1. Inventory Management
Chapter 13

2. Learning Objectives You should be able to:
Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management
Explain periodic and perpetual review systems
Explain the objectives of inventory management
Describe the A-B-C approach and explain how it is useful
Describe the basic EOQ model and its assumptions and solve typical problems
Describe the economic production quantity model and solve typical problems
Describe the quantity discount model
Describe reorder point models
Describe situations in which the single-period model would be appropriate, and solve typical problems
Instructor Slides

3. Inventory Inventory A stock or store of goods Independent demand items
Items that are ready to be sold or used
A “typical” firm (on “typical” times) has roughly 30% of its current assets and as much as 90% of its working capital invested in inventory
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4. Types of Inventory Raw materials and purchased parts
Work-in-process (WIP) = partially completed goods
Finished goods inventories (manufacturing) or merchandise (retail)
Maintenance and repairs (MRO) inventory
Goods-in-transit to warehouses or customers (pipeline inventory)
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5. Inventory Inventories are a vital part of business:
necessary for operations
contribute to customer satisfaction
But
Costly
May have limited shelf-life
Carrier may have limited space
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6. Functions of Inventory
To meet anticipated demand
“anticipation stock”
To smooth production requirements
seasonal demand
To permit operations
Work-In-Process
To decouple operations
buffer between successive operations in case of a breakdown
To protect against stock-outs
Delayed deliveries or increase in demand
To take advantage of order cycles
minimize purchasing and holding costs or economies of producing in large quantities
To help hedge against price increases
To take advantage of quantity discounts

7. Inventory Costs Purchase cost Holding (carrying) costs Ordering costs
The amount paid to buy the inventory
Holding (carrying) costs
Cost to carry an item in inventory for a length of time, usually a year (rent, equipment, materials, labor, insurance, security, interest and other direct expenses).
Ordering costs
Costs of ordering and receiving inventory
Setup costs (Analogous to ordering costs)
The costs involved in preparing equipment for a job
Shortage costs
Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unit
Lead time
Time interval between ordering and receiving the order
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8. Objectives of Inventory Control
The overall objective of inventory management is to achieve:
Satisfactory levels of customer service
Having the right goods available in the right quantity in the right place at the right time
Focus on size and timing
While keeping inventory costs (ordering and carrying) within reasonable bounds (minimize)
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9. Objectives of Inventory Control
Measures of performance:
Customer satisfaction
Number and quantity of backorders
Customer complaints
Inventory turnover
= (average) cost of goods sold (average) inventory investment
during a period
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10. Inventory Management
Management has two basic functions concerning inventory:
Establish a system for tracking items in inventory
Make decisions about
When to order
How much to order
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11. ABC Classification System
A-B-C approach
Classifying inventory according to some measure of importance, and allocating control efforts accordingly
A items (very important)
10 to 20 percent of the number of items in inventory
about 60 to 70 percent of the annual dollar value
B items (moderately important)
C items (least important)
50 to 60 percent of the number
of items in inventory but
only about 10 to 15 percent of
the annual dollar value
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12. ABC Classification System
How to classify?
For each item, multiply annual volume by unit price to get the annual dollar value.
Arrange annual values in descending order.
A items: the few with the highest annual dollar value
C items: the most with the lowest dollar value.
B items: those in
between #
Annual demand
Unit price
Annual value
Clss
% of items
% of value 8
1,000
4,000
4,000,000 A
5.3
52.7 3
2,400
500
1,200,000 B 6
1,000,000
31.4
40.8 1
2,500
360
900,000 4
1,500
100
150,000 C 10
200
100,000 9
8,000
80,000 2 70
70,000
63.3
6.5 5
700
49,000 7
210
42,000
18,800
7,591,000
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13. Inventory Counting Systems
Periodic System (e.g. small retailer)
Physical count of items in inventory made at periodic intervals
Many items ordered at the same time. Savings in processing and shipping of orders.
vs.
Lack of control between reviews. Having to keep extra stock to protects against shortages.
Perpetual Inventory System (e.g. bank transactions)
System that keeps track of removals from inventory continuously, thus monitoring current levels of each item
An order is placed when inventory drops to a predetermined minimum level (can optimize Q)
Vs.
Added cost of record keeping. Usually has to be accompanied by a periodic physical count.
Note: RFID technology is used by inventory counting systems
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14. Inventory Ordering Models
Economic Order Quantity models:
identify the optimal order quantity
by minimizing total annual costs that vary with order size and frequency
The basic Economic Order Quantity model (EOQ)
The Economic Production Quantity model (EPQ)
The Quantity Discount model*
Other Models
Reorder Point Ordering* (uncertainty, when to order)
Fixed-Order-Interval Model*
Single Period model (perishable items)
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15. Basic Economic Order Quantity Model
The basic EOQ model:
used to find a fixed order quantity that will minimize total annual inventory costs
Purchase price is not included (cost is unaffected by it)
Assumptions:
Only one product is involved
Annual demand requirements are known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts
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16. The Inventory Cycle (EOQ)
Profile of Inventory Level Over Time
Quantity
on hand Q
Receive
order
Place
Lead time
Reorder
point
Usage
rate
Time
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17. Total Annual Cost 13-17 Average number of units in inventory
Number of orders
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18. Goal: Total Cost Minimization
Order Quantity (Q)
The Total-Cost Curve is U-Shaped
Ordering Costs QO
Annual Cost
(optimal order quantity)
Holding Costs
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19. Deriving EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.
Length of order cycle = Q/D
Number of orders = D/Q
The total cost curve reaches its minimum where the carrying and ordering costs are equal.
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20. Example Tire distributer D (Demand)=9,600 tires per year
H (Holding cost)=$16 per unit per year
S (Ordering cost) = $75 per order

21. Example Tire distributer D (Demand)=9,600 tires per year
H (Holding cost)=$16 per unit per year
S (Ordering cost) = $75 per order
Q0=300 tires
TCmin = 4,800
TC curve relatively flat at optimum

22. Economic Production Quantity (EPQ)
The batch mode is widely used in production. In certain instances, the capacity to produce a part exceeds its usage (demand rate)
Assumptions
Only one item is involved
Annual demand requirements are known
Usage rate is constant
Usage occurs continually, but production occurs periodically
The production rate is constant
Lead time does not vary
There are no quantity discounts
Instructor Slides

23. EPQ: Inventory ProfileQp
Imax
Production
and usage
Usage
only
Cumulative
production
Amount
on hand
Time
Instructor Slides

24. EPQ – Total Cost
Solution:
Instructor Slides

25. Example Toy manufacturer makes rubber wheels for dump truck toys.
D=48,000 wheels per year
S=$45
H=$1 per wheel per year
P=800 wheels per day
u=200 wheels per day
Instructor Slides

26. Quantity Discount Model
Take into account quantity discount offered by supplier (add purchase cost to model)
Quantity discount
Price reduction for larger orders offered to customers to induce them to buy in large quantities
Instructor Slides

27. Quantity Discounts*
The total-cost curve with quantity discounts is composed of a portion of the total-cost curve for each price
Adding PD does not change EOQ
Instructor Slides

28. Reorder Point Ordering
When the quantity on hand of an item drops to this amount (quantity-trigger), the item is reordered.
Determinants of the Reorder-Point
The rate of demand
The lead time
The extent of demand and/or lead time variability
The degree of stockout risk acceptable to management
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29. Safety Stock*
Instructor Slides

30. Fixed-order-interval (FOI) model
Orders are placed at fixed time intervals
Reasons for using the FOI model
Supplier’s policy may encourage its use
Grouping orders from the same supplier can produce savings in shipping costs
Some circumstances do not lend themselves to continuously monitoring inventory position
Instructor Slides

31. Fixed-Quantity (ROP) vs. Fixed-Interval Ordering*
Instructor Slides

32. Single-Period Model Single-period model
Model for ordering of perishables and other items with limited useful lives
Period = life of the good.
Items are not carried over to the next period
The goal of the single-period model is to identify the order quantity that will minimize the long-run excess and shortage costs
Two categories of problems:
Demand can be characterized by a continuous distribution
Demand can be characterized by a discrete distribution
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33. Single-Period Model Shortage cost
Generally, the unrealized profit per unit
Cshortage = Cs = Revenue per unit – Cost per unit
Excess cost
Different between purchase cost and salvage value of items left over at the end of the period
Cexcess = Ce = Cost per unit – Salvage value per unit
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34. Continuous Stocking Levels Uniform Demand
Service Level = probability that demand will not exceed the stocking level (S).
Shortage: Demand > S0
Excess: Demand < S0
Service level So
Balance Point
Quantity Ce Cs
So =Optimum
Stocking Quantity
Like a Seesaw, leverage
If demand is not uniformly distributed, consider cumulative probability of demand
So=min+SL*(max-min)
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35. Continuous Stocking Levels Uniform Demand
Sweet cider delivered to bar
Demand uniformly distributed between 300 and 500 liters/week.
Cost=20 cent/liter
Revenue = 80 cent/liter.
Ce=
cost-salvage =.2 $/liter
Cs=
revenue-cost =.8-.2=.6 $/liter
SL=
Cs/(Cs+Ce) =.6/(.6+.2)=.75
So=
min+SL*(max-min)
= *( )=450 liter
Stockout risk =
1-SL = =.25
Service level=75%
So =450
Balance Point
Ce=.2 $/liter
Cs=.6 $/liter
300
500
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36. Discrete Stocking Levels
Cs/(Cs+Ce) may not coincide with a feasible stocking level.
Solution: Stock at the next higher level so that the desired service level is equaled or exceeded.
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37. Discrete Stocking Levels
p = $5.5
v= $0
c= $2
SL= Cs/(Cs+Ce)=
(p-c)/[(p-c)+(c-v)] =
(5.5-2)/[(5.5-2)+(2-0)] =
3.5/(3.5+2)= .636
Q=13 Q
P(R≤Q)
Expected profit 1
0.05
3.5 2
0.1
6.725 3
0.15
9.675 4
0.2
12.35 5
0.25
14.75 6
0.3
16.875 7
0.35
18.725 8
0.4
20.3 9
0.45
21.6 10
0.5
22.625 11
0.55
23.375 12
0.6
23.85 13
0.65
24.05 14
0.7
23.975 15
0.75
23.625 16
0.8 23 17
0.85
22.1 18
0.9
20.925 19
0.95
19.475 20
17.75

38. Discrete Stocking Levels
Shortage (downtime) cost = $4,200
Excess (spare part) cost = $200
SL =
= 4200/( ) = .84
Next level - > 2 spare parts
90% will not run out of spare parts
Spares used
Relative frequency
Cumulative frequency .2 1 .4 .6 2 .3 .9 3 .1
4 or more
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39. Operations Strategy* Too much inventory: Costly to maintain
Tends to hide problems (easier to live with problems than to eliminate them)
Wise strategy = find ways to
Improve demand forecasts = reduce safety stock
Improve inventory management
Reduce Ordering costs
Reduce inventory Holding costs
Reduce variation (e.g., lead-time)
Lean Operations
Supply-Chain Management