples include: Rent, Insurance and Wages
Break-Even Analysis
12/6/2021

Break-Even Analysis
 TOTAL COSTS
 Total Costs is simply Fixed Costs and Variable Costs added
together.
TC = FC + VC
 As Total Costs include some of the Variable Costs then
Total Costs will also change with any changes in
output/sales.
 If output/sales rise then so will Total Costs.
 If output/sales fall then so will Total Costs.
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 Breakeven analysis examines the short run
relationship between changes in volume and changes
in total sales revenue, expenses and net profit
 Also known as C-V-P analysis (Cost Volume Profit
Analysis)
It’s The Point of sales at which the entity earns no
profit and sustains no loss.
Contribution Margin Ratio =
Contribution margin / Sales x 100
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 C-V-P analysis is an important tool in terms of
short-term planning and decision making.
 It looks at the relationship between costs,
revenue, output levels and profit.
 Short run decisions where C-V-P is used include
choice of sales mix, pricing policy etc.
Contribution margin – Fixed cost = 0 Profit
Contribution margin = Fixed cost + 0 Profit
At break even point the target contribution is equal to the fixed cost
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How many units must be sold to breakeven?
 How many units must be sold to achieve a target
profit?
 Should a special order be accepted?
 How will profits be affected if we introduce a
new product or service?
Contribution Margin – Fixed cost = Profit
Contribution margin = Fixed cost + Profit
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 Break even point:-the point at which a company
makes neither a profit or a loss.
 Contribution per unit:-the sales price minus the
variable cost per unit. It measures the
contribution made by each item of output to the
fixed costs and profit of the organisation.
Break even sales in SR = Target CM / Contribution to sales ratio
Break even in units = Target CM / Contribution margin per unit
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 Margin of safety:-a measure in which the
budgeted volume of sales is compared with the
volume of sales required to break even.
 Marginal Cost :– cost of producing one extra
unit of output
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First calculate the Unit Contribution
SP – VC = Unit Contribution
Sr 6.00 – sr 3.00 = sr 3.00
Now calculate Break Even point by using the formula –
Fixed Costs  Unit Contribution
Sr 1,200  sr 3.00 = 400 units
Therefore 400 units must be sold in order to Break Even
Break-Even Analysis SP = sr 6.00
VC = sr 3.00
FC = sr 1,200
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Break Even can also be used to calculate Profit (or
Loss) at a given level of output
For example:
Fuchsia sells Mamoul boxes. How much profit/loss is
made when 5000 Mamoul Boxes are sold?
Each Mamoul Box is sold for 20 sr.
Variable Costs per Mamoul Box are 10 sr.
Fixed Costs total 24,000 sr.
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Firstly, calculate Unit Contribution
SP – VC = Unit Contribution
sr 20.00 – sr 10.00 = sr 10.00
Now calculate Total Contribution when 5,000 Mamoul Boxes
are sold.
Unit Contribution x no of units = Total Contribution
Sr 10.00 x 5,000 = sr 50,000
Now calculate Net Profit at 5,000 units
Total Contribution – Fixed Costs = Net Profit
Sr 50,000 – sr 24,000 = sr 26,000
SP = sr 20.00
VC = sr 10.00
FC = sr 24,000
Sales = 5,000 units
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Another Example
Calculate how many units need to be produced in
order to achieve a Net Profit of sr 25,000 given the
following information
Fixed Costs sr 30,000
Contribution per unit sr 10
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Net Profit = Total Contribution – Fixed Cost
Sr 25,000 = Total Contribution – sr 30,000
therefore Total Contribution = sr 55,000
If unit contribution is sr 10
then 5,500 units will have to be produced in order to
achieve a Total Contribution of sr 55,000.
Therefore the number of units required to achieve a
Net Profit of sr 25,000 is 5,500 units
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The formula used so far assumes that Unit Costs are
known ie Unit Selling Price and Unit Variable Cost
When no unit costs are known, the Profit/Volume Ratio
should be used instead
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P/V Ratio (Profit/Volume Ratio) =
Total Contribution / Sales x 100
If asked to calculate the volume of sales needed
to Break-Even (when no unit costs are given)
the following formula should be used:
Sales at BEP = Fixed Costs / Profit/Volume Ratio
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For Example
Sales sr 60,000
Variable Costs sr 24,000
Fixed Costs sr 14,000
Calculate the P/V Ratio and the BEP
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Sales – Variable Costs = Total Contribution
Sr 60,000 – sr 24,000 = sr 36,000
Total Contribution / Sales = P/V Ratio
(sr 36,000 / sr 60,000) x 100 = 60%
Fixed Costs / P/V Ratio = Sales at BEP
Sr 14,000 / 60% = sr 23,333
Therefore sr 23,333 of Sales are necessary in
order to Break-Even
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Costs/Revenue
Output/Sales
FC
VC
TC
TR
The Break-even point
occurs where total
revenue equals total
costs – the firm, in this
example would have to
sell Q1 to generate
sufficient revenue
(income) to cover its
total costs.
Q1
BEP
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 The difference between budgeted or actual sales
and the breakeven point
 The margin of safety may be expressed in units or
revenue terms
 Shows the amount by which sales can drop before
a loss will be incurred
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Using the following data, calculate the
breakeven point and margin of safety in units:
Selling Price = sr 50
 Variable Cost = sr 40
 Fixed Cost = sr 70,000
 Budgeted Sales = 7,500 units
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 Contribution = sr 50 – sr 40 = sr 10 per unit
 Breakeven point = sr 70,000/sr 10 = 7,000 units
 Margin of safety = 7500 – 7000 = 500 units
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 What if a firm doesn’t just want to breakeven – it
requires a target profit
 Contribution per unit will need to cover profit as
well as fixed costs
 Required profit is treated as an addition to Fixed
Costs
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Using the following data, calculate the level of
sales required to generate a profit of sr 10,000:
 Selling Price = sr 35
 Variable Cost = sr 20
 Fixed Costs = sr 50,000
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 Contribution = sr 35 – sr 20 = sr 15
 Level of sales required to generate profit of sr
10,000:
Sr 50,000 + sr 10,000
Sr 15
=4000 units
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 Costs are either fixed or variable
 Fixed and variable costs are clearly discernable
over the whole range of output
 Production = Sales
 One product/constant sales mix
 Selling price remains constant
 Efficiency remains unchanged
 Volume is the only factor affecting costs
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Absorption
 Fixed costs included in
Product Cost
 FC not treated as period cost –
closing/opening stock values
 Under/over absorption of
costs
 Complies with Financial
Accounting standards
Marginal
 Fixed costs not included
in Product Cost
 FC treated as period cost
 No under/over
absorption of costs
 Does not comply with
Financial Accounting
standards
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• A business may produce a number of products but at the
same time be unable to meet total demand for all products
due to a limiting factor eg machine hours or labour hours.
• In this case the business would decide on the optimum use
of the limited resource by producing all of the demand for
the product which yields the highest contribution per the
limiting factor.
• Having produced all of the demand from that product, the
business would produce the next highest contribution per
the limiting factor and so on until full capacity is reached.
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A business can produce Products A, B and C.
A B C
Contribution per labour
hour
Sr 2 Sr 1 Sr 3
Labour hours per unit 4 4 3
Total demand in units 5,000 5,000 10,000
The factory is limited to 60,000 labour hours.
How many units of each Product should be produced to maximise
profit?
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Produce in the order of the highest Contribution
per Labour Hour ie C then A then B
C A
Demand 10,000 5,000
Labour hrs/unit 3 4
Total lab hrs 30,000 20,000
Total labour hours required to produce all demand for C then A =
50,000 labour hours.
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If Total Labour hours available equals 60,000
and 50,000 is used producing Products C and A,
then 10,000 labour hours are left to produce as
many units as possible for Product B
Product B uses 4 labour hours per unit, therefore
only 2,500 units of Product B can be produced
within the available 60,000 labour hours
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 All Fixed and Variable costs can be identified
 Variable costs are assumed to vary directly with
output
 Fixed costs will remain constant
 Selling prices are assumed to remain constant for
all levels of output
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 The sales mix of products will remain constant –
break even charts cannot handle multi-product
situations
 It is assumed that all production will be sold
 The volume of activity is the only relevant factor
which will affect costs
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 Some costs cannot be identified as precisely
Fixed or Variable
 Semi-variable costs cannot be easily
accommodated in break-even analysis
 Costs and revenues tend not to be constant
 With Fixed costs the assumption that they are
constant over the whole range of output from
zero to maximum capacity is unrealistic
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 Price reduction may be necessary to protect
sales in the face of increased competition
 The sales mix may change with changes in
tastes and fashions
 Productivity may be affected by strikes and
absenteeism
 The balance between Fixed and Variable
costs may be altered by new technology
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 The Point at which Revenues = Costs
 Revenues above the breakeven point result in profit
 Revenues below the breakeven point result in loss
 May be measured in units of output or revenue
dollars
 Represents a “Reality Check”
 Is this level of revenue reasonable?
 If not, what actions would yield a reasonable breakeven
point?
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 Fixed Costs - Costs that do not change in
total with the volume produced or sold
 Variable Costs - Costs that change in direct
proportion with the volume produced or
sold
 Mixed Costs - A combination of fixed and
variable costs
 Semi-variable Cost - Costs that change with
volume produced, but not in direct
proportion 12/6/2021

 Fixed Costs - Costs that do not change in total with
the volume produced or sold.
 Variable Costs - Costs that change in direct
proportion with the volume produced or sold.
 Mixed Costs - A combination of fixed and variable
costs.
 Semi-variable Cost - Costs that change with volume
produced, but not in direct proportion
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Revenue –Costs = Profit
Revenue - Variable Cost - Fixed Cost = Profit
Breakeven Point is where Profit = 0
Revenue - Variable Cost - Fixed Cost = 0
Revenue = Variable Cost + Fixed Cost
Revenue = #Units Sold * Selling Price $/Unit
Variable Cost = #Units Sold * Variable Cost $/Unit
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$
Units Sold 12/6/2021

$

Units Sold
$
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$

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 Raw materials & purchased parts
 Incoming students
 Work in progress
 Current students
 Finished-goods inventories
 (manufacturing firms) or merchandise (retail stores)
 Graduating students
 Replacement parts, tools, & supplies
 Goods-in-transit to warehouses or customers
 Students on leave

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 To meet anticipated demand
 To smooth production requirements
 To decouple components of the production-
distribution
 To protect against stock-outs
 To take advantage of order cycles
 To help hedge against price increases or to take
advantage of quantity discounts
 To permit operations
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Hamed.Ali.Mohamed2@gmail.com

52
 Inventory level
 Low or high
 Customer service levels
 Can you deliver what customer wants?
 Right goods, right place, right time, right quantity
 Inventory turnover
 Cost of goods sold per year / average inventory investment
 Inventory costs, more will come
 Costs of ordering & carrying inventories
Decisions: Order size and time
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 A physical count of items in inventory
 Periodic/Cycle Counting System: Physical count of
items made at periodic intervals
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?
 Continuous Counting System
System that keeps track of
removals from inventory
continuously, thus monitoring
current levels of each item
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 Two-Bin System - Two containers of inventory;
reorder when the first is empty.
 Universal Bar Code - Bar code printed on a label
that has information about the item to which it is
attached.
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 Lead time: time interval between ordering and
receiving the order, denoted by LT
 Holding (carrying) costs: cost to carry an item in
inventory for a length of time, usually a year, denoted
by H
 Ordering costs: costs of ordering and receiving
inventory, denoted by S
 Shortage costs: costs when demand exceeds supply
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 A system to keep track of inventory
 A reliable forecast of demand
 Knowledge of lead times
 Reasonable estimates of
 Holding costs
 Ordering costs
 Shortage costs
 A classification system
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Classifying inventory according to some measure of
importance and allocating control efforts accordingly.
Importance measure= price*annual sales
A - very important
B - mod. important
C - least important
Annual
$ volume
of items
A
B
C
High
Low
Few Many
Number of Items
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58
 Fixed Order Size - Variable Order Interval Models:
 1. Economic Order Quantity, EOQ
 2. Economic Production Quantity, EPQ
 3. EOQ with quantity discounts
All units quantity discount
 3.1. Constant holding cost
 3.2. Proportional holding cost
 4. Reorder point, ROP
 Lead time service level
 Fill rate
 Fixed Order Interval - Variable Order Size Model
 5. Fixed Order Interval model, FOI
 Single Order Model
 6. Newsboy model
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 Assumptions:
 Only one product is involved
 Annual demand requirements known
 Demand is even throughout the year
 Lead time does not vary
 Each order is received in a single delivery
 Infinite production capacity
 There are no quantity discounts
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60
Profile of Inventory Level Over Time
Quantity
on hand
Q
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Reorder
point
Usage
rate
Time
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 Length of an inventory cycle
From one order to the next = Q/D
 Inventory held over entire inventory cycle
Area under the inventory level = ½ Q (Q/D)
 Average inventory held
= Inventory held over a cycle / cycle length
= Q/2
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62
Annual
carrying
cost
Annual
ordering
cost
Total cost = +
Q
2
H
D
Q
S
TC = +
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64
Order Quantity
(Q)
The Total-Cost Curve is U-Shaped
Ordering Costs
QO
Annual
Cost
(optimal order quantity)
TC
Q
H
D
Q
S
 
2
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65
Using calculus, we take the derivative of the total
cost function and set the derivative (slope) equal
to zero and solve for Q.
The total cost curve reaches its minimum where
the carrying and ordering costs are equal.
Q =
2DS
H
=
2(Annual Demand )(Order or Setup Cost )
Annual Holding Cost
OPT
DSH
EOQ
Q 2
)
cost(
Total 

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Demand, D = 12,000 computers per year.
Holding cost, H = 100 per item per year. Fixed cost, S =
$4,000/order.
Find EOQ, Cycle Inventory, Optimal Reorder Interval
and Optimal Ordering Frequency.
EOQ = 979.79, say 980 computers
Cycle inventory = EOQ/2 = 490 units
Optimal Reorder interval, T = 0.0816 year = 0.98 month
Optimal ordering frequency, n=12.24 orders per year.
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Annual
carrying
cost
Purchasing
cost
TC = +
Q
2
H
D
Q
S
TC = +
+
Annual
ordering
cost
PD
+
Note that P is the price.
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Cost
EOQ
TC with PD
TC without PD
PD
0 Quantity
Adding Purchasing cost
doesn’t change EOQ
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69
 Production done in batches or lots
 Capacity to produce a part exceeds the part’s
usage or demand rate
 Assumptions of EPQ are similar to EOQ except
orders are received incrementally during
production
 This corresponds to producing for an order with finite
production capacity
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 Only one item is involved
 Annual demand is known
 Usage rate is constant
 Usage occurs continually
 Production rate p is constant
 Lead time does not vary
 No quantity discounts
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Usage
Usage
Production
&
Usage
Production
&
Usage
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Q/p
D
p-D
Q/D
Time
(Q/p)(p-D)
Average inventory held=(1/2)(Q/p)(p-D)
Total cost=(1/2)(Q/p)(p-D)H+(D/Q)S
D
p
p
H
DS
Q


2
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73
Demand, D = 12,000 computers per year. p=20,000
per year. Holding cost, H = 100 per item per year.
Fixed cost, S = $4,000/order.
Find EPQ.
EPQ = EOQ*sqrt(p/(p-D))
=979.79*sqrt(20/8)=1549 computers
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Deterministic demand case
 Anticipation stock
 For known future demand
 Cycle stock
 For convenience, some operations are performed occasionally and stock
is used at other times
 Why to buy eggs in boxes of 12?
 Pipeline stock or Work in Process
 Stock in transfer, transformation. Necessary for operations.
 Students in the class
Stochastic demand case
 Safety stock
 Stock against demand variations
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 Reorder Point - When the quantity on hand of an
item drops to this amount, the item is reordered.
We call it ROP.
 Safety Stock - Stock that is held in excess of
expected demand due to variable demand rate
and/or lead time. We call it ss.
 (lead time) Service Level - Probability that
demand will not exceed supply during lead time.
We call this cycle service level, CSL.
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Lead Times
time
inventory
Shortage
An inventory cycle
ROP
Q
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LT Time
Expected demand
during lead time
Maximum probable demand
during lead time
ROP
Quantity
Safety stock
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Cycle service level: percentage of cycles with
shortage
ROP]
time
lead
during
[Demand
inventory]
t
[Sufficien
inventory
sufficient
has
cycle
single
a
y that
Probabilit
0.7
7
.
0
otherwise
1
shortage,
has
cycle
a
if
0
Write
10
1
0
1
0
1
1
1
0
1
1
:
cycles
10
consider
example
For















CSL
CSL
CSL
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ROP
Risk of
a stockout
Service level
Probability of
no stockout
Expected
demand Safety
stock
0 z
Quantity
z-scale
ROP = E(DLT) + z σDLT
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 The rate of demand
 The lead time
 Demand and/or lead time variability
 Stockout risk (safety stock)
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 Orders are placed at fixed time intervals
 Order quantity for next interval?
 Suppliers might encourage fixed intervals
 May require only periodic checks of inventory levels
 Items from same supplier may yield savings in:
 Ordering
 Packing
 Shipping costs
 May be practical when inventories cannot be closely
monitored
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• A single order must cover the demand until the next order
arrives. Exposure to random demand during not only lead
time but also before.
• Requires higher safety stock than variable order interval
models.
• May provide savings in set up / ordering costs.
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 Single period model: model for ordering of
perishables and other items with limited useful lives.
 Shortage cost: generally the unrealized profits per
unit, $55 for L.L.Bean. We call this underage.
 Excess cost: difference between purchase cost and
salvage value of items left over at the end of a period,
$5 for L.L.Bean. We call this overage.
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 Too much inventory
 Tends to hide problems
 Easier to live with problems than to eliminate them
 Costly to maintain
 Wise strategy
 Reduce lot sizes
 Reduce set ups
 Reduce safety stock
 Aggregate negatively correlated demands
 Remember component commonality
 Delayed postponement
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The economic production quantity (EPQ) model is used in
manufacturing situations where inventory is replenished at a
finite rate given by the production rate of the item under
consideration.
We define two more variables:
p: Production rate per day (daily production)
d: Demand rate per day (daily demand)
Note: p and d must be defined in the same time unit. For
example these could be weekly instead of daily rates.
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Suppose
p = 50 units/day
d = 10 units/day
EPQ = 500 (production quantity, Q); Note: the optimal value
of Q is EPQ or QP
In this case we will need 10 days to produce 500 units
(EPQ/p = 500/50).
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During these ten days, we produce 50 units per day but also
use 10 units per day.
Therefore, we are building up inventory at the rate of 40 (p-d
=50-10) units per day.
At the end of 10 days, the total number of units in inventory
is 400 (40 * 10). This is the maximum inventory level, Imax.
After 50 days, the next batch consisting of EPQ units is
scheduled for production. This is how the cycles continue.
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At the end of the 10th day, we stop producing this item and
then continue to meet the demand from the inventory. The
inventory will last for 40 days (400/10) because we have 400
units in stock and the demand rate is 10 units/day.
The production cycle thus consists of 50 days. For the first 10
days we produce and use the item. For the next 40 days, there
is no production and there is only the usage of the item.
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90
The maximum inventory level as explained
earlier is Imax = Q (1- d/p) = 400.
Average Inventory = (Imax)/2
Annual Setup Cost = (D/Q)S
Annual Holding Cost =
EPQ is obtained by equating the annual setup
cost with annual holding cost and then solving
for Q. The expression for EPQ is given on the
RHS.










p
d
H
DS
EPQ
1
2






















p
d
Q
H
H
ax
1
2
2
Im

















p
d
Q
H
S
Q
D
TVC 1
2

Annual Demand (D) = 50,000 units, Setup Cost (S) =$25.00
per set up, Inventory Holding Cost (H) = $5.00 per unit per
year.
Production rate (p) = 500 units per day.
Number of working days = 250. Demand occurs only during
the working days. Therefore, (d) = 50,000/250 = 200.
EPQ (QP) = 912.87 =
Imax = 548.
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92
Quantity discount model is used when the vendor (supplier)
offers a discount for buying in large quantities.
For example, the supplier may quote a price of $ 10.00 per
unit for order size 1 to 999 and $ 9.50 for order size of 1,000
or more.
This scenario is also called a “price break” at quantity 1,000.
There could be several price breaks.
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The annual demand (D) for an item is 240,000 units. The ordering cost per order
(S) is $ 30.00. The inventory carrying cost per unit per year (H) is 30% of the cost
(price) of the item, that is, H = 30% of C.
The vendor has quoted the following costs (prices).
Price 1: $ 2.80 for order quantity less than or equal to 29,999.
Price 2: $ 2.77 for order quantity 30,000 and above.
Find the Economic Order quantity.
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To solve this problem we will compare the total costs for both
prices. As in the EOQ model, the economic order quantity is
given by the following equation,
QO =
and, the total cost (TC) is given by the following equation:
TC = (D/Q)*S + (Q/2)*H + D*C
94 12/6/2021

Start calculations by finding EOQ at the lower price ($ 2.77).
The inventory carrying cost for this price is $0.83 (= 30% of $ 2.77) per
unit per year and the economic order quantity for this price is 4,163.
However, we cannot buy 4,163 units at the price of $ 2.77 because the
minimum quantity specified by the vendor at this price is 30,000.
Therefore, we have to buy at least 30,000 units to obtain this price
discount.
We calculate the total cost TC (at 30,000). Using the TC equation,
TC (at 30,000) = (240,000/30,000)*30 + (30,000/2)*0.83 + 240,000*2.77 = $ 677,505.00
95 12/6/2021

Now calculate the EOQ for the higher price $ 2.80.
The value of H for this price is $ 0.84 (30% of $ 2.80).
The economic order quantity is 4,140.
This quantity is feasible because we can by up to 29,999 units at $ 2.80 per
unit.
The total cost, TC(at 4,140) will be:
TC (at 4,140) = = (240,000/4,140)*30 + (4,140/2)*0.84 + 240,000*2.80 = $ 675,477.93.
The order quantity for this example is 4,140
since TC (at 4,140) < TC (at 30,000).
96 12/6/2021

Some materials are more important than others.
Importance can be established in the following two
ways:
o Material Criticality
o Annual Dollar Volume of Materials
97 12/6/2021

There are various definitions of ‘‘critical’’ that fit different
situations. For example, a part is critical when:
o A part failure causes product or process failure.
o Part failure can have a probability (not a certainty) of stopping
the process or product.
o Part failure reduces production output by a significant
amount.
o Danger involved in using materials. Flammability,
explosiveness, and toxicity of fumes are crucial safety factors
for materials management.
98 12/6/2021

Whichever definition of criticality is used, the procedure is to list first the
most critical parts.
Next, systematically rank-order parts according to their relative
criticality.
The concept of criticality should reflect the costs of failures, including
safety dangers, loss of life, and losses in production output.
Curves similar to the figure on
RHS can be created for such
situations.
99

ABC categories are based on sorting materials by their annual dollar
volume.
Dollar volume is the surrogate for potential savings that can be made by
improving the inventory management of specific materials.
Accordingly, all parts, components, and other materials used by a
company should be listed and then rank ordered by their annual dollar
volume.
Start with those items that have the highest levels of dollar volume and
rank order them from the highest to the lowest levels.
o The top 25 percent of these materials are called A-type items.
o The next 25 percent are called B-type items.
o The bottom 50 percent are called C-type items.
100 12/6/2021

However, there is no fixed convention that A, B, and C class breaks must
occur at 25 and 50 percent.
Companies differ with respect to what percent of all items stocked
account for 75 percent of their total annual dollar volume.
The figure on RHS portrays a
typical case where 20 to 30 percent
of all items carried account for as
much as 70 to 80 percent of the
company’s total dollar volume.
101

Item Stock
Number
Annual Volume
(Units)
Unit Cost Annual Dollar Volume
Percentage of
Annual Dollar
Volume
Cumulative % of
Annual Dollar
Volume
Percentage of
Number of
Items Stocked
Cumulative % of
Number of Items
Stocked
Category
P 1250 $92.00 $115,000.00 40.17% 40.17% 10.00% 10.00% A
Q 530 $168.00 $89,040.00 31.10% 71.26% 10.00% 20.00% A
R 1970 $18.75 $36,937.50 12.90% 84.17% 10.00% 30.00% B
S 430 $42.20 $18,146.00 6.34% 90.50% 10.00% 40.00% B
T 990 $13.80 $13,662.00 4.77% 95.27% 10.00% 50.00% B
U 680 $12.50 $8,500.00 2.97% 98.24% 10.00% 60.00% C
V 2150 $0.98 $2,107.00 0.74% 98.98% 10.00% 70.00% C
W 210 $9.80 $2,058.00 0.72% 99.70% 10.00% 80.00% C
X 1250 $0.52 $650.00 0.23% 99.93% 10.00% 90.00% C
Y 335 $0.64 $214.40 0.07% 100.00% 10.00% 100.00% C
Total $286,314.90
102 12/6/2021

Lead time (LT) is the interval that elapses between the recognition that an
order should be placed and the delivery of that order. See Figure below.
The diminishing stock level reaches a threshold (or limen) called QRP -
the stock level of the reorder point.
The threshold triggers the order for replenishment.
The stock level at the reorder point, RP, is enough to meet orders until the
replenishment supply arrives and is ready to be used.
103 12/6/2021

Eight lead-time (LT) considerations that apply to EOQ or
EPQ or both:
 The amount of time required to recognize the need to
reorder.
 The interval for doing whatever clerical work is needed to
prepare the order.
 Mail, e-mail, EDI, or telephone intervals to communicate
with the supplier (or suppliers) and to place the order(s).
 Time that takes the supplier’s organization to react to the
placement of an order?
104 12/6/2021

 Delivery time including loading, transit, and unloading.
 Processing of delivered items by the receiving department.
 Inspection to be sure items match specifications.
 Time delays in updating records The effect of such delays on
the production schedule must be considered.
The eight lead-time components are added to get the lead time.
Lead times are usually variable.
Safety stocks may be increased to deal with variable lead times.
105 12/6/2021

Order point policies (OPP) define the stock level at which an
order will be placed. The reorder point (RP), triggers an
order for more stock.
OPP systems specify the number of units to order and when
to order.
We will discuss the following two systems
 Periodic, also known as fixed time, inventory systems.
 Perpetual, also known as fixed quantity, inventory systems.
106 12/6/2021

The interval between orders is fixed while the ordered amount varies.
The order size is determined by the amount of stock on-hand when the
record is read.
It is the date that triggers the review and the order being placed.
See the figure on RHS.
107 12/6/2021

Perpetual, also known as fixed quantity, inventory systems continuously record
inventory received from suppliers and withdrawn by employees.
An order is placed when reorder point is reached.
The amount ordered is same (generally EOQ or EPQ) in each cycle.
The interval between placing orders is different in each cycle because of demand
variability.
108 12/6/2021

Shortages occur whenever actual demand in the lead-time period exceeds QRP.
The likelihood of a shortage will be decreased by increasing the value of safety(
buffer) stock.
Determining safety (buffer) stock level requires an economic balancing situation
between the cost of going out of stock versus the cost of carrying more
inventory.
The large buffer stock means that the carrying cost of stock is high to make
sure that the actual cost of stock-outages is small.
The stock level of the reorder point (QRP) is equal to the expected (average)
demand during the lead time period plus the safety stock (SS) quantity.
Thus,
109
QRP = LT + SS
12/6/2021

The expected demand during lead time is a function of average demand
per day (d) and the magnitude of lead time (LT) and is determined as
It may be noted that calculation of demand during lead time becomes
complex if lead time also varies.
110 12/6/2021

The value of SS depends on the variability of demand and the service level.
The service level is a measure of the stock-out situations allowed. For
example, a 95% service level means that there will be no out-of-stock
situation 95% of the time during lead time.
Assuming that the demand follows a normal distribution the value of SS can
be determined as
SS = zσLT
where, σLT is the standard deviation of demand during lead time and z is a
measure of the service level that we want to provide. z is called standard
normal random variable and can be found from its statistical table. For the
95% service level the value of z = 1.65.
111 12/6/2021

The two-bin system is a smart way of continuously
monitoring the order point.
It is a simple self-operating perpetual inventory system.
See the figure below.
112 12/6/2021

Thanks For Attention
&
Hope it will Help You All
12/6/2021

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