Inventory Management: Economic Order Quantity

COST MANAGEMENT

COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning.Cengage Learning and South-Western are trademarks used herein under license.

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Accounting & ControlHansen▪Mowen▪Guan

Chapter 21Inventory Management:

Economic Order Quantity, JIT, and the Theory of Constraints

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Study Objectives

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.

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Just-in-Case Inventory Management

• Three types of inventory costs can be readily identified with inventory:– The cost of acquiring inventory.– The cost of holding inventory.– The cost of not having inventory on hand when

needed.

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

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

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.

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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.

Carrying Costs: The costs of carrying inventory.Examples: Insurance, inventory taxes, obsolescence, opportunity cost of capital tied up in inventory, and storage.

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Economic Order Quantity

TC = PD/Q + CQ/2


Where

TC = The total ordering (or setup) and carrying cost

P =The cost of placing and receiving an order (or the cost of setting up a production run)

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

D =The known annual demand

C =The cost of carrying one unit of stock for one year

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Economic Order Quantity illustratedAssume

P =$40 per orderD =25,000 unitsC =$2 per unit

EOQ = 2DP C

= (2 25,000 50) $2

= 1,000,000= 1,000

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Reorder point = rate of usage × lead time

= 4 × 100 = 400 units

An order should be placed when inventory drops to 400 units.

When to Order or Produce

Example: Assume that the average rate of usage is 100 parts per day. Assume also that the lead time is 4 days. What is the reorder point?

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Demand Uncertainty and ReorderingTo avoid running out of parts, organizations often choose to carry safety stock (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 (100)Difference 20Lead time × 4Safety stock 80


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JIT Inventory Management

• JIT reduces the costs of acquiring inventory to insignificant levels by– Drastically reducing setup time– 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

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JIT Inventory ManagementAvoidance of Shutdown: the JIT approach• Total preventive maintenance

– to reduce machine failures• Total quality control

– To reduce defective parts• The Kanban system

– To control production

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• The Kanban system is responsible for ensuring that the necessary products are produced in the necessary quantities at the necessary time.

• A card system is used to monitor work in process– A withdrawal Kanban– A production Kanban– A vendor Kanban

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• Managing discounts and price increases– Traditional: holding inventories– JIT: negotiate long-term contracts

• Vendors– Careful selection; consider more than price– Close to production facility– Establish more extensive supplier involvement

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JIT Limitations• Patience in implementation 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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Basic Concepts ofConstrained Optimization

Every firm faces limited resources and limited demand for each product.

– External constraints (e.g., market demand)– Internal constraints (e.g., machine or labor

time availability)

Constrained optimization is choosing the optimal mix given the constraints faced by the firm.

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Linear Programming

Example: Two products, X and Y, provide contribution margins of $300 and $600, respectively.

The objective is to maximize total contribution margin.

The objective function:Z = $300X + $600Y


A method that searches among possible solutions until the optimal solution is identified

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Linear Programming


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Internal constraints:X+Y 80

X + 3Y 1202C + Y 90

External constraints:X 60Y 100

Linear ProgrammingX+Y 80

X + 3Y 1202C + Y 90

X 60Y 100X 0Y 0

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

Linear Programming

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

C is the optimal solution!


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Theory of Constraints

Measures of Systems Performance– Throughput*

• The rate at which an organization generates money through sales

– Inventory• The money the organization spends in turning

materials into throughput

– Operating expenses• The money the organization spends in turning

inventories into throughput

Sales Unit-level-Rev Var ExpTime*Throughput =

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Five-Step Method for Improving Performance • Identify an organization’s constraints.• Exploit the binding constraints.• Subordinate everything else to the decisions

made in Step 2.• Elevate the organization’s binding constraints.• Repeat the process as a new constraint

emerges to limit output.

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COST MANAGEMENT

COPYRIGHT © 2009 South-Western Publishing, a division of Cengage Learning.Cengage Learning and South-Western are trademarks used herein under license.

31

Accounting & ControlHansen▪Mowen▪Guan

End Chapter 21

Inventory Management: Economic Order Quantity

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