Inventory Decision Making

1
Chapter 7

• Inventory Decision Making

2
Fundamental Approaches to Managing Inventory

• Basic issues are simple
• how much to order and
• when to order
• where to store inventory and
• what items to order.
• Traditionally, conflicts were usually presentas
  customer service levels increased, investment in
  inventory also increased.
• Recent emphasis is on increasing customer service
  and reducing inventory investment.

3
Fundamental Approaches to Managing Inventory

• Four factors might permit this apparent paradox,
  that is, the firm can achieve higher levels of
  customer service without actually increasing
  inventory
• More responsive order processing
• Ability to strategically manage logistics data
• More capable and reliable transportation
• Improvements in the location of inventory

4
Figure 7-1 Relationship between
Inventory and Customer Service Level
5
Key Differences among Approaches to Managing
Inventory

• Three differences of approach
• Dependent versus Independent Demand
• Pull versus Push
• Systemwide versus single-facility solutions
• Each approach has models developed for approach
  solution to the inventory problem.

6
Key Differences among Approaches to Managing
Inventory

• 1. Dependent versus Independent Demand
• Dependent demand is directly related to the
  demand for another product.
• Independent demand is unrelated to the demand for
  another product.
• For many manufacturing processes, demand is
  dependent.
• For many end-use items, demand is independent.

7
Key Differences among Approaches to Managing
Inventory

• Of the inventory management processes in this
  chapter, JIT, MRP and MRPII are generally
  associated with items having dependent demand.
• Alternatively, DRP and the EOQ models are
  generally associated with items exhibiting
  independent demand.

8
Key Differences among Approaches to Managing
Inventory

• 2. Pull versus Push
• Pull approach is a reactive system, relying on
  customer demand to pull product through a
  logistics system. MacDonalds is an example.
• Push approach is a proactive system, and uses
  inventory replenishment to anticipate future
  demand. Catering businesses are examples of push
  systems.

9
Key Differences among Approaches to Managing
Inventory

• Pull versus Push
• Pull systems respond quickly to sudden or abrupt
  changes in demand, involve one-way
  communications, and apply more to independent
  demand situations.
• Push systems use an orderly and disciplined
  master plan for inventory management, and apply
  more to dependent demand situations.

10
Key Differences among Approaches to Managing
Inventory

• 3. systemwide versus single-facility approach
• Is to estimate whether the selected approach
  would apply to the whole system, or is
  appropriate to a single facility

11
On the Line American Cancer Society

• ACS constructed a world class automated order
  fulfillment center in Atlanta.
• Order cycle time was reduced to five business
  days.
• Centralized storage reduced waste and
  obsolescence of educational materials.
• Centralized shipment reduced freight rates.
• The new center saved 8 million in the first year
  alone.

12

• We now look at models of
• Fixed order cost with condition of Certainty
• Fixed order cost with condition of Uncertainty

13
1. Fixed Order Quantity Approach (Condition of
Certainty) Inventory Cycles

• In this example, each cycle starts
• with 4,000 units
• Demand is constant at the rate
  of 800 units per day.
• When inventory falls below 1,500 units, an order
  is placed for an additional 4,000 units.
• After 5 days the inventory is completely used.
• Just as the 4,000th unit is sold, the next order
  of 4,000 units arrives and a new cycle begins.

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Figure 7-2 Fixed Order Quantity Model
under the Condition of Certainty
15
Fixed Order Quantity Approach (Condition of
Certainty) Simple EOQ Model

• Simple EOQ Model Assumptions
• Continuous, constant, known and infinite rate of
  demand on one item of inventory.
• A constant and known replenishment time.
• Satisfaction of all demand.
• Constant cost, independent of order quantity or
  time.
• No inventory in transit costs.
• No limits on capital availability.

16
Fixed Order Quantity Approach (Condition of
Certainty) Simple EOQ Model

• Simple EOQ Model Variables
• R annual rate of demand
• Q quantity ordered (lot size in units)
• A order or setup cost
• V value or cost of one unit in dollars
• W carrying cost per dollar value in percent
• S VW annual storage cost in /unit per year
• t time in days
• TAC total annual costs in dollars per year

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Figure 7-3 Inventory Carrying Cost
18
Figure 7-4 Order or Setup Cost
19
Figure 7-5 Inventory Costs
20
Fixed Order Quantity Approach (Condition of
Certainty) Simple EOQ Model

• TAC QVW AR or TAC QS AR
• 2 Q 2 Q
• First term is the average carrying cost
• Second term is order or setup costs per year

21
Figure 7-6 Sawtooth Model
22
Fixed Order Quantity Approach (Condition of
Certainty) Simple EOQ Model

• TAC QVW AR or TAC QS AR
• 2 Q 2 Q
• Solving for Q gives the following expressions
• Q v 2 RA or Q v 2RA or Q v 2RA
• VW or S VW S

23
Fixed Order Quantity Approach (Condition of
Certainty) Simple EOQ Model

• Where R 3600 units V 100 W 25
  S (or VW) 25 A 200 per order
• Q v 2 RA or Q v 2RA or Q
  v 2RA
• VW or S VW
  S
• v 23600200 v 23600200
• 10025 25
• Q 240 units Q 240 units

24
Figure 7-7 Sawtooth Models
25
Table 7-1 Total Costs for Various EOQ
Amounts
26
Figure 7-8 Graphical Representation of the EOQ
Example
27
1. Fixed Order Quantity Approach (Condition of
Certainty)

• Summary and Evaluation of the
  Fixed Order Quantity Approach
• EOQ is a popular inventory model.
• EOQ doesnt handle multiple locations as well as
  a single location.
• EOQ doesnt do well when demand is not constant.
• Minor adjustments can be made to the basic model.
• Newer techniques will ultimately take the place
  of EOQ.

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2. Fixed Order Quantity Approach (Condition of
Uncertainty)

• Uncertainty is a more normal condition.
• Demand is often affected by exogenous
  factors---weather, forgetfulness, etc.
• Lead times often vary regardless of carrier
  intentions.
• Examine out Figure 7-9.
• Note the variability in lead times and demand.

29
Figure 7-9 2. Fixed Order Quantity Model under
Conditions of Uncertainty
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2. Fixed Order Quantity Approach (Condition of
Uncertainty)

• Reorder Point A Special Note
• With uncertainty of demand, the reorder point
  becomes the average daily demand during lead time
  plus the safety stock.
• Based on rate of probability
• Examine Figure 7-9 again.

31
Fixed Order Quantity Approach (Condition of
Uncertainty)

• Uncertainty of Demand Affects Simple EOQ Model
  Assumptions
• a constant and known replenishment time.
• constant cost/price, independent of order
  quantity or time.
• no inventory in transit costs.
• one item and no interaction among
  the inventory items.
• infinite planning horizon.
• no limit on capital availability.

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Notes for the following tables

• Assume k 10, each unit,v 100,
• carrying cost,w 25, A200,R3600
• Table 7-1 illustrates the rate of probability of
  shortage
• Table 7-2 shows the units of shortage
• Table 7-3 combines Tables 7-1 and 7-2
• Table 7-4 computes all relevant values

33
Table 7-2 Probability Distribution of Demand
during Lead Time
Demand Probability
100 units 0.01
110 0.06
120 0.24
130 0.38
140 0.24
150 0.06
160 0.01
34
Table 7-3 Possible Units of Inventory Short or
in Excess during Lead Time with Various Reorder
Points
Actual Demand Reorder Points Reorder Points Reorder Points Reorder Points Reorder Points Reorder Points Reorder Points
Actual Demand 100 110 120 130 140 150 160
100 0 10 20 30 40 50 60
110 -10 0 10 20 30 40 50
120 -20 -10 0 10 20 30 40
130 -30 -20 -10 0 10 20 30
140 -40 -30 -20 -10 0 10 20
150 -50 -40 -30 -20 -10 0 10
160 -60 -50 -40 -30 -20 -10 0
35
Table 7-3 Possible Units of Inventory Short or
in Excess during Lead Time with Various Reorder
Points
Actual Demand Proba-bility Reorder Points Reorder Points Reorder Points Reorder Points Reorder Points Reorder Points Reorder Points
Actual Demand Proba-bility 100 110 120 130 140 150 160
100 0.01 0.0 0.1 0.2 0.3 0.4 0.5 0.6
110 0.06 -0.6 0 0.6 1.2 1.8 2.4 3.0
120 0.24 -4.8 -2.4 0 2.4 4.8 7.2 9.6
130 0.38 -11.4 -7.6 -3.8 0 3.8 7.6 11.4
140 0.24 -9.6 -7.2 -4.8 -2.4 0 2.4 4.8
150 0.06 -3.0 -2.4 -1.8 -1.2 -0.6 0 0.6
160 0.01 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0
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Table 7-4 Calculation of Lowest-Cost Reorder Point Table 7-4 Calculation of Lowest-Cost Reorder Point Table 7-4 Calculation of Lowest-Cost Reorder Point Table 7-4 Calculation of Lowest-Cost Reorder Point Table 7-4 Calculation of Lowest-Cost Reorder Point Table 7-4 Calculation of Lowest-Cost Reorder Point Table 7-4 Calculation of Lowest-Cost Reorder Point Table 7-4 Calculation of Lowest-Cost Reorder Point
Dmnd 100 110 120 130 140 150 160
(e) 1 0.0 0.1 0.8 3.9 10.8 20.1 30.0
(VW)e2 0 2.50 20 97.50 270 502.50 750
(g)3 30 20.1 10.8 3.9 0.8 0.1 0.0
Ggw 4 3100 300 201 108 39 8 1 0
GR/Q 5 4500 3015 1620 585 120 15 0
TAC 25 4500 3018 1640 682.50 390 517.50 750
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Note for Table 7-4

• e expected excess per cycle
• of values above diagonal line of Table 7.4
• g expected shorts per cycle
• of values below diagonal line of Table 7.4
• K stockout cost in dollars
• G gk expected stockout cost per cycle
• G (R/Q) 5 expected stockout per year
• Refer to page 241 of text for calculation.

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Fixed Order Quantity Approach (Condition of
Certainty) Expanded EOQ Model

• Where R 3600 units V 100 W 25
  A 200 per order G 8
• Q v 2 R(A G)
• VW
• v 2 3600 (200 8)
• 100 25
• Q approximately 242 units

39
Fixed Order Quantity Approach (Condition of
Certainty) Expanded EOQ Model

• Where R 3600 units V 100 W 25
  A 200 per order G 8 Q
  242 e 10.8
• TAC QVW AR eVW GR
• 2 Q Q
• TAC (24210025) (2003600)
  (10.810025) (83600)
• 2
  242 242
• TAC 3025 2975
  270 119
• TAC 6389 (New value for TAC when
  uncertainty introduced)

40
Fixed Order Quantity Approach (Condition of
Uncertainty) Conclusions

• Following costs will rise to cover the
  uncertainty
• Stockout costs.
• Inventory carrying costs of safety stock
• Results may or may not be significant.
• In text example, TAC rose 389 or approximately
  6.5.
• The greater the dispersion of the probability
  distribution, the greater the cost disparity.

41
Figure 7-10 Area under the Normal Curve
42
Table 7-5 Reorder Point Alternatives and
Stockout Possibilities
43
Fixed Order Interval Approach

• A second basic approach
• Involves ordering at fixed intervals and varying
  Q depending upon the remaining stock at the time
  the order is placed.
• Less monitoring than the basic model
• Examine Figure 7-11.
• Amount ordered over each five weeks in the
  example varies each week.

44
Figure 7-11 Fixed Order Interval Model
(with Safety Stock)
45
Summary and Evaluation of EOQ Approaches to
Inventory Management

• Four basic inventory models
• Fixed quantity/fixed interval
• Fixed quantity/irregular interval
• Irregular quantity/fixed interval
• Irregular quantity/irregular interval
• Where demand and lead time are known, basic EOQ
  or fixed order interval model best.
• If demand or lead time varies, then safety stock
  model should be used

46
Summary and Evaluation of EOQ Approaches to
Inventory Management

• Relationship to ABC analysis
• A items suited to a fixed quantity/irregular
  interval approach.
• C items best suited to a irregular
  quantity/fixed interval approach.
• Importance of trade-offs
• Familiarity with EOQ approaches assists the
  manager in trade-offs inherent in inventory
  management.

47
Summary and Evaluation of EOQ Approaches to
Inventory Management

• New concepts
• JIT, MRP, MRPII, DRP, QR, and ECR also take into
  account a knowledge and understanding of
  applicable logistics trade-offs.
• Number of DCs (distribution centers)
• The issue of inventory at multiple locations in a
  logistics network raises some interesting
  questions concerning the number of DCs, the SKUs
  at each, and their strategic positioning.

48
Additional Approaches to Inventory Management

• Five approaches to inventory management that have
  special relevance to supply chain management
• JIT (Just in Time)
• MRP (Materials Requirements into Planning)
• DRP (Distribution Resource Planning)
• QR (Quick Response)
• ECR (Efficient Consumer Response)

49
1. JIT Time-Based Approaches to Replenishment
Logistics

• Definition and Components of JIT Systems -
  designed to manage lead times and eliminate
  waste.
• Kanban - refers to the informative signboards on
  carts in a Toyota system of delivering parts to
  the production line. Each signboard details the
  exact quantities and necessary time of
  replenishment.
• JIT operations - Kanban cards and light warning
  system communicate possible production
  interruptions.
• Fundamental concepts - JIT can substantially
  reduce inventory and related costs.

50
1. JIT (cont.)

• Definition and Components of JIT Systems -
  designed to manage lead times and eliminate
  waste.
• Goal is zero inventory, and zero defects.
• Similarity to the two-bin system - one bin fills
  demand for part, the other is used when the first
  is empty.
• Reduces lead times through requiring small and
  frequent replenishment.

51
1. JIT (cont.)

• JIT is a widely used and effective strategy for
  managing the movement of parts, materials,
  semi-finished products from points of supply to
  production facilities.
• Product should arrive exactly when a firm needs
  it, with no tolerance for early or late
  deliveries.
• JIT systems place a high priority on short,
  consistent lead times.

52
1. JIT versus EOQ Approaches to Inventory
Management

• Six major differences
• 1. JIT attempts to eliminate excess inventories
  for both buyer and seller.
• 2. JIT systems involve short production runs with
  frequent changeovers.
• 3. JIT minimizes waiting lines by delivering
  goods when and where needed.

53
1. JIT versus EOQ Approaches to Inventory
Management

• 4. JIT uses short, consistent lead times to
  satisfy inventory needs in a timely manner.
• 5. JIT relies on high-quality incoming products
  and on exceptionally high-quality inbound
  logistics operations.
• 6. JIT requires a strong, mutual commitment
  between buyer and seller, emphasizing quality and
  win-win outcomes for both partners.

54
Table 7-6 EOQ versus JIT Attitudes and Behaviors
55
1. JIT (cont.)

• JIT versus Traditional Inventory Management
• Reduces excess inventories
• Shorter, more frequent production runs
• Minimize waiting lines by delivering materials
  when and where needed
• Short, consistent lead times through proximate
  location
• Quality stressed throughout supply chain
• Win-win relationships necessary to a healthy
  supply chain

56
2. JIT (cont.)

• Examples of JIT Successes
• Apple Computers increase in IT from 10 weeks to
  2 weeks resulted in 18-month 20 million payback
  on plant.
• GM increased production by 100, but inventories
  increased by only 6.
• Norfolk Southern mini-train hauls direct from one
  GM plant to another without switching delays.
• Ryder handles all inbound logistics for Saturn.

57
Note for Figure 7-12 (next)

• It shows JIT-based manufacturing use
  time-sequenced motor carrier pickup from
  suppliers in conjunction with rail-motor to meet
  JIT requirements.

58
Figure 7-12The Orderly Pickup Concept
59
2 MRP Time-Based Approaches to Replenishment
Logistics

• A Materials Requirements Planning (MRP) system
  consists of a set of logically related
  procedures, decision rules, and records designed
  to translate a master production schedule into
  time-phased net inventory requirements for each
  component item needed to implement this schedule.
• MRPs re-plan net requirements based on changes in
  schedule, demand, etc.

60
2. MRP (cont.)

• Goals of an MRP
• Ensure the availability of materials, components,
  and products for planned production.
• Maintain lowest possible inventory
  level.
• Plan manufacturing activities, delivery
  schedules, and purchasing activities.

61
2. MRP (cont.)

• Key elements of an MRP
• Master production schedule
• Bill of materials file
• Inventory status file
• MRP program
• Outputs and reports

62
Figure 7-13 An MRP System
63
Figure 7-14 Relationship of Parts to Finished
Product MRP Egg Timer Example
64
Table 7-7 Inventory Status File MRP Egg Timer
Example
Product Gross Req. Inventory Net Req. Lead Time
Egg Timers 1 0 1 1
Ends 2 0 2 5
Supports 3 2 1 1
Bulbs 1 0 1 1
Sand 1 0 1 4
65
Figure 7-15 Master Schedule MRP Egg Timer
Example
66
Time-Based Approaches to Replenishment Logistics
MRP

• Principal advantages of MRP
• Maintain reasonable safety stock.
• Minimize or eliminate inventories.
• Identification of process problems.
• Production schedules based on actual demand.
• Coordination of materials ordering.
• Most suitable for batch or intermittent
  production schedules.

67
2. MRP (cont.)

• Principal shortcomings of MRP
• Computer intensive.
• Difficult to make changes once operating.
• Ordering and transportation costs may rise.
• Not usually as sensitive to short-term
  fluctuations in demand.
• Frequently become quite complex.
• May not work exactly as intended.

68
3 Distribution Resource Planning

• MRP sets a master production schedule and
  explodes into gross and net requirements.
• DRP starts with customer demand and works
  backwards toward establishing a realistic
  system-wide plan for ordering the necessary
  finished products.
• Then DRP works to develop a time-phased plan for
  distributing product from plants and warehouses
  to the consumer.

69
3. Distribution Resource Planning (cont.)

• DRP develops a projection for each SKU (stock
  keep unit) and requires17
• Forecast of demand for each SKU.
• Current inventory level for each SKU.
• Target safety stock.
• Recommended replenishment quantity.
• Lead time for replenishment.

70
Table 7-8 DRP Table for Chicken Noodle Soup
Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning Columbus Distribution CenterDistribution Resource Planning
Month January January January January January February February February February February March March
Week 1 1 2 3 4 5 6 7 8 8 9 9
CN Soup Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1 Current BOH4314 Q3800 SS1956 LT1
Forecast 974 974 974 974 974 989 1002 1002 1002 1002 1002 1061
Schedule Receipt 0 0 0 3800 0 0 0 3800 3800 0 0 0
BOH-End 3340 2366 2366 5192 4218 3229 2227 5025 5025 4023 4023 2962
Planned Order 0 3800 3800 0 0 0 3800 0 0 0 0 3800
71
Figure 7-16 Combining DRP Tables
72
Inventory at Multiple Locations The Square Root
Law (SQL)

• Used to reduce inventory at multiple locations.
• As locations increase, inventory also increases,
  but not in the same ratio as the growth in
  facilities.
• The square root law (SRL) states that total
  safety stock can be approximated by multiplying
  the total inventory by the square root of the
  number of future facilities divided by the
  current number of facilities.

73
Inventory at Multiple Locations The Square Root
Law

• X2 (X1) v(n2/n1)
• Where
• n1 number of existing facilities
• n2 number of future facilities
• X1 total inventory in existing facilities
• X2 total inventory in future facilities

74
Square Root Law Example

• Current distribution 40,000 units
• Eight facilities shrinking to two
• Using the square root law
• X2 (40,000) v(2/8)
• X2 20,000 units

75
Table 7-9 Example Impacts of Square Root Law on
Logistics Inventories
Warehouses vn Total Av Inv Change
1 1.0000 3,885 ---
2 1.4142 5,494 141
3 1.7321 6,729 173
4 2.0000 7,770 200
5 2.2361 8,687 224
10 3.1623 12,285 316
15 3.8730 15,047 387
20 4.4721 17,374 447
23 4.7958 18,632 480
25 5.0000 19,425 500
76
Figure 7-17 Four Directions for
Replenishment Logistics
77
4. Quick Response (QR)

• Structure of QR
• Shorter, compressed time horizons.
• Real-time information available by SKU.
• Seamless, integrated logistics networks with
  rapid transportation, cross-docking and effective
  store receipt and distribution systems.

78
4 Quick Response (QR) (cont.)

• Structure of QR
• Partnership relationships present among supply
  chain members.
• Redesign of manufacturing processes to reduce lot
  sizes, changeover times and enhanced flexibility.
• Commitment to TQM.

79
Figure 7-18Basic Elements of Quick Response (QR)
80
5. Efficient Consumer Response (ECR)

• Structure of ECR
• Grocery industry estimates U.S. savings at
  approximately 30 billion.
• Ultimate goal is a responsive, consumer-driven
  system in which distributors and suppliers work
  together as business allies to maximize consumer
  satisfaction and minimize cost. Accurate
  information and high-quality products flow
  through a paperless system between manufacturing
  and check-out counter with minimum degradation or
  interruption

81
Figure 7-19 Efficient Consumer Response Broad
Operating Capabilities Tailored to Each Unique
Partner
82
Chapter 7 Summary and Review Questions

• Students should review their knowledge of the
  chapter by checking out the Summary and Study
  Questions for Chapter 7.

• This is the last slide for Chapter 7

83
Figure A7-1 Sawtooth Model Modified for
Inventory in Transit
84
Figure A7-2 EOQ Costs Considering Volume
Transportation Rate
85
Table 7A-1 Annual Savings, Annual Cost, and Net
Savings by Various Quantities Using Incentive
Rates
86
Figure A7-3 Net Savings Function for Incentive
Rate
87
End of Chapter 7 and 7A Slides

• Inventory Decision Making