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1

Critical Path

longest path from start to finish

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2

ES

Earliest start time = max[EF times of all activities immediately preceding activity]

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3

LS

Latest start time = LF – t

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4

EF

Earliest finish time = ES + t

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5

LF

Latest finish time = min[LS times of all activities immediately following activity]

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6

Slack

subtraction of either LatestStart - EarliestStart or LatestFinish - EarliestFinish

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7

Process

turning inputs into outputs

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8

Backward integration

owning and controlling entities upstream (earlier on in the chain → strawberry farms, dairy farms)

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9

Forward Integration

owning and controlling entities downstream (closer to the consumer → food trucks, deli restaurants)

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10

4 Costs of Quality

External failure, Internal failure, Appraisal, Prevention

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11

Causes of Variation: Common Causes

(completely unavoidable)

purely random; unidentifiable factors

e.g. diameter varies by 0.0001 in.

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12

Causes of Variation: Assignable Causes

(the real reason why; to investigate)

Variation-causing factors that can be identified

e.g. poorly trained employee

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13

Types of Variable Charts (continuous numerical data)

R-charts, xbar-charts

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14

Types of Attribute Charts (discrete numerical data)

p-charts, c-charts

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15

Variables (to measure performance)

weight, length, volume, or time

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16

Variable Data Examples

How long did the customer wait? What was diameter of the pizza? Temp of food? Weight of chicken?

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17

Attributes (to measure performance)

yes-no counts (yes, defect or no defect)

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Attribute Data Examples

Food sent back to kitchen? Bill correct or not? Did food leave the kitchen < 147 degrees? Was the pizza larger than 12 in?

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19

SPC

Statistical Process Control

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20

Step 1: Calculating X-bar & R-Chart UCL & LCL

within each sample (will either be by row or by column), calculate the range and the average

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21

Step 2: Calculating X-bar & R-Chart UCL & LCL

then calculate the average of all sample ranges and averages to compute x-bar and R-bar

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22

Step 3: Calculating X-bar & R-Chart UCL & LCL

based on n (aka sample size), identify A2, D3, D4 values on the chart to be used in the formulas

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23

What makes a process out of control

run = is when you have 5 consecutive sample points either to the upperside or lowerside of your nominal value

reached past UCL or LCL

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24

Using Control Charts for Process Improvement

Sample the process

Find the assignable cause

Eliminate the problem

Repeat the cycle

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25

Variable charts involve ____ measurements

precise

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26

Attribute charts involve measuring by ____

counting the # of defects

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27

R-bar & X-bar charts _____

have to be done together

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28

p-charts & c-charts _____

are less expensive $$$ than other charts

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29

p-bar =

total defectives / total observations

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30

c-chart UCL & LCL steps

calculate average number of defects per item (total defects observed / total # of observed items) = c-bar

take c-bar + z (whatever sigma, ex 3) * sqrt c-bar = UCL

take c-bar - z (whatever sigma, ex 3) * sqrt c-bar = LCL

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31

What makes c-Charts different?

c-Charts: defects on __ one unit__ (e.g. how many scratches are on one piece of plexiglass (c = 4)

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32

Six Sigma Quality: DMAIC Cycle

D - Define

M - Measure

A - Analyze

I - Improve

C - Control

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33

WBS stands for ____

Work Breakdown Structure

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34

5 Steps to Planning Projects

Define work breakdown structure

Diagram the network

Develop the schedule

Analyze cost-time trade-offs

Assess risks

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35

WBS First Level (after starting a business)

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WBS Second Level

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WBS Third Level

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38

AON stands for

Activity-on-Node

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39

EOQ (an Inventory Model) stands for ____

Economic Order Quantity

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40

The Q System (an Inventory Model) is the _____

Continuous Review System

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41

Aspects of the Continuous Review (Q) System

constant lead times introduced now

two models

certain demand and uncertain demand

Inventory position (IP) = OH (on hand inventory) + SR (scheduled receipts) - BO (backorders)

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Continuous Review → continuously checking IP after every withdrawal….

Rule:

if IP > R do not place an order

if IP <= R, place an order of size Q

Eg walmart checkout

(R means Reorder point)

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43

The P System (an Inventory Model) is the _____

Periodic Review System

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44

Aspects of Periodic Review (P) Systems

Fixed interval reorder system (order once a week or month)

Q may vary with each order

IP reviewed periodically instead of continuously, new order after every review

TBO (Time Between Orders) fixed at P

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Periodic Review → Only check your inventory position after every P time periods…

Always place an order of size Qt = T - IPt

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46

Comparatively, P Systems (single-bin system)

convenient to administer

orders may be combined

IP only required at review

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47

Comparatively, Q Systems (two-bin system)

individual review frequencies

possible quantity discounts

lower, less-expensive safety stocks

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48

What is the average cost of inventory?

30-35% of product’s value (about 1/3)

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49

Examples of Pressures for High Inventory

Customer Service/On-Time delivery, Quantity discounts, Transportation costs, Setup & Ordering costs, Supplier’s prices about to increase

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50

Examples of Pressures for Low Inventory

Pilferage (stealing), Storage and handling costs, Obsolescence (becomes obsolete soon, short product lifetime), Interest or opportunity cost, Insurance on assets, End of year taxes

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51

Is inventory bad?

Not necessarily

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52

Physical Inventory

Raw materials, component parts, work in process (WIP), finished goods

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53

Conceptual Inventory

Cycle Inventory

Safety Stock Inventory

Anticipation Inventory

Pipeline Inventory

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54

EOQ Assumption: Demand rate is ____

constant

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55

EOQ Assumption: No constraints on ____

lot size (Q) --- any size Q is possible!

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56

EOQ Assumption: Only costs are _____

holding (storing an item) and ordering (administrative costs)

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EOQ Assumption: Decisions for items are _____

independent (no correlation between different products; we’re just ordering final products)

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58

EOQ Assumption: No uncertainty in _____

lead time or supply

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59

Lead Time =

Time between placing an order and receiving it

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60

Lot sizing

Two Decisions:

When to order?

How much to order?

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61

Cycle Inventory

saw-tooth diagram (max Q units, min 0 units)

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62

Safety Stock Inventory

Protects against uncertainties in demand, lead time, and/or supply

Operations not disrupted

Avoid customer service problems

**Place order earlier than needed**

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Anticipation Inventory

Absorbs uneven rates of demand

Predictable, seasonal demand patterns

Anticipating supplier strike

Stockpile during low demand

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64

Pipeline Inventory

Inventory moving from point to point in material flow system

eg parts traveling on trucks (inbound)

eg materials moving between operations (within plant)

eg finished goods shipped to distribution center (outbound)

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65

ABC Analysis

Classifying inventory to best manage it

Class A: 20% of the items make up 80% of the total dollar value (TVs in the back; protect them)

Class B: 30% of the items make up like 25%

Class C: 50% of the items make up like 5%

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66

Holding cost _____ as Lot Size (Q) increases

Holding cost increases

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67

Ordering cost _____ as Lot Size (Q) increases

ordering cost decreases

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68

Total cost ____ as Lot Size (Q) increases

Total cost decreases initially, then increases (like a Nike swoosh)

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69

EOQ Variables are

D = Annual Demand

Q = Lot Size

S = Cost of Setup Ordering Cost (?)

H = Holding cost

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70

Aspects of a Push System

Production trigger is based on forecasts or desired inventory levels

No bounds on inventory

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71

When to use a Push system?

Example: Convenient store (inventory has built up; waiting for you to buy it, based off of forecasts)

Long setups (spread the costs over the course of the setup) & Variety of products (will have to produce an array of colors in batches to offer customers)

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72

Aspects of a Pull System

Production trigger is actual consumption of inventory

Imposes a bound on inventory

Eg. Kanban

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73

When to use a Pull system?

Small setups & Few product lines

Example: custom cakes

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74

Kanban

Visual display to decrease throughput time e.g. must have 3 in your inbox, 0 in your outbox to start working (airplane example)

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75

Idle time

sitting waiting for a unit

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76

Cycle time

time in between finished goods getting off the assembly line

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77

Supply Chain

Two or more parties linked by a flow of material, information, & money, often global in scope

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78

Bullwhip

order variation increases as you go upstream towards the supplier

Supplier → M → R → Customer (looks like a bullwhip with the handle at the customer and the wavy end of variability is at the supplier)

downstream is going → to the customer, upstream is going to the supplier <-

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79

Stockout

when you run out of a product, you will no longer be selling the product anymore

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80

Backorder

Ran out of a product but eventually are going to fulfill the order

(cumulation of these would be a backlog)

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81

Center of Gravity

Determine x and y coordinates in the middle (may not be feasible right at this point but start there and go out)

x* and y*

example: where you pinpoint the starting point to the realtor

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82

Load-distance score

Select site that minimizes distances “loads” must travel

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83

Horizontal Pattern of Demand

Data cluster about a horizontal line as time progresses

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84

Trend Pattern of Demand

Data consistently increase or decrease

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85

Seasonal Pattern of Demand

Data consistently show peaks and valleys

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86

Cyclical Pattern of Demand

Data reveal gradual increases and decreases over extended periods

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87

Time-Series Methods

Simple moving averages

Weighted moving averages

Exponential smoothing

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88

Simple Moving Average

Simple;

Dt = actual demand in period t

n = total number of periods in the average

F t+1 = forecast for period t + 1

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Weighted Moving Average

weights on historical demand (weight more recent demand more heavily, lowering

more control

Ft+1 = forecasted demand for period t + 1

Dt = actual demand in period t

Wi = assigned weight

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Exponential Smoothing

forecasting software

really strong results

Ft+1 = forecasted demand for period t + 1

Dt = actual demand in period t

sigma = smoothing parameter

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91

Trend-Adjusted Exponential Smoothing

At = exponentially smoothed average of the series in period t

Tt = exponentially smoothed average of the trend in period t

sigma, Beta = smoothing parameters

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92

CFE

= Cumulative Forecast Error

*A measurement of the total forecast error that assesses the bias in a forecast.*

if CFE is negative, we are overestimating

asses **bias**

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93

MSE

= Mean Squared Error

measure of variability

Square Error = error ^2

*A measurement of the dispersion of forecast errors.*

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94

Square Error

= error ^2

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95

MAD

= Mean Absolute Deviation

another indication of variability

Absolute Error = ABS(Actual - Predicted)

A measurement of the dispersion of forecast errors.

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96

Absolute Error

= ABS(Actual - Predicted)

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97

MAPE

= Mean Absolute Percent Error

average of the absolute percent errors; telling us amount of error relative to the size of demand

Absolute % Error = (Absolute Error / ACTUAL DEMAND) * 100%

big deal to be off by 10 diamonds at a small jewelry store versus 10 cotton balls at a large manufacturing plant

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98

Absolute % Error

= (Absolute Error / ACTUAL DEMAND) * 100%

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99

Error

Difference between actual and predicted

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100

Error relative to size of demand is related to _____

MAPE (Mean Absolute Percent Error)

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