Inventory Management

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Managing Inventories with Batching

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Outline

 Little’s Law Revisited

 Five Basic Reasons to Hold Inventory

 ABC Analysis

 Determining Batch sizes in the presence of fixed setup cost

(EOQ model)

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Related Readings  Operations Management (10th Edition, Prentice Hall): First part of

Chapter 9, pages 307-319

 Matching Supply with Demand (3rd Edition, McGraw-Hill): Sections

2.1-2.5 and 7.6-7.7, pages 10-27 and 126-134

 Operations Management (13th Edition, Pearson): Part of Chapter

12, pages 491-492 and 495-501

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Little’s Law Revisited

 Little’s Law links the three operational measures in steady state:

I = R×T

 Years (days, weeks, months) of Supply:

 Turnover Ratio (or Turns):

Inventory I [units]

Throughput R [units/unit time]

... ...... ......

Flow Time T [unit time]

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Inventory Measures  Stock Keeping Units (SKUs)

 Number of (unique) product items kept in stock

 Average inventory value  SUM { units in stock * unit cost }

 Weeks of supply =

 Similarly for days of supply, months of supply, etc.

 Inventory Turnover =

Question: Given the inventory turnover, how long does it take for a product to flow through the firm on average?

cost)(atsalesweeklyaverage

valueinventoryaverage

valueinventoryaverage

cost)(atsalesannualaverage

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Inventory turnover (2003) =

Flow time (2003) = Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Inventory turnover (2003) = 16,945/3,047 = 5.56 per year

Flow time (2003) = 1/5.56 = 0.18 years = 66 days Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Inventory turnover (2002) =

Flow time (2002) = Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Inventory turnover (2002) = 15,146/2,763 = 5.48 per year

Flow time (2002) = 1/5.48 = 0.18 years = 66 days Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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More on the inventory turnover …

“The longer you keep it the faster it deteriorates – you

can literally see the stuff rot… Because of their short

product lifecycles, computer components depreciate

anywhere from a half to a full point a week. Cutting

inventory is not just a nice thing to do. It's a financial

imperative.”

-- Dell's CEO, Kevin Rollins

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Five Basic Reasons to hold inventory

 Pipeline inventory

 Seasonal Inventory

 Cycle Inventory

 Decoupling Inventory/Buffers

 Safety Inventory

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Disadvantages of Holding Inventories

 Expense

 Opportunity cost of capital

 Obsolescence

 Out of fashion

 Delays → Reduced Responsiveness

 Masking Underlying Problems

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Identifying Critical Inventory Items

 Thousands of items are held in inventory by a typical

organization, but only a small fraction of them deserves

management’s closest attention and tightest control.

 ABC analysis: The process of dividing items into three

classes, according to their dollar usage, so that

managers can focus on items that have the highest

dollar value.

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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ABC Analysis

10 20 30 40 50 60 70 80 90 100

Percentage of items

P e rc

e n

ta g

e o

f d

o ll a r

v a lu

e

100 —

90 —

80 —

70 —

60 —

50 —

40 —

30 —

20 —

10 —

0 —

Class C

Class A

Class B

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Production/Inventory Strategies  Make-to-stock: A strategy that involves holding items in

stock for immediate delivery. Example: fashion manufacturers.

 Assemble-to-order (e.g., finish-to-order, or package-to- order): A strategy for producing a wide variety of products from relatively few assemblies and components after the customer orders are received. Example: Dell Computer.

 Make-to-order: A strategy used by manufacturers that make products to customer specifications (typically in low volume). Example: customized golf club manufacturers.

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Fundamental questions in inventory management

 How much to order or produce (Batch size)?

 When to order?

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Batch Size Q (units) in the Presence of Fixed Setup Cost: EOQ Model  Economies of Scale

 A fixed cost is incurred each time an order is placed. (E.g., making a trip to the supermarket, sending a truck to pick up an order, setting up a machine, etc.)

 The supplier offers quantity discounts.

 Costs of Carrying Inventories  Money tied up, cost of capital

 Storage costs

 Obsolescence costs

==> Larger order size.

==> Smaller order size.

The Economic Order Quantity (EOQ) Model

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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The Economic Order Quantity (EOQ) Model

 The EOQ model is concerned with purchasing/production

decisions for a single product, managed in a “make-to-stock”

strategy.

 Consider the following decision problem for a firm:

 Demand rate is deterministic and constant over time.

 There is an inventory holding cost for each unit on hand

 There is an ordering/setup cost for each ordering/batch production

 Constant and deterministic supply lead-time

 No shortages are allowed

How should the firm manage its inventory?

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Model Parameters D = demand per year

Q = order quantity (decision variable)

K = fixed charge per order; c = variable cost per unit

H = annual inventory holding cost per unit

(Sometimes expressed as h = the percentage of the item’s value; i.e., H=h*c)

Cycle inventory: inventory on-hand at the firm during each ordering cycle

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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The Replenishment Process

Q units

Throughput rate = Demand = D

How many orders are placed every year?

Answer: D/Q orders per year.

How often are orders placed?

Answer: Every Q/D years (this is called the time between orders, or TBO).

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Graphic Presentation of On-Hand Inventory

Inventory depletion (demand rate)

Receive order

1 cycle

O n

-h a n

d i n

v e n

to ry

( u

n it

s )

Time

Q

Average cycle inventory

Q — 2

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Costs Associated with the Lot Size Q  The trade-off considered: Large vs. small Q?

 Average cost components:  Annual cost of items sold:

 Policy-related costs  Annual ordering costs:

 Annual holding costs:

 Average annual costs:

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Costs Associated with the Lot Size Q  The trade-off considered: Large vs. small Q?

 Average cost components:  Annual cost of items sold: D*c (this is independent of the policy

parameter Q)

 Policy-related costs  Annual ordering costs: K*D/Q

 Annual holding costs: H*Q/2 = h*c*Q/2

 Average annual costs:

= Annual policy-related cost Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Examples 12.1 and 12.2 (Museum of Natural History Gift Shop)

Bird feeder sales are 18 units per week, and the

supplier charges $60 per unit. The cost of placing an

order (K) with the supplier is $45. Annual holding cost

(H) is 25% of a feeder’s value, based on operations 52

weeks per year.

Management chose a 390-unit lot size (Q) so that new

orders could be placed less frequently. What is the

annual policy related costs (A1) of using a 390-unit lot

size (rounded to the nearest integer)?

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Examples 12.1 and 12.2 (Cont’d) Answer:

 Data:

 D = 18 units/week * 52 week/year = 936 units/year

 H = 25% * $60 = $15 per unit of inventory, per year.

 Costs:

Next, how to derive the EOQ?

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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3000 —

2000 —

1000 —

0 — | | | | | | | | 50 100 150 200 250 300 350 400

Lot Size (Q)

A n n u a l co

st (

d o lla

rs ) Total cost

Holding cost

Ordering cost

Current cost

Current Q

Lowest cost

Best Q (EOQ)

Example 12.2 (Cont’d):

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Finding the Optimal Economic Order Quantity (EOQ)

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Example 12.2 (Cont’d)

 EOQ:

Therefore, we set EOQ = 75 units

 The average annual policy-related costs are:

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

What is the EOQ (rounded to the nearest integer)?

If the EOQ policy is used, what is the new policy related cost

(rounded to the nearest integer)?

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Optimal (Economic) Order Quantity

 EOQ =

 A1(Q*) =

 A(Q*) =

 Increase in K and/or D increases Q*

 Increase in H decreases Q*

 If the demand doubles, Q* increase only times.

H

KD2

KDH2

DcKDH 2

2

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang

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Summary

 Little’s Law: I = R×T

 Five Basic Reasons to Hold Inventory

 ABC Analysis

 Determining Batch Sizes:  The EOQ Model: tradeoff between fixed ordering cost and

inventory cost

Class 15 -- Managing Inventories with Batching MGT 303 Prof. Yang