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Inventory Inventory Management: Management:

Economic Order Economic Order Quantity, JIT, and Quantity, JIT, and

the Theory of the Theory of ConstraintsConstraints

Prepared by Douglas Cloud

Pepperdine University

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1. Describe the just-in-case inventory management model.

2. Discuss just-in-time (JIT) inventory management.

3. Explain the basic concepts of constrained optimization.

4. Define the theory of constraints, and tell how it can be used to manage inventory.

ObjectivesObjectives

After studying this After studying this chapter, you should chapter, you should

be able to:be able to:

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Just-in-Case Inventory Just-in-Case Inventory ManagementManagement

Three types of inventory costs can be readily identified with inventory:

(1) The cost of acquiring inventory.

(2) The cost of holding inventory.

(3) The cost of not having inventory on hand when needed.

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1. Ordering Costs: The costs of placing and receiving an order.

Examples: Clerical costs, documents, insurance for shipment, and unloading.

2. Carrying Costs: The costs of carrying inventory.Examples: Insurance, inventory taxes, obsolescence,

opportunity cost of capital tied up in inventory, and storage.

Economic Order QuantityEconomic Order Quantity

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3. Stock-Out Costs: The costs of not having sufficient inventory.

Examples: Lost sales, costs of expediting (extra setup, transportation, etc.) and the costs of interrupted production.

4. Setup Costs: The costs of preparing equipment and facilities so they can be used to produce a particular product or component.

Examples: Setup labor, lost income (from idled facilities), and test runs.

Economic Order QuantityEconomic Order Quantity

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1. To balance ordering or setup costs and carrying costs2. Demand uncertainty3. Machine failure4. Defective parts5. Unavailable parts6. Late delivery of parts7. Unreliable production processes8. To take advantage of discounts9. To hedge against future price increases

Traditional Reasons for Traditional Reasons for Carrying InventoryCarrying Inventory

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Economic Order QuantityEconomic Order Quantity

TC = PD/Q + CQ/2

The total ordering (or setup) and carrying cost

The cost of placing and receiving an

order (or the cost of setting up a

production run)

The known annual demand

The number of units ordered each time an order is placed (or the lot size for

production)

The cost of carrying one unit of stock for

one year

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An EOQ IllustrationAn EOQ Illustration

EOQ = 2PD/C

D = 25,000 units

Q = 500 units

P = $40 per order

C = $2 per unit

EOQ = (2 x 25,000 x $40) / $2

EOQ = 1,000,000

EOQ = 1000 units

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Reorder point = Rate of usage x Lead time

Example: Assume that the average rate of usage is 4 units per day for a component. Assume also that the time required to place and receive an order is 10 days. What is the reorder point?

Reorder point = 4 x 10 = 40 units

Thus, an order should be placed when inventory drops to 40 units.

When to Order or ProduceWhen to Order or Produce

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The Reorder PointThe Reorder Point

Reorder point = Rate of usage x Lead time

1000

800

600

400

200

0

2 4 6 8 10 12 14 16 18 20

Reorder Point

(EOQ)

Days

Inventory (units)

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Demand Uncertainty and ReorderingDemand Uncertainty and ReorderingTo avoid running out of parts, organizations often choose to carry safety stock. Safety stock is extra inventory carried to serve as insurance against fluctuations in demand.

Example: If the maximum usage of the VCR part is 120 units per day, the average usage is 100 units per day, and the lead time is four days, the safety stock is 80.

Maximum usage 120Average usage -100Difference 20Lead time x 4Safety stock 80

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Example Involving SetupsExample Involving Setups

Expedition Company manufactures edgers. The manager is trying to determine the size of the

production run. The controller has supplied the following information:

Average demand for edgers: 720 per dayMaximum demand for edgers: 780 per dayAnnual demand for edgers: 180,000Unit carrying cost: $4Setup cost: $10,000Lead time: 22 days

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Example Involving SetupsExample Involving Setups

EOQ = 2PD/C

EOQ = (2 x 180,000 x $10,000)/$4

EOQ = 900,000,000

EOQ = 30,000 edgers

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Example Involving SetupsExample Involving SetupsSafety stock:

Maximum usage 780Average usage 720Difference 60Lead time x 22Safety stock 1,320

Reorder point = (Average usage x Lead time) + Safety stockReorder point = (720 x 22) + 1,320Reorder point = 17,160 edgers

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JIT reduces the costs of acquiring inventory to insignificant levels by:

1. Drastically reducing setup time

2. Using long-term contracts for outside purchases

Carrying costs are reduced to insignificant levels by reducing inventories to insignificant levels.

Setup and Carrying Costs: The JIT Approach

JIT Inventory ManagementJIT Inventory Management

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JIT Inventory ManagementJIT Inventory Management

Due-Date Performance: The JIT SolutionLead times are reduced so that the company can meet requested delivery dates and to respond quickly to customer demand.

Lead times are reduced by: reducing setup times

improving quality

using cellular manufacturing

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JIT Inventory ManagementJIT Inventory Management

Avoidance of Shutdown: The JIT Approach Total preventive maintenance to reduce

machine failures

Total quality control to reduce defective parts

The use of the Kanban system is also essential

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What is the Kanban System?What is the Kanban System?

A card system is used to monitor work in process A withdrawal Kanban

A production Kanban

A vendor KanbanThe Kanban system The Kanban system

is responsible for is responsible for ensuring that the ensuring that the

necessary products necessary products are produced in the are produced in the necessary quantities necessary quantities

at the necessary time.at the necessary time.

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Withdrawal Kanban

Item no.__________________________ Preceding Process

Item name_____________________________________

Computer Type_________________________________

Box Capacity_____________________Subsequent Process

Box Type_______________________________________________

15670T07

Circuit Board

TR6547 PC

CB Assembly

8

C Final Assembly

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Production Kanban

Item no.__________________________ Preceding Process

Item name_____________________________________

Computer Type___________________

Box Capacity_____________________Box Type______________________________

15670T07

Circuit Board

TR6547 PC

CB Assembly

8

C

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Vendor Kanban

Item no.____________________Name of Receiving Company

Item name_____________________________________

Box Capacity___________________

Box Type___________________ _ _Time to Deliver__________________________________________

Name of Supplier_________________________________________

15670T07

Circuit Board

8

Electro PC

A8:30 A.M., 12:30 P.M., 2:30 P.M.

Receiving Gate

75

Gerry Supply

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The Kanban Process

WithdrawalWithdrawalStoreStore

CB CB StoresStores

Lot with P-Kanban

ProductionOrdering Post

(6) Signal

CB Assembly

Remove(4) P-KanbanAttach toPost

(5) AttachW-Kanban

(1) Remove W-Kanban Attach to Post

Withdrawal Post

(2), (3)

(7)

Final Assembly

(1)

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Discounts and Price Increases: JIT Purchasing Versus Holding Inventories Careful vendor selection Long-term contracts with vendors

Prices are stipulated (usually producing a significant savings)

Quality is stipulated The number of orders placed are reduced

JIT Inventory ManagementJIT Inventory Management

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JIT LimitationsJIT Limitations• Patience in implications

is needed.

• Time is required.

• JIT may cause lost sales and stressed workers.

• Production may be interrupted due to an absence of inventory.

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Linear ProgrammingLinear Programming

The unit contribution margins are $300 and $600 for X and Y, respectively.

Z = $300X + $600 Y

Total contribution margin

This equation is called the objective function, the function to be optimized.

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Linear ProgrammingLinear Programming

Internal constraints:X + Y 80X + 3Y

1202X + Y 90

External constraints:X 60

Y 100

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Linear ProgrammingLinear Programming

X + Y 80X + 3Y 1202X + Y 90

X 60Y 100X 0Y 0

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Multiple Constrained ResourceMultiple Constrained Resource

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20 40 60 80 100 120 140

Y 100

X 60

X + Y 80

X + 3Y 120

2X + Y 90

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Multiple Constrained ResourceMultiple Constrained Resource

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20 40 60 80 100 120 140

A

BC

D

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Linear ProgrammingLinear Programming

Corner Point X-Value Y-Value Z = $300X + $600Y

A 0 0 $ 0B 0 40 24,000C 30 30 27,000D 45 0 13,500

C is the optical solution!

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Throughput Inventory Operating expenses

Three Measures of Systems Performance:

Theory of Constraints

(Sales revenue – Unit-level variable expenses)/Time

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1. Identify an organization’s constraints.

2. Exploit the binding constraints.

3. Subordinate everything else to the decisions made in Step 2.

4. Elevate the organization’s binding constraints.

5. Repeat the process as a new constraint emerges to limit output.

Five-Step Method for Improving Performance

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The Drum-Buffer-Rope SystemThe Drum-Buffer-Rope System

Materials

Process AProcess A

Process CProcess C

Rope

Drummer ProcessDrummer Process

Time Buffer

Final ProcessFinal Process

Finished Goods

Initial ProcessInitial Process

Process BProcess B

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New Constraint Set: Schaller Co.New Constraint Set: Schaller Co.

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20 40 60 80 100 120 140 160 200 220 240

Y 100

X 60

X + Y 80

2X + Y 90

X + 3Y 240

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New Constraint Set: Schaller Co.New Constraint Set: Schaller Co.

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20 40 60 80 100 120 140 160 200 220 240

A

BC

D

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End ofEnd of

ChapterChapter

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