basic intro of Inventory

1. Inventory

2. 1- 2
Inventory Management-III
 History
1915 F.W.Harris (Westinghouse)
Lot size formula (EOQ model); independently
developed byWilson and sold to many
companies as
an integral part of an inventory control scheme.
1931 F.E. Raymond (MIT)
Wrote the first full length book.
WWII Christmas tree problem (Newsboy problem)
Whitin’s stochastic extension of the EOQ model.
Early Computer made it possible to handle large data
requirement
1950’s Of the inventory models, Whitin published a
book on
stochastic inventory models in 1953.

3. 1- 3
Inventory Management-IV
1958 Arrow, Karlin and Scarf published their now
classical
book, which is a definitive work on inventory
theory,
inspired a great deal of research for next
decade.
Mid Material requirement planning (MRP)
1970’s Books by Orlicky,Wight in 1974

4. What is inventory?
A physical resource that
a firm holds in stock with
the intent of selling it or
transforming it into a
more valuable state.
Purpose of inventory
management
• How many units to order?
• when to order? discount

5. PURPOSE OF INVENTORY
 Reduction of cost is main aspect to be competitive in market
using inventory management
 Improvement of profits
 Improvement of Efficiency of a firm
 Reduction of capital investment improves return on investment

8. Types of Inventories
Raw materials
Purchased parts and supplies
Finished Goods
Work-in-process (partially completed products )
Items being transported
Tools and equipment

9. Raw Materials – Basic inputs that are converted into finished
product through the manufacturing process
Work-in-progress – Semi-manufactured products need some
more works before they become finished goods for sale
Finished Goods – Completely manufactured products ready
for sale
Supplies – Office and plant materials not directly enter
production but are necessary for production process and do
not involve significant investment.

10. Functions of Inventory
1. To decouple or separate various parts of
the production process
2. To decouple the firm from fluctuations
in demand and provide a stock of goods
that will provide a selection for
customers
3. To take advantage of quantity discounts
4. To hedge against inflation

11. The Material Flow Cycle
Input Wait for Wait to Move Wait in queue Setup Run Output
inspection be moved time for operator time time
Cycle time
95% 5%

15. Inventory Management
• ABC Analysis
• Record Accuracy
• Cycle Counting
• Control of Service Inventories

16. Classifying Inventory Items
ABC Classification (Pareto Principle)
In any Retail organization there are large numbers of
inventories to be maintained. It is not practical to have
very stringent inventory control system for each & every
item. So with the modus of having an effective Purchase
& stores control we implement ABC Inventory
Classification model Known as Always Better Control
(ABC) based upon Pareto rule ( 80/20 rule)

17. ABC Analysis
 Divides inventory into three classes
based on annual dollar volume
 Class A - high annual dollar volume
 Class B - medium annual dollar volume
 Class C - low annual dollar volume
 Used to establish policies that focus on
the few critical parts and not the many
trivial ones

19. ABC Analysis
Item
Stock
Number
Percent of
Number of
Items
Stocked
Annual
Volume
(units) x
Unit
Cost =
Annual
Dollar
Volume
Percent of
Annual
Dollar
Volume Class
#10286 20% 1,000 $ 90.00 $ 90,000 38.8% A
#11526 500 154.00 77,000 33.2% A
#12760 1,550 17.00 26,350 11.3% B
#10867 30% 350 42.86 15,001 6.4% B
#10500 1,000 12.50 12,500 5.4% B
72%
23%

20. ABC Analysis
Item
Stock
Number
Percent of
Number of
Items
Stocked
Annual
Volume
(units) x
Unit
Cost =
Annual
Dollar
Volume
Percent of
Annual
Dollar
Volume Class
#12572 600 $ 14.17 $ 8,502 3.7% C
#14075 2,000 .60 1,200 .5% C
#01036 50% 100 8.50 850 .4% C
#01307 1,200 .42 504 .2% C
#10572 250 .60 150 .1% C
8,550 $232,057 100.0%
5%

21. C Items
ABC Analysis
A Items
B Items
Percentofannualdollarusage
80 –
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 – | | | | | | | | | |
10 20 30 40 50 60 70 80 90 100
Percent of inventory items

22. Inventory Models
 Independent demand – finished goods, items
that are ready to be sold
 E.g. a computer
 Dependent demand – components of finished
products
 E.g. parts that make up the computer
 Holding, Ordering, and Setup Costs

23. Inventory Models for Independent Demand
 The Basic Economic Order Quantity (EOQ) Model (How
much should we order)
 Reorder Points (ROP or R) (When should we order)
 Production Order Quantity Model (POQ)
 Quantity Discount Models
 Minimizing Costs
 Probabilistic Models and Safety Stock
 Other Probabilistic Models
 Periodic review (P) systems (Fixed Interval Reorder
systems)
 Continuous review (Q) systems (Reorder point systems
ROP)
Need to determine when and how much to order

24. Independent Versus
Dependent Demand
 Independent demand - the demand for item
is independent of the demand for any other
item in inventory
 Dependent demand - the demand for item
is dependent upon the demand for some
other item in the inventory

25.  Lead time: time interval between ordering
and receiving the order
 Holding (carrying) costs: cost to carry an item
in inventory for a length of time, usually a
year
 Ordering costs: costs of ordering and
receiving inventory
 Shortage costs: costs when demand exceeds
supply
Key Inventory Terms

26. General Framework for Inventory Models-I
 Demand
- certainty
- risk, probability distribution of demand
- uncertainty, nothing known
 Lead time:The period between the order time and the
delivery time
- certainty
- risk, probability distribution of demand
- uncertainty
 Inside or Outside Procurement
- purchased from outside; pure inventory problem
- integrated with production smoothing if inside

27. General Framework for Inventory Models-
II
 Static and Dynamic Problems
- Static: one period problem, classic examples are
Christmas tree and newsboy problem
- Dynamic: decisions over time
 Behavior of Demand throughTime and forVarious Items
- Stationary Demand: EOQ models
- Time-dependent Demand:WW model, Silver/Meal Heuristic
- Dependent Demand: MRP

28. General Framework for Inventory Models-
III
 Relevant Inventory Costs
- Price orVariable Production Costs: quantity
discounts
- Ordering or Setup Costs
- Holding or Inventory or Carrying Costs
- Stock out/Shortage costs

29. General Framework for Inventory Models-
III
 Information technology allows us to easily keep and update
information
 Simple inventory system can include:
- forecasting module
- determination of order points and order quantities
- monitoring of inventory levels
 Costs
- holding costs including opportunity costs
- ordering or setup costs
- shortage costs or service levels
 CapacityConstraints
- demand distribution
- lead times
Will not consider speculative costs.

30. Multi period model –The Economic Order Quantity
• Demand is known and deterministic: D units/year
• We have a known ordering cost, S, and immediate replenishment
• Annual holding cost of average inventory is H per unit
• Purchasing cost C per unit
Supplier DemandRetailer

31. What is the optimal quantity to order ?
Total Cost = Purchasing Cost + OrderingCost + Inventory Cost
Purchasing Cost = (total units) x (cost per unit)
OrderingCost = (number of orders) x (cost per order)
Inventory Cost = (average inventory) x (holding cost)
= D x C
D
Q
x S
Q
2
x H

32. Basic EOQ Model
1. Demand is known, constant, and independent
2. Lead time is known and constant
3. Receipt of inventory is instantaneous and
complete
4. Quantity discounts are not possible
5. Only variable costs are setup and holding
6. Stock outs can be completely avoided
Important assumptions
Economic Order Quantity (EOQ) is the lot size that minimizes
total annual inventory holding and ordering costs.

33. 12-33
 Only one item is involved
 Annual demand is known
 Usage rate is constant
 Usage occurs continually
 Production rate is constant
 Lead time does not vary
 No quantity discounts
Economic Production Quantity
Assumptions

34. Finding the optimal quantity to order…
Let’s say we decide to order in batches of Q…
Number of periods will
be
D
Q
Time
TotalTime
Period over which demand for Q has occurred
Q Inventory position
The average
inventory for each
period is… Q
2
Q
2
Receiving order
Inventory depletion
(demand rate) or

35. Minimizing Costs
Objective is to minimize total costs
Annualcost
Order quantity
Curve for total
cost of holding
and setup
Holding cost
curve
Setup (or order)
cost curve
Minimum
total cost
Optimal order
quantity (Q*)
Q
Total Annual Cycle-Inventory Costs

36. The EOQ cost Model
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual setup cost = (Number of orders placed per year)
x (Setup or order cost per order)
Annual demand
Number of units in each order
Setup or order
cost per order
=
Annual setup cost = S
D
Q
= (S)D
Q

37. The EOQ Model
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Annual holding cost = (Average inventory level)
x (Holding cost per unit per year)
Order quantity
2
= (Holding cost per unit per year)
= (H)Q
2
Annual setup cost = S
D
Q
Annual holding cost = HQ
2

38. The EOQ Model
Q = Number of pieces per order
Q* = Optimal number of pieces per order (EOQ)
D = Annual demand in units for the inventory item
S = Setup or ordering cost for each order
H = Holding or carrying cost per unit per year
Optimal order quantity is found when annual setup cost equals
annual holding cost
Annual setup cost = S
D
Q
Annual holding cost = H
Q
2
D
Q
S =
Q
2
Solving for Q*
2DS = Q2H
Q2 = 2DS/H
Q* = 2DS/H
H

39. An EOQ Example
Determine optimal number of needles to order
D = 1,000 units
S = $10 per order
H = $.50 per unit per year
Q* =
2DS
H
Q* =
2(1,000)(10)
0.50
= 40,000 = 200 units
Cont….

40. Determine optimal number of needles to order
D = 1,000 units Q*= 200 units
S = $10 per order
H = $.50 per unit per year
= N =Expected number
of orders
Demand
Order quantity
D
Q*
1,000
2 00
=
N = =5 orders per year
=T =
Expected time
between orders
Number of working days per year
N= 5 orders per year
N
=
250
5
= 50 days between
orders
Cont….
T =50 days between orders
Total annual cost = Setup cost + Holding cost
D
Q
S +
Q
2 HTC=

1,000* ($10)
200
2000* ($0.50)
2
+
TC = $100

41. Reorder Points Model (ROP or R)
 EOQ answers the “how much” question
 The reorder point (ROP) tells “when to order”
ROP =
Lead time for a new
order in days
Demand
per day
= d x L
d =
D
Number of working days in a year

42. Reorder Point Curve
Q*
ROP
(units)
Inventorylevel(units)
Time (days)
Lead time = L
Slope = units/day = d

43. Reorder Point Example
Demand = 8,000 iPods per year
250 working day year
Lead time for orders is 3 working days
ROP = d x L
d =
D
Number of working days in a year
= 8,000/250 = 32 units
= 32 units per day x 3 days = 96 units

44. ROP = Lxd
Receive
order
Time
Inventory
Order
Quantity
Q
Place
order
Lead Time
Reorder
Point
(ROP)
If demand is known exactly, place an order
when inventory equals demand during lead
time.
d: demand per period
L: Lead time in periods
Q:When shall we order?
A: When inventory = ROP or R
Q: How much shall we order?
A: Q = EOQ

45. Economic Order Quantity - EOQ
Q* =
2SD
H
Example:
Assume a car dealer that faces demand for 5,000 cars per year, and that it costs $15,000 to
have the cars shipped to the dealership. Holding cost is estimated at $500 per car per year.
How many times should the dealer order, and what should be the order size?
Q* =
2*15000*5000
500
= 548
What if the lead time to receive cars is 10 days? (when should you place your order?)
Since D is given in years, first convert: 10 days = 10/365 yrs
10
365
D =R =
10
365
5000 = 137
So, when the number of cars on the lot reaches 137, order 548 more cars.

46. Fixed time Period model
 Orders placed at the end of a fixed period
 Inventory counted only at end of period
 Order brings inventory up to target level
 Only relevant costs are ordering and holding
 Lead times are known and constant
 Items are independent from one another
Fixed-Period (P) Systems

47. Fixed-Period (P) Systems
On-handinventory
Time
Q1
Q2
Target quantity (T)
P
Q3
Q4
P
P

48. Fixed-Period (P) Example
Order amount (Q) = Target (T) - On-hand inventory - Earlier
orders not yet received + Back orders
Q = 50 - 0 - 0 + 3 = 53 jackets
3 jackets are back ordered No jackets are in stock
It is time to place an order Target value = 50

49. Fixed-Period Systems
 Inventory is only counted at each review
period
 May be scheduled at convenient times
 Appropriate in routine situations
 May result in stockouts between periods
 May require increased safety stock

50.  based on reorder point - When inventory is
depleted to ROP, order replenishment of
quantity EOQ.
Q - System Inventory Control

51. CONTINUOUS REVIEW INVENTORY SYSTEMS (Q SYSTEMS)
Continuous review system: review the on-hand quantity of an item each time an inventory
withdrawal occurs, and decide whether a replenishment order should be placed at that time order
quantity is fixed but the time between orders ("order cycle") varies.
Reorder point system (fixed order quantity system): reorder a fixed quantity Q whenever the
inventory position falls to or below a predetermined reorder point R.
Inventory position: the ability of inventory to satisfy future demand for an item.
IP = OH + SR - BO where:
•IP = inventory position of the item (in units)
•OH = number of units on-hand
•SR = number of units scheduled to be received ("open order")
•BO = number of units back-ordered or allocated

52. CONTINUOUS REVIEW INVENTORY SYSTEMS (Q SYSTEMS): SELECTINGTHE
REORDER POINT R
Reorder point R = amount of inventory required to meet expected demand during the lead time plus
amount of safety stock held to meet unanticipated demand.
R = L + B
where:
•R = reorder point
•L = expected demand during lead time
•B = amount of safety stock

53. PERIODIC REVIEW SYSTEMS (P SYSTEMS)
Periodic review system (periodic order system, fixed interval reorder system, order-up
to system): review on-hand quantity of an item after a stated number of periods (P). After each review,
order an amount equal to a target inventory level (T) minus the current inventory position (IP) time
between orders ("order cycle") is fixed but the order quantity varies. Review interval (P) may be dictated
by supplier or may be calculated based on the economic order quantity or other considerations.
PERIODIC REVIEW SYSTEMS (P SYSTEMS): SELECTINGTHETARGET INVENTORY
LEVELT
The new order must be such that the resulting inventory position IP will be large enough to satisfy
demand until the next review (P periods from now) plus the lead time (L) for that next order to arrive.
Target inventory levelT = average demand during review interval time P and during lead time L +
safety stock
T = DP+L + B = DP+L + z(sigmaP+L)
where:
•DP+L = average demand during P and L
•B = amount of safety stock
•z = desired number of standard deviations to provide safety stock protection
•sigma P+L = standard deviation of demand during P and L

54. COMPARISONOF Q SYSTEMSAND P SYSTEMS
Continuous review system (Q system):
•This system requires continual monitoring of inventory levels.
•Less safety stock is required because demand during only the lead time must be covered.
•Fixed order quantities are desirable or, in some cases, mandatory.
•Review and replenishment intervals can be set on an item-by-item basis.
Periodic review systems (P system):
•It is easier to combine orders to same supplier, which may reduce per unit purchase and/or
transportation costs.
•Reordering at fixed intervals often is convenient.
•Inventory position must be known only at review time; thus, a perpetual inventory system
is not required.

55. COMPARISON OF Q AND P SYSTEMS
P Systems
 Convenient to administer
 Orders for multiple items from the same supplier may be combined
 Inventory Position (IP) only required at review
 Systems in which inventory records are always current are called
Perpetual Inventory Systems
 Review frequencies can be tailored to each item
 Possible quantity discounts
 Lower, less-expensive safety stocks
Q Systems

56. Comparative Advantages
 Primary advantages of P systems
 Convenient
 Orders can be combined
 Only need to know IP when review is made
 Primary advantages of Q systems
 Review frequency may be individualized
 Fixed lot sizes can result in quantity discounts
 Lower safety stocks