1. Role of Inventory Management
Chapter 13
Role of Inventory Management

2. Copyright 2011 John Wiley & Sons, Inc.
Lecture Outline
Elements of Inventory Management
Inventory Control Systems
Economic Order Quantity Models
Quantity Discounts
Reorder Point
Order Quantity for a Periodic Inventory System
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3. Copyright 2011 John Wiley & Sons, Inc.
What Is Inventory?
Stock of items kept to meet future demand
Purpose of inventory management
how many units to order
when to order
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4. Supply Chain Management
Bullwhip effect
demand information is distorted as it moves away from the end-use customer
higher safety stock inventories to are stored to compensate
Seasonal or cyclical demand
Inventory provides independence from vendors
Take advantage of price discounts
Inventory provides independence between stages and avoids work stoppages
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5. Quality Management in the Supply Chain
Customers usually perceive quality service as availability of goods they want when they want them
Inventory must be sufficient to provide high-quality customer service in QM
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6. Copyright 2011 John Wiley & Sons, Inc.
Types of Inventory
Raw materials
Purchased parts and supplies
Work-in-process (partially completed) products (WIP)
Items being transported
Tools and equipment
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7. Copyright 2011 John Wiley & Sons, Inc.
Two Forms of Demand
Dependent
Demand for items used to produce final products
Tires for autos are a dependent demand item
Independent
Demand for items used by external customers
Cars, appliances, computers, and houses are examples of independent demand inventory
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8. Copyright 2011 John Wiley & Sons, Inc.
Inventory Costs
Carrying cost
cost of holding an item in inventory
Ordering cost
cost of replenishing inventory
Shortage cost
temporary or permanent loss of sales when demand cannot be met
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9. Inventory Control Systems
Continuous system (fixed-order-quantity)
constant amount ordered when inventory declines to predetermined level
Periodic system (fixed-time-period)
order placed for variable amount after fixed passage of time
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10. Copyright 2011 John Wiley & Sons, Inc.
ABC Classification
Class A
5 – 15 % of units
70 – 80 % of value
Class B
30 % of units
15 % of value
Class C
50 – 60 % of units
5 – 10 % of value
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11. Copyright 2011 John Wiley & Sons, Inc.
ABC Classification
1 $ 60 90
PART UNIT COST ANNUAL USAGE
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12. Copyright 2011 John Wiley & Sons, Inc.
ABC Classification
9 $30,
8 16,
2 14,
1 5,
4 4,
3 3,
6 3,
5 3,
10 2,
7 1,
TOTAL % OF TOTAL % OF TOTAL
PART VALUE VALUE QUANTITY % CUMMULATIVE A B C
$85,400
Example 10.1
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13. Copyright 2011 John Wiley & Sons, Inc.
ABC Classification
% OF TOTAL % OF TOTAL
CLASS ITEMS VALUE QUANTITY
A 9, 8,
B 1, 4,
C 6, 5, 10,
Example 10.1
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14. Economic Order Quantity (EOQ) Models
optimal order quantity that will minimize total inventory costs
Basic EOQ model
Production quantity model
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15. Assumptions of Basic EOQ Model
Demand is known with certainty and is constant over time
No shortages are allowed
Lead time for the receipt of orders is constant
Order quantity is received all at once
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16. Copyright 2011 John Wiley & Sons, Inc.
Inventory Order Cycle
Demand rate
Time
Lead time
Order placed
Order receipt
Inventory Level
Reorder point, R
Order quantity, Q
Average inventory Q 2
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17. Copyright 2011 John Wiley & Sons, Inc.
EOQ Cost Model
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =
CoD Q
Annual carrying cost =
CcQ 2
Total cost =
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18. Copyright 2011 John Wiley & Sons, Inc.
EOQ Cost Model
TC =
CoD Q
CcQ 2
= – Q2 Cc
TC Q
0 = –
C0D
Qopt =
2CoD
Deriving Qopt
Proving equality of costs at optimal point =
Q2 =
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19. Copyright 2011 John Wiley & Sons, Inc.
EOQ Cost Model
Order Quantity, Q
Annual cost ($)
Total Cost
Carrying Cost =
CcQ 2
Slope = 0
Minimum total cost
Optimal order
Qopt
Ordering Cost =
CoD Q
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20. Copyright 2011 John Wiley & Sons, Inc.
EOQ Example
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
Qopt =
2CoD Cc
2(150)(10,000)
(0.75)
Qopt = 2,000 gallons
TCmin =
CoD Q
CcQ 2
TCmin =
(150)(10,000)
2,000
(0.75)(2,000)
TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt
= 10,000/2,000
= 5 orders/year
Order cycle time = 311 days/(D/Qopt)
= 311/5
= 62.2 store days
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21. Production Quantity Model
Order is received gradually, as inventory is simultaneously being depleted
AKA non-instantaneous receipt model
assumption that Q is received all at once is relaxed
p - daily rate at which an order is received over time, a.k.a. production rate
d - daily rate at which inventory is demanded
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22. Production Quantity Model
Q(1-d/p)
Inventory
level
(1-d/p) Q 2
Time
Order
receipt period
Begin
order
receipt
End
Maximum
inventory level
Average
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23. Production Quantity Model
p = production rate d = demand rate
Maximum inventory level = Q d
= Q 1 - Q p d
Average inventory level = 2
TC =
CoD
CcQ
Qopt =
2CoD
Cc 1 -
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24. Production Quantity Model
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day
Qopt = = = 2,256.8 gallons
2CoD
Cc 1 - d p
2(150)(10,000)
32.2
150
TC = = $1,329
CoD Q
CcQ 2
Production run = = = days per order
2,256.8
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25. Production Quantity Model
Number of production runs = = = 4.43 runs/year D Q
10,000
2,256.8
Maximum inventory level = Q = 2,
= 1,772 gallons d p
32.2
150
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26. Solution of EOQ Models With Excel
The optimal order size, Q, in cell D8
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27. Solution of EOQ Models With Excel
The formula for Q in cell D10
=(D4*D5/D10)+(D3*D10/2)*(1-(D7/D8))
=D10*(1-(D7/D8))
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28. Solution of EOQ Models With OM Tools
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29. Copyright 2011 John Wiley & Sons, Inc.
Quantity Discounts
Price per unit decreases as order quantity increases
TC = PD
CoD Q
CcQ 2
where
P = per unit price of the item D = annual demand
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30. Quantity Discount Model
Qopt
Carrying cost
Ordering cost
Inventory cost ($)
Q(d1 ) = 100
Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 )
ORDER SIZE PRICE
$10
100 – (d1)
(d2)
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31. Copyright 2011 John Wiley & Sons, Inc.
Quantity Discount
QUANTITY PRICE
$1,400
,100
Co = $2,500
Cc = $190 per TV
D = 200 TVs per year
Qopt = = = 72.5 TVs
2CoD Cc
2(2500)(200)
190
TC = PD = $233,784
CoD
Qopt
CcQopt 2
For Q = 72.5
TC = PD = $194,105 Q
CcQ
For Q = 90
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32. Quantity Discount Model With Excel
=(D4*D5/E10)+(D3*E10/2)+C10*D5
=IF(D10>B10,D10,B10)
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33. Copyright 2011 John Wiley & Sons, Inc.
Reorder Point
Inventory level at which a new order is placed
R = dL
where
d = demand rate per period
L = lead time
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34. Copyright 2011 John Wiley & Sons, Inc.
Reorder Point
Demand = 10,000 gallons/year
Store open 311 days/year
Daily demand = 10,000 / 311 = gallons/day
Lead time = L = 10 days
R = dL = (32.154)(10) = gallons
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35. Copyright 2011 John Wiley & Sons, Inc.
Safety Stock
Safety stock
buffer added to on hand inventory during lead time
Stockout
an inventory shortage
Service level
probability that the inventory available during lead time will meet demand
P(Demand during lead time <= Reorder Point)
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36. Variable Demand With Reorder Point
point, R Q LT
Time
Inventory level
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37. Reorder Point With Safety Stock
point, R Q LT
Time
Inventory level
Safety Stock
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38. Reorder Point With Variable Demand
R = dL + zd L
where
d = average daily demand
L = lead time
d = the standard deviation of daily demand
z = number of standard deviations
corresponding to the service level
probability
zd L = safety stock
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39. Reorder Point For a Service Level
Probability of
meeting demand during
lead time = service level
Probability of
a stockout
Safety stock
zd L dL
Demand R
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40. Reorder Point For Variable Demand
The paint store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 gallons per day
L = 10 days
d = 5 gallons per day
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= gallons
Safety stock = z d L
= (1.65)(5)( 10)
= 26.1 gallons
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41. Determining Reorder Point with Excel
The reorder point formula in cell E7
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42. Order Quantity for a Periodic Inventory System
Q = d(tb + L) + zd tb + L - I
where
d = average demand rate
tb = the fixed time between orders
L = lead time
sd = standard deviation of demand
zd tb + L = safety stock
I = inventory level
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43. Periodic Inventory System
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44. Fixed-Period Model With Variable Demand
d = 6 packages per day
sd = 1.2 packages
tb = 60 days
L = 5 days
I = 8 packages
z = 1.65 (for a 95% service level)
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2)
= packages
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45. Fixed-Period Model with Excel
Formula for order size, Q, in cell D10
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46. Simulation Decision Analysis Tools and Technique
Chapter 13
Simulation Decision Analysis Tools and Technique

47. Lecture Outline Monte Carlo Simulation Computer Simulation with Excel
Areas of Simulation Application

48. Copyright 2011 John Wiley & Sons, Inc
Simulation
Mathematical and computer modeling technique for replicating real-world problem situations
Modeling approach primarily used to analyze probabilistic problems
It does not normally provide a solution; instead it provides information that is used to make a decision
Physical simulation
Space flights, wind tunnels, treadmills for tires
Mathematical-computerized simulation
Computer-based replicated models
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49. Monte Carlo Simulation
Select numbers randomly from a probability distribution
Use these values to observe how a model performs over time
Random numbers each have an equal likelihood of being selected at random
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50. Probability Distribution of Demand
LAPTOPS DEMANDED FREQUENCY OF PROBABILITY OF
PER WEEK, x DEMAND DEMAND, P(x)
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51. Roulette Wheel of Demand90 80 60 20
x = 2
x = 0
x = 4
x = 3
x = 1
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52. Generating Demand from Random Numbers
DEMAND, RANGES OF RANDOM NUMBERS,
x r
0 0-19
r = 39
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53. Copyright 2011 John Wiley & Sons, Inc
Random Number Table
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54. Copyright 2011 John Wiley & Sons, Inc
15 Weeks of Demand
WEEK r DEMAND (x) REVENUE (S)
,300
,600
,600
,600
,300
,900
,200
,300
,200
,300
,200
,200
,600
 = 31 $133,300
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55. Computing Expected Demand
Estimated average demand = 31/15 = 2.07 laptops/week
E(x) = (0.20)(0) + (0.40)(1) + (0.20)(2)
+ (0.10)(3) + (0.10)(4)
= 1.5 laptops per week
Difference between 1.5 and 2.07 is due to small number of periods analyzed (only 15 weeks)
Steady-state result
average result which stays constant after enough trials
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56. Random Numbers in Excel
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57. Simulation in Excel Enter this formula in G6 and copy to G7:G20
Enter “=4300*G6” in H6 can copy to H7:H20
Generate random number for cells F6:F20 with the formula “=RAND()” in F6 and copying to F7:F20
=AVERAGE(G6:G20)
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58. Simulation in Excel
Spreadsheet “frozen” at row 16 to show first 10 weeks and last 6
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59. Decision Making with Simulation
=G6*50 entered into cell L6 and copied to L7:L105
This formula entered in G7 and copied to G8:G105
=VLOOKUP (F6,LOOKUP,2) in H6 and copied to H7:H105
Shortages computed by entering =MIN(G6-H6,0) in I6 and copying to I7:I105
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60. Decision Making with Simulation
New formula for two laptops ordered per week.
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61. Areas of Simulation Application
Waiting Lines/Service
Complex systems for which it is difficult to develop analytical formulas
Determine how many registers and servers are needed to meet customer demand
Inventory Management
Traditional models make the assumption that customer demand is certain
Simulation is widely used to analyze JIT without having to implement it physically
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62. Areas of Simulation Application
Production and Manufacturing Systems
Production scheduling, production sequencing, assembly line balancing, plant layout, and plant location analysis
Machine breakdowns typically occur according to some probability distributions
Capital Investment and Budgeting
Capital budgeting problems require estimates of cash flows, often resulting from many random variables
Simulation has been used to generate values of cash flows, market size, selling price, growth rate, and market share
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63. Areas of Simulation Application
Logistics
Random variables include, distance, transport modes, shipping rates, and schedules
Allows analysis of different distribution channels
Service Operations
Police departments, fire departments, post offices, hospitals, court systems, airports
Complex operations where only simulation can be employed
Environmental and Resource Analysis
Impact of manufacturing plants, waste-disposal facilities, nuclear power plants, waste and population conditions, feasibility of alternative energy sources
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