SIM Unit-3 Economic order quantity (EOQ) Derivation of EOQ formula, reasons to modify EOQ to suit to real life situations, Just in time, Lead-time analysis, Effect of long lead-time on costs and profitability, elements of lead-time, inventory models: safety stocks, fixation of re-order level and desired inventory level, designing of Q and P models of inventory control.

1. Unit-III
 Economic order quantity (EOQ)
 Derivation of EOQ formula,
 reasons to modify EOQ to suit to real life situations,
 Just in time,
 Lead-time analysis,
 Effect of long lead-time on costs and profitability,
 elements of lead-time,
 inventory models:
 safety stocks,
 fixation of re-order level and
 desired inventory level,
 designing of Q and P models of inventory control.

2. EOQ

3. Derivation of EOQ formula
■ ReferenceSIM_REF_EOQformulaDerivation.pdf

5. https://www.youtube.com/watch?v=XN0MMp2zdRk

7. JIT
■ Just-in-time (JIT) is an inventory strategy companies employ to increase efficiency and
decrease waste by receiving goods only as they are needed in the production process,
thereby reducing inventory costs.This method requires producers to forecast demand
accurately.
■ This inventory supply system represents a shift away from the older just-in-case strategy,
in which producers carried large inventories in case higher demand had to be met
■ BREAKING DOWN 'Just InTime - JIT'
■ A good example would be a car manufacturer that operates with very low inventory levels,
relying on its supply chain to deliver the parts it needs to build cars.The parts needed to
manufacture the cars do not arrive before or after they are needed; instead, they arrive just
as they are needed.

8. JIT
Advantages
■ Just-in-time inventory control has
several advantages over traditional
models. Production runs remain
short, which means manufacturers
can move from one type of product
to another very easily.This method
reduces costs by eliminating
warehouse storage needs.
Companies also spend less money
on raw materials because they buy
just enough to make the products
and no more.
Disadvantages
■ The disadvantages of just-in-time
inventories involve disruptions in the
supply chain. If a supplier of raw
materials has a breakdown and cannot
deliver the goods on time, one supplier
can shut down the entire production
process.A sudden order for goods that
surpasses expectations may delay
delivery of finished products to clients.

9. Lead time analysis
■ Lead time is the amount of time that elapses between when a process starts and its completion.
Lead time is examined closely in manufacturing, supply chain management and project
management, as companies want to reduce the amount of time it takes to deliver products to the
market. Companies look at preprocessing, processing and post processing and compare each
against benchmarks to determine where slowdowns are occurring.
BREAKING DOWN 'LeadTime'
■ Lead time reduction streamlines operations and improves productivity, increasing a company’s
output and revenue. In contrast, longer lead times negatively affect the manufacturing process. A
number of issues affect a company’s lead time.
Inventory
■ Disorganized inventory increases lead time. Keeping all necessary parts organized onsite allows
easy assembly of finished products. Reducing the number of surplus parts helps as well. One
solution is for companies to use kitting services, which group together specific components
needed for a project. Workers save time choosing from smaller lots of items, keeping production
more organized and efficient

10. Stock-Outs
■ Stock-outs make building
equipment impossible
because required parts are
missing. For example,
management may have
underestimated the amount of
stock needed or failed to place
a replenishment order.
Because suppliers cannot
replenish materials
immediately, waiting for the
new inventory costs the
company time and money,
especially when the items are
not available for weeks or
months. A vendor-managed
inventory (VMI) program
provides automated stock
replenishment from an off-site
supplier using Just inTime
(JIT) inventory management
for ordering and delivering
components based on usage.
Building Completely Onsite
■ Building each part of a finished
product onsite takes longer
than completing specific parts
offsite, reducing output
and return on
investment (ROI). Having sub-
assemblies offsite saves hours
of onsite production. Because
products take less time
completing, the company can
make and sell more in less
time, increasing customer
satisfaction and the
company’s bottom line
Supply Chain Sources
■ Lead time varies among supply chain sources, causing difficulty predicting
when to expect delivery of items and coordinating production.This results
in excess inventory, which strains a company’s budget, and non-production
due to stock-outs, which strains revenue. AVMI program
helps consolidate suppliers that store required components and ship them
as needed. Since everything arrives together, shipping and receiving costs
decrease, and scheduling builds becomes easier.
Shipping Delays
■ Shipping delays due to raw
material shortages, natural
disasters, human error or
other issues affect lead
time.Working with a
supplier who keeps
inventory on hand while
continuously monitoring a
company’s usage helps
alleviate the issue.

11. Effect of long lead-time on costs and
profitability
■ Suppliers provide an estimate of lead
time, but these numbers are not
always accurate.The differences
between your expected receipt date
and actual receipt date can become
expensive from the resulting
unplanned over stocks, out of stocks,
and deflated consumer opinions. Lead
time tracking and lead time
forecasting are mission critical to the
success of your supply chain.
■ LeadTime Forecasting like Demand
Forecasting should use a set of math
algorithms to calculate the correct lead
time days to use in planning purchase
orders. Also, like Demand Forecasting,
the LeadTime Forecast should move
up and down according to changes in
market, business influences and
seasonality of product.
■ The ability of LeadTime forecast to
be accurate and dynamically
updated decreases the amount of
safety stock needed in your
inventory.The resulting lead time
forecast is then multiplied by the
daily demand forecast for each day
moving forward to determine how
many units will need to be carried on
the shelves to maintain service level
in between orders.

12. Lead time forecasting accuracy heavily influences your inventory optimization success by
impacting both safety stock and consumer opinion of your customer service capability.
When to place the inventory replenishment order or when to place the new product order
should be based in part on lead time days.
■ While some companies use a single lead time forecast number for all vendors, the
reality is that all vendors and products are not the same. Start reviewing how many
products have a bad lead time that is to short, which means you run out and have lost
sales.Calculate your lost sales for those out-of stock days (you do have a method to
calculate lost sales, right?) and sum the total lost sales across six months to see how
much money you are losing.
■ Now look at all those skulocs that had overstock where the actual lead time was less
than the expected lead time across the last six months. Sum the cost of the excess
inventory and, multiply the result by 10%, and then you have a conservative estimate
of your overstock carrying cost. In reality, your actual costs are probably double that
number. Finally, add the overstock cost and the lost sales cost together to see a six
month total.

13. Inventory models:
■ ReferenceSIM_REF_invemtorymodels.ppt (Slides after this)
■ ReferenceSIM_REF_INVENTMODELS.doc (check out the document uploaded in my
profile with title: SIM Referene INVENTMODELS)
■ Read these both: will take a few hours , but understand the whole math thingy
Inventory model is a mathematical model that helps business in determining the optimum
level of inventories that should be maintained in a production process, managing
frequency of ordering, deciding on quantity of goods or raw materials to be stored,
tracking flow of supply of raw materials and goods to provide uninterrupted service to
customers without any delay in delivery.

14. 14
INVENTORY MODELS
Outline
■ Deterministic models
– The Economic Order Quantity (EOQ) model
– Sensitivity analysis
– A price-break Model
■ Probabilistic Inventory models
– Single-period inventory models
– A fixed order quantity model
– A fixed time period model

16. 16
Probabilistic Inventory Models
■ The demand is not known. Demand characteristics
such as mean, standard deviation and the
distribution of demand may be known.
■ Stockout cost: The cost associated with a loss of
sales when demand cannot be met. For example, if
an item is purchased at $1.50 and sold at $3.00, the
loss of profit is $3.00-1.50 = $1.50 for each unit of
demand not fulfilled.

17. 17
Single- and Multi- Period Models
■ The classification applies to the probabilistic demand
case
■ In a single-period model, the items unsold at the end
of the period is not carried over to the next period.
The unsold items, however, may have some salvage
values.
■ In a multi-period model, all the items unsold at the
end of one period are available in the next period.
■ In the single-period model and in some of the multi-
period models, there remains only one question to
answer: how much to order.

18. 18
SINGLE-PERIOD MODEL
■ Computer that will be obsolete before the next order
■ Perishable product
■ Seasonal products such as bathing suits, winter
coats, etc.
■ Newspaper and magazine

19. 19
Trade-offs in a Single-Period Models
Loss resulting from the items unsold
ML= Purchase price - Salvage value
Profit resulting from the items sold
MP= Selling price - Purchase price
Trade-off
Given costs of overestimating/underestimating demand
and the probabilities of various demand sizes
how many units will be ordered?

20. 20
Consider an order quantity Q
Let P = probability of selling all the Q units
= probability (demandQ)
Then, (1-P) = probability of not selling all the Q units
We continue to increase the order size so long as
MLMP
ML
Por
MLPMPP



,
)1()(

21. 21
Decision Rule:
Order maximum quantity Q such that
where P = probability (demandQ)
MLMP
ML
P



22. 22
Demand Characteristics

23. 23
A FIXED ORDER QUANTITY MODEL
Purchase-order can be placed at any time
On-hand inventory count is known always
Lead time for a high speed modem is
two weeks and it has the following
sales history in the last 25 weeks:
Quantity/Week Frequency
75-80 1
70-75 3
65-70 9
60-65 8
55-60 4
Will you order
now if number
of items on
hand is:
a. 200
b. 150
c. 100

24. 24
A Fixed Order Quantity Model
■ The same quantity, Q is ordered when inventory on
hand reaches a reorder point, R

25. 25
A Fixed Order Quantity Model
• An order quantity of EOQ works well
• If demand is constant, reorder point is the same as
the demand during the lead time.
• If demand is uncertain, reorder point is usually set
above the expected demand during the lead time
• Reorder point = Expected demand + Safety stock

26. 26
Safety Stock
Lead Time
Time
Expected demand
during lead time
Quantity
Safety stock
Reorder Point

27. 27
Trade-Off with Safety Stock
• Safety Stock - Stock held in excess of expected
demand to protect against stockout during lead time.
Safety stock  Holding cost  Stockouts 
Safety stock  Holding cost  Stockouts 

28. 28
Acceptable Level of Stockout
Ask the manager!!
Acceptable level of stockout reflects management’s tolerance
A related term is service level.
Example: if 20 orders are placed in a year and management
can tolerate 1 stockout in a year, acceptable level of
stockout = 1/20 = 0.05 = 5% and the service level = 1- 0.05
= 0.95.

29. 29
Computation of Safety Stock

30. Safety Stock (S):
■ It is the extra stock that is always maintained to mitigate any future risks arising due
to stock-outs because of shortfall of raw materials or supply, breakdown in machine or
plant, accidents, natural calamity or disaster, labour strike or any other crisis that may
the stall the production process.
■ The quantity of safety stock is often derived by analysing historical data and is set to
an optimized level by evaluating carefully the current cost of inventory and losses that
may be incurred due to future risk.

31. Fixation of re-order level and
■ Fixed Reorder Quantity System
■ Fixed Reorder Period System.

32. Fixed Reorder Quantity System.
■ Fixed Reorder Quantity System is an Inventory Model, where an alarm is raised
immediately when the inventory level drops below a fixed quantity and new orders are
raised to replenish the inventory to an optimum level based on the demand.The point at
which the inventory is ordered for replenishment is termed as Reorder Point.The
inventory quantity at Reorder Point is termed as Reorder Level and the quantity of new
inventory ordered is referred as Order Quantity.
■ Average Demand (DAv): It is the average number of order requests made per day.
■ Average LeadTime (TL):The time required to manufacture goods or product.
■ Average LeadTime Demand (DL): Average number of orders requested during the Lead
Time
■ Average LeadTime Demand (DL) = Average Demand (DAv) X Average LeadTime (TL)

33. Reorder Level (RL):
■ Reorder level is the inventory level, at which an alarm is triggered immediately to
replenish that particular inventory stock. Reorder level is defined, keeping into
consideration the Safety Stock to avoid any stock-out and Average LeadTime Demand
because even after raising the alarm, it would take one complete process cycle (Lead
Time) till the new inventories arrive to replenish the existing inventory.
■ Reorder Level (RL) = Safety Stock (S) + Average LeadTime Demand (DL)
■ Order Quantity (O): Order quantity is the Demand (Order requests) that needs to be
delivered to the customer.
■ Minimum Level:At least Safety Stock has to be always maintained to avoid any future
stock- outs as per the standard practices of inventory management.
■ Minimum Level (LMin) = Safety Stock (S)
■ Maximum Level:The maximum level that can be kept in stock is safety stock and the
demand (the quantity ordered).
■ Maximum Level (LMax) = Safety Stock (S) + OrderQuantity (O)

34. Inventory Model: Fixed Reorder Quantity System

35. Fixed Reorder Period System.
■ Fixed Reorder Period System is an Inventory Model of managing inventories, where an alarm is
raised after every fixed period of time and orders are raised to replenish the inventory to an
optimum level based on the demand. In this case replenishment of inventory is a continuous
process done after every fixed interval of time.
■ Regular Intervals (R): Regular Interval is the fixed time interval at the end of which the
inventories would be reviewed and orders would be raised to replenish the inventory
■ Inventory on Hand (It): Inventory on hand is the Inventory level measured at any given point
of time.
■ Maximum Level (M): It is the maximum level of inventory allowed as per the production
guidelines.The maximum level is derived by analysing historical data.
■ Order Quantity: In this system, inventory is reviewed at regular intervals (R), inventory on
hand (It) is noted at the time of review and order quantity is placed for a quantity of (M) – (It).
■ Order Quantity (O) = (M) – (It).

36. Inventory Model: Fixed Reorder Period System

37. Example: Inventory is replenished at every regular interval of 5 days.The maximum
allowable inventory is 800 Units.The inventory reviewed on Day-5, Day-10, Day -15
and Day -20 were 387 Units, 201 Units, 498 Units and 127 Units respectively.
■ Regular Intervals (R) = 5 Days
■ Maximum Level (M) = 800 Units
■ Inventory on Hand: I5 = 387 Units, I10 = 201 Units, I15 = 498 Units and I20 = 127 Units
■ Order Quantity (O) = (M) – (It).
■ Order Quantity (O5) = 800 – 387 = 413 Units
■ Order Quantity (O10) = 800 – 201 = 599 Units
■ Order Quantity (O15) = 800 – 498 = 302 Units
■ Order Quantity (O15) = 800 – 127 = 673 Units

38. Desired inventory level
■ Application based question- if asked.

39. Designing of Q and P models of
inventory control
■ Check references

40. references
■ https://www.slideshare.net/BilalAhmad54/economic-order-quantity-and-inventory-
management
Author: BilalAhmed