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Inventory

(Chapter 12)

Production & Operations Management

INFO 335-71

Week 3 and 4

Learning Objectives

⚫ Describe the different types and uses of

inventory

⚫ Describe the objectives of inventory

management

⚫ Calculate inventory performance measures

⚫ Understand relevant costs associated with

inventory

⚫ Perform ABC inventory control & analysis

⚫ Understand the role of cycle counting in

inventory record accuracy

Learning Objectives – cont'd

⚫ Understand inventory’s role in service organizations

⚫ Calculate order quantities

⚫ Evaluate the total relevant costs of different inventory policies

⚫ Understand why companies don’t always use the optimal order quantity

⚫ Understand how to justify smaller order sizes

⚫ Calculate appropriate safety stock inventory policies

⚫ Calculate order quantities for single-period inventory

Functions of Inventory

⚫ Geographical specialization allows us to specialize

production across different locations

⚫ Decoupling allows us to run processes for

maximum economic lot sizes within a single facility

⚫ Supply/Demand balancing accommodates the

elapsed time between inventory availability and

consumption

⚫ Buffering uncertainty accommodates uncertainty

related to

• Demand in excess of forecast or • Unexpected delays in delivery (aka safety stock)

Types of Inventory

Objectives of Inventory Management

Inventory Investment Measures Example: The Coach

Motor Home Company has annual cost of goods sold

(COGS) of $10,000,000. The average inventory value

at any point in time is $384,615. Calculate inventory

turnover and weeks/days of supply.

⚫ Inventory Turnover:

⚫ Weeks/Days of Supply:

turnsinventory 26 $384,615

0$10,000,00

valueinventory average

sold goods ofcost annual Turnover ===

2weeks 0/52$10,000,00

$384,615

dollarsin usage weekly average

dollarsin handon inventory average Supply of Weeks ===

days 10 0/260$10,000,00

$384,615 Supply of Days ==

Relevant Inventory Costs

Name Definition

Item Cost Includes price paid for the item plus

other direct costs associated with

the purchase

Holding Costs Include the variable expenses

incurred by the plant related to the

volume of inventory held (15-25%)

Capital Costs The higher of the cost of capital or

the opportunity cost for the company

Relevant Inventory Costs – cont’d

Item Definition

Ordering/Setup

Cost

Fixed, constant dollar amount incurred

for each order placed

Shortage Costs Loss of customer goodwill, back order

handling, and lost sales

Risk costs

(Inventory

Shrink)

Obsolescence, damage, deterioration,

theft, insurance and taxes

Storage costs Included the variable expenses for

space, workers, and equipment related

to the volume of inventory held

9JIT – Just-in-time; VMI – Vendor managed inventory

Inventory Record Accuracy

⚫ Inaccurate inventory records can cause:

• Lost sales • Disrupted operations • Poor customer service • Lower productivity • Planning errors and expediting

Inventory Record Accuracy

⚫ Two methods for checking record accuracy:

• Cycle counting - daily counting of pre-specified items provides the following advantages:

• Timely detection and correction of inaccurate records • Elimination of lost production time due to unexpected

stock outs

• Structured approach using employees trained in cycle counting

• Periodic counting - physical inventory is taken periodically, usually annually

• Steps: Count, Verify, Collect tickets, Reconcile

Which type of counting method to use?

ABC Inventory Classification

ABC classification is a method for determining level of control and frequency of review of inventory items

⚫ A Pareto analysis (80/20 rule) can be done to segment items into value categories depending on annual dollar volume

A Items typically 20% of the items accounting for 80% of the

inventory value-use Q system

B Items typically an additional 30% of the items accounting for 15%

of the inventory value-use Q or P

C Items Typically the remaining 50% of the items accounting for

only 5% of the inventory value-use P

Example: The AAU Corp. is considering doing an

ABC analysis on its entire inventory but has

decided to test the technique on a small sample

of 15 of its SKU’s. The annual usage and unit

cost of each item is shown below

ABC Inventory Analysis Procedure

Step 1: Calculate the annual dollar usage for each item

Step 2: List the items in descending order based on

annual dollar usage

Step 3: Calculate the cumulative annual dollar volume

Step 4: Classify the items into groups

Step 1. Calculate the

annual dollar volume for

each item

Step 2: Descending list/$ usage

Step 3: Calculate cumulative $

Step 4: Classify the ABC items

Graphical ABC Classification

of Materials

⚫ The A items (106 and 110) account for 60.5% of the value and 13.3% of the items

⚫ The B items (115,105,111,and 104) account for 25% of the value and 26.7% of the items

⚫ The C items make up the last 14.5% of the value and 60% of the items

⚫ How might you control each item classification? Different ordering rules for each?

AAU Corporation

Determining Order Quantities

Inventory management and control are managed

with SKU (stock control units)

Term Definition

Lot-for-lot Order exactly what is needed

Fixed-order quantity Specifies the number of units to order whenever an order is placed

Min-max system Places a replenishment order when the on- hand inventory falls below the predetermined minimum level.

Order n periods Order quantity is determined by total demand for the item for the next n periods

Replenishment policy – how much to order and when

Mathematical Models for

Determining Order Quantity

⚫ Economic Order Quantity (EOQ)

• An optimizing method used for determining order quantity and reorder points

• Part of continuous review system which tracks on-hand inventory each time a withdrawal is made

⚫ Quantity Discount Model

• Modifies the EOQ process to consider cases where quantity discounts are available

⚫ Economic Production Quantity (EPQ)

• A model that allows for incremental product delivery

EOQ Assumptions

⚫ Demand is known & constant - no safety stock is required

⚫ Lead time is known & constant

⚫ No quantity discounts are available

⚫ Ordering (or setup) costs are constant

⚫ All demand is satisfied (no shortages)

⚫ The order quantity arrives in a single shipment

Economic Order Quantity,

essentially the quantity placed on

order with the supplier

Reorder Point

Saw-tooth model

Total Annual Inventory Cost with

EOQ Model (Q System)

Total annual cost =

annual ordering cost + annual holding costs

2DS Q and H;

Q S

D TCQ =



  

 +



  

 =

Continuous (Q) Review System Example: A computer

company has annual demand of 10,000. They want to

determine EOQ for circuit boards which have an annual

holding cost (H) of $6/unit, and an ordering cost (S) of

$75. They want to calculate TC and the reorder point

(R) if the purchasing lead time is 5 days.

⚫ EOQ (Q)

⚫ Reorder Point (R)

⚫ Total Inventory Cost (TC)

units 500 $6

$75*10,000*2

2DS Q ===

units 200days 5* days 250

10,000 Time Leadx Demand DailyR ===

$3000$1500$1500$6 2

500 $75

500

10,000 TC =+=



  

 +



  

 =

Net operating days

Why Companies Don’t Always

Use Optimal Order Quantity

⚫ It is not unusual for companies to order less or

more than the EOQ for several reasons:

• They may not have a known uniform demand; • Some suppliers have minimum order quantity that

are beyond the demand.

⚫ EOQ provides a benchmark for other policies; is

more expensive; need to justify

Justifying Smaller Order Quantities

⚫ JIT or “Lean Systems” would recommend reducing order

quantities to the lowest practical levels

⚫ Benefits from reducing Q’s:

• Improved customer responsiveness (inventory = Lead time) • Reduced Cycle Inventory • Reduced raw materials and purchased components

⚫ Justifying smaller EOQ’s:

⚫ Reduce Q’s by reducing setup time. “Setup reduction” is a

well documented, structured approach to reducing S

2DS Q =

Quantity Discount Model

⚫ Same as the EOQ model, except:

• Unit price depends upon the quantity ordered

⚫ The total cost equation becomes:

 

  

 +



  

 = H

Q S

D TC

QD CD+ C = unit price D = annual demand in units

Quantity Discount Procedure

⚫ 9 Steps

1. Calculate the EOQ at the lowest price

2. Determine whether the EOQ is feasible at that price (Will vendor sell quantity at that price?)

3. If yes, stop – if no, continue

4. Check the feasibility of EOQ at the next higher price

Quantity Discount Procedure

- cont'd

5. Continue until you identify a feasible EOQ

6. Calculate the total costs (including total item cost) for the feasible EOQ model

7. Calculate the total costs of buying at the minimum quantity required for each of the cheaper unit prices

8. Compare the total cost of each option & choose the lowest cost alternative

9. Any other issues to consider?

Quantity Discount Example: Collin’s Sport store is

considering going to a different hat supplier. The

present supplier charges $10/hat and requires lots of

490 hats. The annual demand is 12,000 hats, the

ordering cost is $20, and the inventory carrying cost

is 20% of the hat cost, a new supplier is offering hats

at $9 in lots of 4000. Who should he buy from? ⚫ EOQ at lowest price $9. Is it feasible?

⚫ Since the EOQ of 516 is not feasible, calculate the total cost (C) for

each price to make the decision

⚫ 4000 hats at $9 each saves $19,320 annually. Space?

hats 516 $1.80

20)2(12,000)( EOQ$9 ==

( ) ( ) ( )

( ) ( ) ( ) $101,66012,000$9$1.80 2

4000 $20

4000

12,000 C

$120,98012,000$10$2 2

490 $20

490

12,000 C

$10

=++=

111,660

Economic Production

Quantity (EPQ)

Same assumptions as the EOQ except: inventory arrives in increments & draws down as it arrives

Calculating EPQ

⚫ Total cost:

⚫ Maximum inventory:

• d=avg. daily demand rate • p=daily production rate

⚫ Calculating EPQ

 

  

 +



  

 = H

I S

D TC

MAX

EPQ

 

  

 −=

d 1QI

MAX

 

  

 −

d 1H

2DS EPQ

EXAM 3 – up until this point

Determining Safety Stock and

Service Levels

⚫ If demand or lead time is uncertain, safety stock can be added to improve order-cycle service levels

• R = dL +SS • Where SS =zσdL, and Z is the

number of standard deviations and σdL is standard deviation of the demand during lead time

⚫ Order-cycle service level

• The probability that demand during lead time will not exceed on-hand inventory

• A 95% service level (stockout risk of 5%) has a Z=1.645

Normal Distribution

340.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359

0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753

0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141

0.3 0.6179 0.6217 0.6255 0.6293 0.6331 0.6368 0.6406 0.6443 0.6480 0.6517

0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879

0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224

0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549

0.7 0.7580 0.7611 0.7642 0.7673 0.7704 0.7734 0.7764 0.7794 0.7823 0.7852

0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133

0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389

1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621

1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830

1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015

1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177

1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319

1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441

1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545

1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633

1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706

1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767

2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817

2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857

2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890

2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916

2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936

2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952

2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964

2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974

2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981

2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990

How many σ

are needed for

a 99% service

level?

Z=2.33

What is the

service level

if .85 σ are

kept (z=.85)?

80%

Periodic Review Systems (P

System)

⚫ Orders are placed at specified, fixed-time intervals (e.g. every Friday), for a order size (Q) to bring on-hand inventory (OH) up to the target inventory (TI), similar to the min-max system.

⚫ Advantages are: • No need for a system to continuously monitor item • Items ordered from the same supplier can be reviewed on

the same day saving purchase order costs

⚫ Disadvantages: • Replenishment quantities (Q) vary • Order quantities may not qualify for quantity discounts • On the average, inventory levels will be higher than Q

systems; more stockroom space needed

Fixed Time-Period Inventory System: Cycle Stock, Safety Stock and Lead Time

Courtesy: Jacobe and Chase, Operations and SCM, 3e

T = Review Period or RP

L= Lead Time

T+L = Protection Period

Protection Period

Periodic Review Systems:

Calculations for TI

⚫

Demand for the bird feeder is normally distributed with a mean of

18 units per week and a standard deviation in weekly demand of 5

units. The review period is 4 weeks with a lead time of 2 weeks,

and the business operates 52 weeks per year. Calculate the target

inventory level for a cycle-service level of 90 percent.

We now find the standard deviation of demand over the protection

interval (P + L) = 6:

Before calculating TI, we also need a z value. For a 90 percent cycle-service level z = 1.28. The safety stock becomes

Safety stock = zσRP + L = 1.28(12.25) = 15.68 or 16 units

We now solve for T:

= (18 units/week)(6 weeks) + 16 units = 124 units

T = Average demand during the protection interval + Safety stock

= d(RP + L) + safety stock

units 12.2565 ==+= +

LRP dLRP



Inventory Management Across

The Organization

⚫ Inventory management policies affect functional

areas throughout

• Accounting is concerned of the cost implications of inventory

• Marketing is concerned as stocking decision affect the level of customer service

• Information Systems tracks and controls inventory records

• Other: • Purchasing is concerned with workload • Manufacturing is concerned with cost efficiency

BACKUP SLIDES

Customer Service Level

Measurements

⚫ Percentage of Orders Shipped on Schedule

• Good measure if orders have similar value (Doesn’t capture) . • If one company represents 50% of your business but only 5% of

your orders, 95% on schedule could represent only 50% of

value

⚫ Percentage of Line Items Shipped on Schedule

• Recognizes not all orders are equal, but doesn’t capture $ value of orders. More expensive to measure. Ok for finished goods.

• A 90% service level might mean shipping 225 items out of the total 250 line items totaled from 20 orders scheduled

⚫ Percentage Of $ Volume Shipped on Schedule

• Recognizes the differences in orders in terms of both line items and $ value

Customer Service

Unit fill rate = Total units delivered / Total units ordered

Line fill rate = # of order lines delivered complete / Total order lines

Order fill rate = Total complete orders delivered / Total orders

(Orders shipped complete)

Customer Service

⚫Fill rate example

Orders

Received

Total

Units

Ordered

Total

Order

Lines

Total

Units

Delivered

Total

Complete

Order

Lines

Delivered

Total

Complete

Orders

Delivered

1,000 20,000 5,000 19,500 4,800 910

What is the Unit Fill Rate?

Line Fill Rate?

Order Fill Rate?

Single Period Inventory Model

⚫ The SPI model is designed for products that share the

following characteristics:

• Sold at their regular price only during a single-time period • Demand is highly variable but follows a known probability

distribution

• Salvage value is less than its original cost so money is lost when these products are sold for their salvage value

⚫ Objective is to balance the gross profit of the sale of

a unit with the cost incurred when a unit is sold after

its primary selling period

Extra Material

SPI Model Example: T-shirts are purchase in multiples

of 10 for a charity event for $8 each. When sold

during the event the selling price is $20. After the

event their salvage value is just $2. From past events

the organizers know the probability of selling

different quantities of t-shirts within a range from 80

to 120

Payoff Table

Prob. Of Occurrence .20 .25 .30 .15 .10 Customer Demand 80 90 100 110 120

# of Shirts Ordered Profit

80 $960 $960 $960 $960 $960 $960

90 $900 $1080 $1080 $1080 $1080 $1040

Buy 100 $840 $1020 $1200 $1200 $1200 $1083

110 $780 $ 960 $1140 $1320 $1320 $1068

120 $720 $ 900 $1080 $1260 $1440 $1026

Sample calculations: Payoff (Buy 110)= sell 100($20-$8) –((110-100) x ($8-$2))= $1140

Expected Profit (Buy 100)= ($840 X .20)+($1020 x .25)+($1200 x .30) +

($1200 x .15)+($1200 x .10) = $1083 Extra Material