chapter 10 - inventory decision making

Chapter 10:

Inventory Decision Making

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Learning Objectives - After reading this chapter, you should be able to do the following:

Understand the fundamental differences among approaches to managing inventory.

Appreciate the rationale and logic behind the Economic Order Quantity (EOQ) approach to inventory decision making, and be able to solve some problems of a relatively straightforward nature.

Understand alternative approaches to managing inventory --- JIT, MRP, and DRP.

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Learning Objectives

Realize how variability in demand and order cycle length affects inventory decision making.

Know how inventory will vary as the number of stocking points decreases or increases.

Recognize the contemporary interest in and relevance of time-based approaches to inventory management.

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Learning Objectives

Make needed adjustments to the basic EOQ approach to respond to several special types of applications.

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Fundamental Approaches to Managing Inventory

Basic issues are simple…how much to order and when to order.

Additional issues are…where to store inventory and what items to order.

Traditionally, conflicts were usually present…as customer service levels increased, investment in inventory also increased.

Recent emphasis is on increasing customer service and reducing inventory investment.

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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

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Figure 10-1 Relationship between Inventory and Customer Service Level

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Key Differences among Approaches to Managing Inventory

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.

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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.

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Pull versus Push Pull approach is a “reactive” system,

relying on customer demand to “pull” product through a logistics system. MacDonald’s is an example.

Push approach is a “proactive” system, and uses inventory replenishment to anticipate future demand. Catering businesses are examples of push systems.

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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.

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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.

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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 10-2 Fixed Order Quantity Model under the Condition of Certainty

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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.

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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 10-3 Inventory Carrying Cost

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Figure 10-4 Order or Setup Cost

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Figure 10-5 Inventory Costs

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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

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Figure 10-6 Sawtooth Model

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TAC = QVW + AR or TAC = QS + AR 2 Q 2 Q

Solving for Q gives the following expressions:

Q = √ 2 RA or Q = √ 2RA or Q = √ 2RA VW or S VW S

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Where R = 3600 units V = $100; W = 25%; S (or VW)= $25; A = $200 per order

Q = √ 2 RA or Q = √ 2RA or Q = √ 2RA

VW or S VW S

√ 2*3600*$200 √ 2*3600*$200

$100*25% $25

Q = 240 units Q = 240 units

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Figure 10-7 Sawtooth Models

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Table 10-1 Total Costs for Various EOQ Amounts

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Figure 10-8 Graphical Representation of the EOQ Example

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Fixed Order Quantity Approach (Condition of Certainty)

Summary and Evaluation of the Fixed Order Quantity Approach: EOQ is a popular inventory model. EOQ doesn’t handle multiple locations as well as a

single location. EOQ doesn’t 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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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 10-9. Note the variability in lead times and

demand.

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Figure 10-9 Fixed Order Quantity Model under Conditions of Uncertainty

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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.

Examine Figure 10-9 again.

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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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Table 10-2 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

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Table 10-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points

Actual Deman

d

Reorder Points

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

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Table 10-3 Possible Units of Inventory Short or in Excess during Lead Time with Various Reorder Points

Actual Deman

d

Proba-bility

Reorder Points

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 10-4 Calculation of Lowest-Cost Reorder Point

Dmnd

100 110 120 130 140 150 160

(e) 0.0 0.1 0.8 3.9 10.8 20.1 30.0

(VW) 0 $2.50 $20 $97.50$27

0$502.5

0$75

0

(g) 30 20.1 10.8 3.9 0.8 0.1 0.0

G=gw

$300 $201 $108 $39 $8 $1 $0

GR/Q$450

0$301

5$162

0$585

$120

$15 $0

TAC$450

0$301

8$164

0$682.5

0$39

0$517.5

0$75

0

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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 = √ 2 R(A + G)

VW

√ 2 * 3600 * ($200 + 8)

$100 * 25%

Q = approximately 242 units

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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 = 242; e = 10.8

TAC = QVW + AR + eVW + GR 2 Q Q

TAC = (242*$100*25%) + (200*3600) + (10.8*$100*25%) + (8*3600) 2 242 242

TAC = $3025 + $2975 + $270 + $119

TAC = $6389 (New value for TAC when uncertainty introduced)

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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.

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Figure 10-10 Area under the Normal Curve

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Table 10-5 Reorder Point Alternatives and Stockout Possibilities

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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 10-11. Amount ordered over each five weeks in

the example varies each week.

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Figure 10-11 Fixed Order Interval Model (with Safety Stock)

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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

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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.

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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 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.

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Additional Approaches to Inventory Management

Three 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)

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Time-Based Approaches to Replenishment Logistics: JIT

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.

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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.

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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.

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JIT versus EOQ Approaches to Inventory Management

Six major differences: First, JIT attempts to eliminate excess

inventories for both buyer and seller. Second, JIT systems involve short

production runs with frequent changeovers.

Third, JIT minimizes waiting lines by delivering goods when and where needed.

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JIT versus EOQ Approaches to Inventory Management

Fourth, JIT uses short, consistent lead times to satisfy inventory needs in a timely manner.

Fifth, JIT relies on high-quality incoming products and on exceptionally high-quality inbound logistics operations.

Sixth, JIT requires a strong, mutual commitment between buyer and seller, emphasizing quality and win-win outcomes for both partners.

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Table 10-6 EOQ versus JIT Attitudes and Behaviors

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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

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Time-Based Approaches to Replenishment Logistics: JIT Examples of JIT Successes:

Apple Computer’s 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.

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Figure 10-12The Orderly Pickup Concept

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Time-Based Approaches to Replenishment Logistics: MRP

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.

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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.

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

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Figure 10-13 An MRP System

Master Production Schedule

MRP Program

Output and Reports

Bill of Material File Inventory Status File

Customer Orders Demand Forecasts

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Figure 10-14 Relationship of Parts to Finished Product: MRP Egg Timer Example

1 Egg Timer

2 Ends 1 Bulb 3 Supports

1 Gram of Sand

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Table 10-7 Inventory Status File: MRP Egg Timer Example

ProductGross 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

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Figure 10-15 Master Schedule: MRP Egg Timer Example

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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.

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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.

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Time-Based Approaches to Replenishment Logistics: 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.

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Time-Based Approaches to Replenishment Logistics: Distribution Resource Planning

DRP develops a projection for each SKU and requires17: Forecast of demand for each SKU. Current inventory level for each SKU. Target safety stock. Recommended replenishment

quantity. Lead time for replenishment.

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Table 10-8 DRP Table for Chicken Noodle Soup

Columbus Distribution Center–Distribution Resource Planning

Month January February March

Week 1 2 3 4 5 6 7 8 9

CN Soup Current BOH=4314; Q=3800; SS=1956; LT=1

Forecast 974 974 974 974 989 1002 1002 1002106

1

Schedule Receipt

0 0380

00 0 0 3800 0 0

BOH-End

3340

2366

5192

4218

3229

2227 5025 4023296

2

Planned Order

0380

00 0 0 3800 0 0

3800

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Figure 10-16 Combining DRP Tables

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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.

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Inventory at Multiple Locations – The Square Root Law

X2= (X1) * √(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

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Square Root Law Example

Current distribution 40,000 units Eight facilities shrinking to two Using the square root law:

X2 = (40,000) * √(2/8) X2 = 20,000 units

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Table 10-9 Example Impacts of Square Root Law on Logistics Inventories

Warehouses

√n 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%

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Figure 10-17 Four Directions for Replenishment Logistics

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Time-Based Approaches to Replenishment Logistics: 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.

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Time-Based Approaches to Replenishment Logistics: Quick Response (QR)

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.

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Figure 10-18Basic Elements of Quick Response (QR)

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Time-Based Approaches to Replenishment Logistics: 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…”

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Figure 10-19 Efficient Consumer Response: Broad Operating Capabilities Tailored to Each Unique Partner

Chapter 10: Summary and Review

Questions

Students should review their knowledge of the chapter by checking out the Summary and

Study Questions for Chapter 10.

This is the last slide for Chapter 10

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Figure A10-1 Sawtooth Model Modified for Inventory in Transit

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Figure A10-2 EOQ Costs Considering Volume Transportation Rate

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Table 10A-1 Annual Savings, Annual Cost, and Net Savings by Various Quantities Using Incentive Rates

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Figure A10-3 Net Savings Function for Incentive Rate

End of Chapter 10 and 10A Slides

Inventory Decision Making

chapter 10 - inventory decision making

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