Operations Management Final

Critical Path

Critical Path

longest path from start to finish

ES

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

LS

Latest start time = LF – t

EF

Earliest finish time = ES + t

LF

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

Slack

subtraction of either LatestStart - EarliestStart or LatestFinish - EarliestFinish

Process

turning inputs into outputs

Backward integration

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

Forward Integration

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

4 Costs of Quality

External failure, Internal failure, Appraisal, Prevention

Causes of Variation: Common Causes

(completely unavoidable)

• purely random; unidentifiable factors

• e.g. diameter varies by 0.0001 in.

Causes of Variation: Assignable Causes

(the real reason why; to investigate)

• Variation-causing factors that can be identified

• e.g. poorly trained employee

Types of Variable Charts (continuous numerical data)

R-charts, xbar-charts

Types of Attribute Charts (discrete numerical data)

p-charts, c-charts

Variables (to measure performance)

weight, length, volume, or time

Variable Data Examples

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

Attributes (to measure performance)

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

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?

SPC

Statistical Process Control

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

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

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

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

Using Control Charts for Process Improvement

Sample the process

Find the assignable cause

Eliminate the problem

Repeat the cycle

Variable charts involve ____ measurements

precise

Attribute charts involve measuring by ____

counting the # of defects

R-bar & X-bar charts _____

have to be done together

p-charts & c-charts _____

are less expensive $$$ than other charts

p-bar =

total defectives / total observations

c-chart UCL & LCL steps

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

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

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

What makes c-Charts different?

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

Six Sigma Quality: DMAIC Cycle

D - Define

M - Measure

A - Analyze

I - Improve

C - Control

WBS stands for ____

Work Breakdown Structure

5 Steps to Planning Projects

1. Define work breakdown structure

2. Diagram the network

3. Develop the schedule

4. Analyze cost-time trade-offs

5. Assess risks

WBS First Level (after starting a business)

WBS Second Level

WBS Third Level

AON stands for

Activity-on-Node

EOQ (an Inventory Model) stands for ____

Economic Order Quantity

The Q System (an Inventory Model) is the _____

Continuous Review System

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)

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)

The P System (an Inventory Model) is the _____

Periodic Review System

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

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

Always place an order of size Qt = T - IPt

Comparatively, P Systems (single-bin system)

• convenient to administer

• orders may be combined

• IP only required at review

Comparatively, Q Systems (two-bin system)

• individual review frequencies

• possible quantity discounts

• lower, less-expensive safety stocks

What is the average cost of inventory?

30-35% of product’s value (about 1/3)

Examples of Pressures for High Inventory

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

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

Is inventory bad?

Not necessarily

Physical Inventory

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

Conceptual Inventory

1. Cycle Inventory

2. Safety Stock Inventory

3. Anticipation Inventory

4. Pipeline Inventory

EOQ Assumption: Demand rate is ____

constant

EOQ Assumption: No constraints on ____

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

EOQ Assumption: Only costs are _____

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

EOQ Assumption: Decisions for items are _____

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

EOQ Assumption: No uncertainty in _____

lead time or supply

Lead Time =

Time between placing an order and receiving it

Lot sizing

Two Decisions:

1. When to order?

2. How much to order?

Cycle Inventory

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

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

Anticipation Inventory

• Absorbs uneven rates of demand

  • Predictable, seasonal demand patterns

  • Anticipating supplier strike

• Stockpile during low demand

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)

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%

Holding cost _____ as Lot Size (Q) increases

Holding cost increases

Ordering cost _____ as Lot Size (Q) increases

ordering cost decreases

Total cost ____ as Lot Size (Q) increases

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

EOQ Variables are

D = Annual Demand

Q = Lot Size

S = Cost of Setup Ordering Cost (?)

H = Holding cost

Aspects of a Push System

• Production trigger is based on forecasts or desired inventory levels

• No bounds on inventory

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)

Aspects of a Pull System

• Production trigger is actual consumption of inventory

• Imposes a bound on inventory

• Eg. Kanban

When to use a Pull system?

• Small setups & Few product lines

• Example: custom cakes

Kanban

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

Idle time

sitting waiting for a unit

Cycle time

time in between finished goods getting off the assembly line

Supply Chain

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

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 <-

Stockout

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

Backorder

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

(cumulation of these would be a backlog)

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

Load-distance score

Select site that minimizes distances “loads” must travel

Horizontal Pattern of Demand

Data cluster about a horizontal line as time progresses

Trend Pattern of Demand

Data consistently increase or decrease

Seasonal Pattern of Demand

Data consistently show peaks and valleys

Cyclical Pattern of Demand

Data reveal gradual increases and decreases over extended periods

Time-Series Methods

1. Simple moving averages

2. Weighted moving averages

3. Exponential smoothing

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

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

Exponential Smoothing

• forecasting software

• really strong results

• Ft+1 = forecasted demand for period t + 1

  • Dt = actual demand in period t

  • sigma = smoothing parameter

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

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

MSE

= Mean Squared Error

• measure of variability

• Square Error = error ^2

A measurement of the dispersion of forecast errors.

Square Error

= error ^2

MAD

= Mean Absolute Deviation

• another indication of variability

• Absolute Error = ABS(Actual - Predicted)

A measurement of the dispersion of forecast errors.

Absolute Error

= ABS(Actual - Predicted)

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

Absolute % Error

= (Absolute Error / ACTUAL DEMAND) * 100%

Error

Difference between actual and predicted

Error relative to size of demand is related to _____

MAPE (Mean Absolute Percent Error)