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Operations Management Inventory Management Chapter 12 - Part I PowerPoint Presentation
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Operations Management Inventory Management Chapter 12 - Part I - PowerPoint PPT Presentation


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Operations Management Inventory Management Chapter 12 - Part I. Outline. Functions of Inventory. ABC Analysis. Inventory Costs . Inventory Models for Independent Demand. Economic Order Quantity (EOQ) Model. Production Order Quantity (POQ) Model. Quantity Discount Model.

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outline
Outline
  • Functions of Inventory.
  • ABC Analysis.
  • Inventory Costs .
  • Inventory Models for Independent Demand.
    • Economic Order Quantity (EOQ) Model.
    • Production Order Quantity (POQ) Model.
    • Quantity Discount Model.
  • Probabilistic Models with Varying Demand.
  • Fixed Period Systems.
types of inventory
Types of Inventory
  • Raw materials.
  • Work-in-progress.
  • Maintenance/repair/operating (MRO) supply.
  • Finished goods.
the functions of inventory
The Functions of Inventory
  • To ”decouple” or separate various parts of the production process.
  • To smooth production (link supply and demand).
  • To provide goods for customers (quick response).
  • To take advantage of quantity discounts.
    • Buy more to get a reduced price.
  • To hedge against inflation and upward price changes (speculation).
    • Buy more now if you think price will rise.
disadvantages of inventory
Disadvantages of Inventory
  • High cost - $$$$$
    • Money tied up in inventory could be better used elsewhere in the organization.
  • Difficult to control.
    • Inventories occur in many places.
  • Hides production problems.
    • Large inventories may overcome poor quality production or poor quality materials.
abc analysis
ABC Analysis
  • Divide inventory into 3 classes based on annual $ volume.
    • Annual $ volume = Annual demand x Unit cost.

A class - Most important.

15-20% of products. 60-80% of value.

B class -Less important.

20-40% of products. 15-30% of value.

C class - Least important.

50-60% of products. 5-10% of value.

abc analysis1
ABC Analysis
  • Sort products from largest to smallest annual $ volume.
  • Divide into A, B and C classes.
  • Focus on A products.
    • Develop class A suppliers more.
    • Give tighter physical control of A items.
    • Forecast A items more carefully.
    • Consider B products only after A products.
classifying items as abc
Classifying Items as ABC

25 products sorted by Annual $ Volume (Sales)

Product Sales %

1 100 14

2 92 13

3 88 12

4 60 8

5 58 8

6 53 7

7 49 7

8 41 6

9 32 4

10 26 4

11 21 3

12 18 2

13 16 2

14-25 66 9

Total 720

100

80

Annual $ Usage (x1000)

60

40

20

0

20

10

15

1

25

5

Product

classifying items as abc1
Classifying Items as ABC

Class

% $ Vol

% Items

A

39%

12% (3/25)

100

B

52%

40% (10/25)

80

C

9%

48% (12/25)

Annual $ Usage (x1000)

60

A

40

20

B

C

0

80

40

60

0

100

20

% of Products

inventory accuracy
Inventory Accuracy
  • Inventory accuracy importance:
    • To determine when and how much to order.
    • To achieve high level of service.
  • Information system tracks inventory, but…
    • Not all items sold are entered (scanned) properly.
    • Some items disappear without being sold (theft, defective, damaged, etc.)
inventory counting
Inventory Counting
  • Count products to verify inventory records.
  • Shut down facility and count everything at one time (once per year).
  • Cycle counting: count items continuously (count some each week).
    • Count A items most frequently (for example, once a month).
    • Count B items less frequently (twice a year).
    • Count C items least frequently (once a year).
inventory for services
Inventory for Services
  • Can be large $.
  • “Shrinkage” (theft) is a problem.
    • Often over 3%!
  • Good personnel selection, training, and discipline is key.
  • Establish tight control of shipments entering and leaving the facility.
    • Enforce procedures for documenting product movement.
  • Information systems can monitor inventory levels and help ensure accuracy.
inventory costs
Inventory Costs
  • Holding costs - Associated with holding or “carrying” inventory over time.
  • Ordering costs - Associated with costs of placing order and receiving goods.
  • Setup costs - Cost to prepare a machine or process for manufacturing an order.
  • Stockout costs- Cost of not making a sale and lost future sales.
holding costs
Holding Costs
  • Investment costs (borrowing, interest).
  • Insurance.
  • Taxes.
  • Storage and handling.
  • Extra staffing.
  • Pilferage, damage, spoilage, scrap.
  • Obsolescence.
inventory holding costs usually 20 30 of total
Category

Investment costs

Housing costs

Material handling costs

Labor cost from extra handling

Pilferage, scrap, and obsolescence

Cost as a

% of Inventory Value

6 - 24%

3 - 10%

1 - 3.5%

3 -5%

2 - 5%

Inventory Holding Costs – Usually 20-30% of Total
ordering costs
Ordering Costs

To order and receive product:

  • Supplies.
  • Forms.
  • Order processing.
  • Clerical support.
  • etc.
setup costs
Setup Costs

To change equipment and setup for new product:

  • Clean-up costs.
  • Re-tooling costs.
  • Adjustment costs.
  • etc.
stockout costs
Stockout Costs

For not making a sale and for lost future sales:

- Customer may wait for a backorder, or

- Cancel order (and acquire product elsewhere).

  • Backorder costs: expediting, special orders, rush shipments, etc.
  • Lost current sale cost.
  • Lost future sales (hard to estimate).
inventory questions
Inventory Questions
  • How much to order (each time)?
    • 100 units, 50 units, 23.624 units, etc.
  • When to order?
    • Every 3 days, every week, every month, etc.
    • When only 5 items are left, when only 10 items are left, when only 20 items are left, etc.
  • Many different models can be used, depending on nature of products and demand.
independent vs dependent demand
Independent vs. Dependent Demand
  • Independent demand - Demand for item is independent of demand for any other item.
  • Dependent demand - Demand for item depends upon the demand for some other item.
    • Example: Demand for car engines depends on demand for new cars.
  • We will consider only independent demand.
inventory models
Inventory Models

How much and when to order?

  • Fixed order-quantity models.
    • 1. Economic order quantity (EOQ).
    • 2. Production order quantity (POQ).
    • 3. Quantity discount.
  • Probabilistic models.
  • Fixed order-period models.
how much and when to order
How Much and When to Order?
  • Given a fixed annual demand for a product.
  • With many small orders:
    • Amount on hand is always small, so inventory is small.
    • Frequent orders means cost of ordering is large.
  • With few large orders:
    • Amount on hand may be large (when order arrives), so inventory may be large.
    • Infrequent orders mean cost of ordering is small.
eoq economic order quanitity models
EOQ – Economic Order Quanitity Models
  • How much to order (each time)?
    • Order size is a constant = Q
    • Q is selected to minimize total cost.
  • When to order?
    • Order when amount remaining = ROP
    • ROP is selected so chance of running out is small.
eoq assumptions
EOQ Assumptions
  • Known and constant demand.
  • Known and constant lead time.
  • Instantaneous receipt of material.
  • No quantity discounts.
  • Only order cost and holding cost.
  • No stockouts.
eoq model how much to order
EOQ Model - How Much to Order?

Annual Cost

Holding Cost Curve

Order Cost Curve

Order Quantity

eoq model how much to order1
EOQ Model - How Much to Order?

Annual Cost

Total Cost Curve

Holding Cost Curve

Order Cost Curve

Order Quantity

Optimal Order Quantity (EOQ=Q*)

why holding costs increase
Why Holding Costs Increase
  • For fixed annual demand, larger order quantities means:
    • Larger inventory (larger amount ordered each time).
    • Larger inventory holding cost.
  • Example: Annual demand = 1200 units
    • Order 600 each time.
      • Maximum inventory = 600
    • Order 50 each time.
      • Maximum inventory = 50
why order costs decrease
Why Order Costs Decrease
  • For fixed annual demand, larger order quantities means:
    • Fewer orders per year.
    • Smaller order cost per year.
  • Example: Annual demand = 1200 units
    • Order 600 each time.
      • 1200/600 = 2 orders per year.
    • Order 50 each time.
      • 1200/50 = 24 orders per year.
deriving an eoq
Deriving an EOQ
  • Develop an expression for total costs.
    • Total cost = order cost + holding cost
  • Find order quantity that gives minimum total cost (use calculus).
    • Minimum is when slope is flat.
    • Slope = Derivative.
    • Set derivative of total cost equal to 0 and solve for best order quantity.
eoq model equations

D

=

=

Expected Number of Orders per year

N

Q

D

S

Order Cost per year

=

Q

(average inventory level)  H

=

Holding Cost per year

EOQ Model Equations

D = Annual demand (relatively constant)

S = Order cost per order

H = Holding (carrying) cost per unit per year

d = Demand rate (units per day, units per week, etc.)

L = Lead time (constant) (in days, weeks, hours, etc.)

Determine: Q = Order size (number of items per order)

Given

eoq model average inventory level

Inventory Level

Order Quantity(Q)

AverageInventory (Q/2)

0

Time

EOQ Model - Average Inventory Level

Maximum inventory = Q Minimum inventory = 0

eoq model equations1

D

=

=

Expected Number of Orders per year

N

Q

D

S

Order Cost per year

=

Q

(average inventory level)  H =

=

Holding Cost per year

EOQ Model Equations

D = Annual demand (relatively constant)

S = Order cost per order

H = Holding (carrying) cost per unit per year

d = Demand rate (units per day, units per week, etc.)

L = Lead time (constant) (in days, weeks, hours, etc.)

Determine: Q = Order size (number of items per order)

Given

Q

H

2

eoq model how much to order2
EOQ Model - How Much to Order?

Annual Cost

Total Cost Curve = (D/Q)S+(Q/2)H

Holding Cost =(Q/2)H

Order Cost Curve = (D/Q)S

Order Quantity

Optimal Order Quantity (EOQ=Q*)

eoq total cost optimization

D

1

S +

H = 0

Q2

2

D

Q

=

Total Cost

S +

H

Q

2

EOQ Total Cost Optimization

Take derivative of total cost with respect to Q and set equal to zero:

Solve for Q to get optimal order size:

×

×

2

D

S

EOQ = Q*

=

H

eoq model equations2

D

=

=

Expected Number of Orders

N

Q*

Working Days / Year

Expected Time Between Orders

=

=

T

N

EOQ Model Equations

D = Annual demand

S = Order cost per order

H = Holding (carrying) cost

×

×

2

D

S

Optimal Order Quantity

=

=

Q*

H

eoq model when to order
EOQ Model - When to order?

D = Annual demand (relatively constant)

d = Demand per day

L = Lead time in days

Determine: ROP = reorder point (number of pieces or items remaining when order is to be placed)

Given

D

Suppose demand is 10 per day and lead time is (always) 4 days.

When should you order?

When 40 are left!

=

d

Working Days / Year

=

×

ROP

d

L

eoq model when to order1

Lead Time = time between placing and receiving an order

Reorder Point (ROP)

4th order

2nd order

3rd order

1st order received

1st order placed

EOQ Model - When To Order

Inventory Level

Q*

Time

eoq example
EOQ Example

Demand = 1200/year

Order cost = $50/order

Holding cost = $5 per year per item

260 working days per year

2 ×1200 ×50

=

= 154.92 units/order; so order 155 each time

Q*

5

1200/year

Expected Number of Orders = N =

= 7.74/year

155

260 days/year

Expected Time Between Orders = T =

= 33.6 days

7.74/year

1200

155

Total Cost =

50 +

5 = 387.10 + 387.50 = $774.60/year

155

2

eoq is robust

1200

Q

Total Cost =

50 +

5

Q

2

EOQ is Robust

Demand = 1200/year

Order cost = $50/order

Holding cost = $5 per year per item

260 working days per year

Q = 155 units/order TC = $774.60/year

Q* = 154.92 units/order TC = $774.60/year = 387.30 + 387.30

Suppose we must order in multiples of 20:

Q = 140 units/order TC = $778.57/year (+0.5%)

Q = 160 units/order TC = $775.00/year (+0.05%)

Cost is nearly optimal!

eoq is robust1

1200

Q

Total Cost =

50 +

5

Q

2

EOQ is Robust

Demand = 1200/year

Order cost = $50/order

Holding cost = $5 per year per item

260 working days per year

Q = 155 units/order TC = $774.60/year

Q* = 154.92 units/order TC = $774.60/year = 387.30 + 387.30

Suppose we wish to order 6 times per year (every 2 months):

Q = 1200/6 = 200 units/order(200/order is 29% above Q*)

TC = $800.00/year = 300.00 + 500.00

(Cost is only 3.3% above optimal: $800 vs. $774.60)

eoq model is robust
EOQ Model is Robust

Annual Cost

Total Cost Curve

Small variation in cost

Order Quantity

154.92

Large variation in order size

robustness
Robustness
  • EOQ amount can be adjusted to facilitate business practices.
  • If order size is reasonably near optimal (+ or - 20%), then cost will be very near optimal (within a few percent).
  • If parameters (order cost, holding cost, demand) are not known with certainty, then EOQ is still very useful.
eoq model when to order2
EOQ Model - When to order?

Demand = 1200/year

Order cost = $50/order

Holding cost = $5 per year per item

260 working days per year

Lead time = 5 days

1200/year

=

= 4.615/day

d

260 days/year

ROP = 4.615 units/day 5 days = 23.07 units

-> Place an order whenever inventory falls to (or below) 23 units