# ELL Blog

This document are my notes and midterm review for the BU 375 Operations course taught at Wilfrid Laurier University. While studying for the midterm, I discovered my own formulae shortcuts, undoubtly due to “blind teaching syndrome” (I made that term up). So let’s begin. I’ll add a divider to let you know what is part of the midterm.

## Appendix

It’s better to have the appendix at the top rather than the bottom, as people know where to find the nitty gritties.

### Control Factors

Out with the ugly table, and in with the new! It’s absurd that at \$500+ per course and hundreds of students, universities do not collaborate with eachother to make course curriculum/content, do not strive for perfect function (notes) and rarely place importance on aesthetics.

Sample Size (n) A2 (x-chart) D3 (R LCL) D4 (R UCL)
2 1.88 0 3.267
3 1.023 0 2.575
4 0.729 0 2.282
5 0.577 0 2.114
6 0.483 0 2.004
7 0.419 0.076 1.924
8 0.373 0.136 1.864
9 0.337 0.184 1.816
10 0.308 0.223 1.777
11 0.285 0.256 1.744
12 0.266 0.283 1.717
13 0.249 0.307 1.693
14 0.235 0.328 1.672
15 0.223 0.347 1.653
16 0.212 0.363 1.637
17 0.203 0.378 1.622
18 0.194 0.391 1.609
19 0.187 0.404 1.596
20 0.180 0.415 1.585
21 0.173 0.425 1.575
22 0.167 0.435 1.565
23 0.162 0.443 1.557
24 0.157 0.452 1.548
25 0.153 0.459 1.541

## Operations Management Introduction

### Transformation Process

• General idea: inputs -> transformation process -> output
• Feedback between inputs <-> process <-> output
• Value is created
• Physical, locational, exchange, physiological, psychological, informational
• Value = Price consumers are willing to pay - Cost to produce

#### Input

• Materials, machines, labor, management, and capital
• These inputs are determined by the requirements for the output

#### Output

• Goods and services

### Major Components of a Firm

#### Primary Areas

• Operatios
• Marketing
• research, packaging
• Finance and Accounting
• Human Resources (HR)
• Outside Suppliers

### Importance

• Middle of the firm
• Opportunity to innovate (internally)
• Results in failure

### Decisions

• Design
• long-term
• Equipment, capacity, layout, location
• Day-to-Day Operations
• Scheduling, quality control, labor requirements, input procurement

## Strategic Planning

### Globalization

• Thinking big
• Foreign markets, production, purchasing, partnerships
• Iterests: cost, international, reliability

### Missing Statement

• What does the firm do and sell?

#### Vision

Direction of the firm in 10 years

#### Values

• Common beliefs

### Order Qualifiers & Winners

Price, Quality, Variety (comparing to competitors), Timeliness, Convenience, Customer Service

#### Order Qualifiers

Basic criteria for product candidacy (functional)

#### Order Winners

Differentiating criteria (aesthetic)

### Strategy

• direction for acheiving a ission
• consistency
• dependent on organization size
• formal (larger)
• mission statement

#### Formulation

• Order qualifiers & winneres
• Positioning (how to compete)
• Deployment

### Positioning / Competitivness

• common goals
• collabortation
• expertise
• learning from past experiences
• cost
• waste elimination
• trades off with quality sometimes
• quality (reducing defects)
• flexibility
• ability to change internal processes to accomodate needs
• speed / delivery
• based on context

### Key performance Indicators (Evaluation)

1. Finances
2. Customers
3. Processes
4. Learning
5. Tools: balanced scorecard worksheet

## Quality

Fitness for use, design. (PDCA) plan, act check, do.

### Products

performance, features, relaibility, conformance (to the design), durability, serviceablility, aesthetics, safety, perceptions

### Serivces

Time, completeness, courtesy, consistency, accessibility, accuracy, responsiveness, HARDER TO EVALUATE

### Total Quality Management (TQM)

• Continuous improvement
• Customer satisfaction
• Involves employees and management
• Performance tracking

### W.E. Demmings

• Statistical quality-control techniques
• Continuous improvement
• Inspect at stages before final
• Responsibility lies with management and employees
• Few suppliers & pick quality > cost

### Six Sigma

• Decreas process variation

### Tools

• Process Flowchart (location of problem)
• Cause-and-Effect (fishbone) diagram (find root cause)
• Check Sheet (form)
• Pareto Analysis (data collection) and Chart
• Scatter Diagram
• Control Chart

### Cost of Quality

Total = cost of achieving good quality + cost of poor quality

#### Good

• Prevetion
• Appraisal/Measuring

#### Poor

• Internal failure
• External failure

#### Quality Index (QI)

Measures quality cost against a base value (e.g. manufacturing, sales, labor hours, quantity)

$QI=\frac{Total\,\,Cost\,\,of\,\,Quality}{Base}\times 100$

## Productivity

### Single-Factor Productivity

$\frac{Output}{Specific\,\,Input}$

where Specific Input could be Labor, Materials, Capital.

### Total Factor Productivity

$\frac{Output}{All\,\,Inputs}$

To calculate multifactor productivity, use a subset of inputs.

### Yield

$Yield=(Initial\,\,Quantity)\times(%good)+(1-%good)(%reworked)$

OR

$Yield=(Initial\,\,Quantity)(%{good}_1)...(%{good}_n)$

### Product Cost

For this one, I have my own simplified formulas.

$Product\,\,Cost=\frac{(mfg\,\,cost)+(rework\,\,cost)(1-%good)(%reworked)}{%good\times(1-%good)(%reworked)}$

This avoids calculating how many units were reworked.

### Quality Productivity Ratio (QPR)

Even for this one, I have my own method, but I’ll include the original in case some information isn’t given.

$QPR=\frac{% good}{(input)(processing\,\,cost)+(1-%good)(%reworked)(rework\,\,cost)}$ $QPR=\frac{good}{(input)(processing\,\,cost)+(reworked)(rework\,\,cost)}$

## Statistical Analysis

• A type I Alpha error is an error that wasn’t supposed to fall outside the control limits. False-positive.
• A type II Beta error is an error that should’ve falled outside the control limits.
• Variations are either random or assignable.
• n refers to sample size or number of observations, and k refers to the number of samples.
• z refers to the sigma count; either 2 or 3
• UCL and LCL stand for upper control limit and lower control limit.

### p-chart

A p-chart is a control limit chart with relation to the proportion of defects. It is used when there are multiple observations per sample and defects are reported.

$\bar p=\frac{total\,\,defects}{nk}$ $\sigma_p=\sqrt{\frac{\bar p(1-\bar p)}{n}}$ $UCL=\bar p+z\sigma_p, LCL=\bar p-z\sigma_p$

### c-chart

Similar to p-chart, except there is only 1 observation per sample.

$\bar c=\frac{total\,\,defects}{k}$ $\sigma_c=\sqrt{\bar c}$ $UCL=\bar c+2\sigma_c, LCL=\bar c-2\sigma_c$

### x-chart

A chart used for checking if process variability is in control.

$\bar{\bar x}=grand\,\,mean = mean\,\,of\,\,means$ $\sigma_x=\frac{\sigma}{\sqrt n}$ $UCL=\bar{\bar x}+z\sigma_x, LCL=\bar{\bar x}-z\sigma_x$

In the case σ is unknown, use the control factors table along with thse formulas:

$UCL=\bar{\bar x}+A_2\bar R, LCL=\bar{\bar x}-A_2\bar R$

### R-chart

A range chart, to test if variability is in control. Use the control factors table to determine factor values or to help you figure out other factor values.

$\bar R=average\,\,range$ $UCL=D_4{\bar R}, LCL=D_3\bar R$

### Reliability

To improve reliability,

• reduce number of components in a series
• increase backup components
• increase individual component reliability

To calculate the relaibility of a process, use these two functions.

#### Series

For components in a series (independents), multiply their reliability scores:

$x_1x_2x_3$

#### Parallel (Backups)

For components that are in parallel (i.e. backups exist), follow this schema,

$x_1+(1-x_1)x_2+(1-x_1)(1-x_2)x_3$

#### System Availability

$SA=\frac{mean\,\,time\,\,between\,\,failures}{MTBF+mean\,\,repair\,\,time}$

### Process Capability Index

When design mean and process mean are the same use cp, otherwise cpk.

If cp and cpk are >= 1, then the process is capable (99.70%). If cp = cpk, then design mean and process mean are the same.

$c_p=\frac{upper\,\,limit-lower\,\,limit}{6\sigma}$

I tweaked the formula for cpk. Instead of dividing both numbers by 3σ, divide only the min.

$c_{pk}=\frac{\min\{{upper\,\,limit-process\,\,mean,process\,\,mean-lower\,\,limit}\}}{3\sigma}$

The number chosen also represents which limit the process (mean) deviated towards.

## Server Model

• Poisson distribution
• First in First Out (FIFO)
• Infinite population because people served can re-join the queue

The lambda variable refers to mean arrival rate and the mu variable refers to mean service rate.

TODO: add table with formulas and descriptions

## Capacity Planning

End of Midterm Review

## Supply Chain Management Strategy & Design

• Chain of organizations and facilities, with varying activities
• Multi-tiered
• Activities
• forecasting, purchasing, product/proces design, manufacturing, quality assurance, inventory management, distribution

### Supply Chain Process

1. Procurement of raw materials and services
2. Production of product and services
3. Storage of products in inventory
4. Taking orders and distribution of products to the customer

### Supply Chain for Service Providers

• Focuses on human resources
• Fewer tiers

### Supply Chain Management (SCM)

• Create maximum value for the end customer
• perfecting coordination and collabortaion of components
• To provide enough supply at the right price, time, and place
• Systemic approach to manage entire flow of information, materials, and services from raw-materials to customers
• Competition becomes between supply chains rather than companies

#### Bullwhip Effect

• Supply chain members farther down the line get information after the members nearer to customers.
• importance of transparency accrorss members
• Safety stock issues
• Lack of accurate demand information
• Order batching results in less orders but larger quantities
• Price fluctuations
• Shortage gaming (placing orders more than is required bc inventory is short supply)
• Solutions
• Coordination by parties for pricing, transportation, and inventory management
• Joint demand information forecast
• Price stabilization
• Discouraging shortage gaming

I believe a solution is for the supplier to force the orderer to tell them when the next order will be. That way, a supplier won’t have to decide whether to anticipate more orders if batch ordering occurs.

### Supply Chain Uncertainty

• Inaccurate demand forecasting
• Long and Varying times for orders
• Late/Incomplete shipments
• Product changes and price fluctuations/discounts
• Batch ordering and inflated orders
• Failures cause chain reactions, leading to lag, lack of supply, and lower sales
• Inventory is used as insurance against uncertainty, however optimality needs to be determined

### Supply Chain Coordination and Integration

• Sharing information
• Coordinated workflow, production, and operations, procurement
• Collaborative Planning, Forecasting, Replenishment (CPFR)
• Entreprise Resource Planning (ERP)

### Information Technology

• Electronic data interchange (EDI)
• Barcode and point-of-sale (POS) data
• Internet
• Blockchain

### Supply Chain Performance

• inventory turnover
• weeks of supply
$Inventory\,\,Turnover=\frac{cost\,\,of\,\,goods\,\,sold}{average\,\,aggregate\,\,value\,\,of\,\,inventory}$

Average aggregate inventory value is the sum of average inventory times value for each item.

$Days\,\,of\,\,Supply=\frac{opDays=365}{Inventory\,\,Turnover}$

Fill Rate = fraction of orders filled within a specific time period.

• low inventory turnover indicatest that a large amount of inventory is required to satisfy demand

• Plan
• Source
• Make
• Deliver
• Enable
• Return

## Project Management

A project is one-time and non-repetitive operational activities or efforts. Clear goal, limited time frame, budget, schedule, resources.

### Project Elements

1. Objective
2. Scope
3. Contract requirements
4. Schedules
5. Resources
6. Personnel
7. Control
8. Risk and problem analysis

### Project Manager

• plans, schedules, executes, controls project
• meeting requirements
• keeps project on track, within budget, and meets quality standards
• expedites work when needed
• resolves conflicts

• Planning
• Scheduling
• Control

### Work Breakdown Structure

1. Identify major components of the project
2. Break down the major components into subcomponents
3. Break down subcomponents into work packages

### Responsibility Assignment Matrix (RAM)

• Organizational breakdown structure (OBS) shows which organizational units are responsible for work items used to develop RAM

### Gantt Chart

• A visual aid for scheduling and control purposes

### CPM & PERT

• Critcal Path Method (CPM) has deterministic task times
• Program Evaluation and Review Technique (PERT) has probabilistic task times
• network path: starting node to finishing node sequence
• critical path: longest network path; determines project duration
• critical activities: activites on the critical path
• slack time: allowable slippage for a path

To calculate expected time of a single activity, use

$t_E=\frac{a + 4m + b}{6}$

Where a is best case time, m is most likely, and b is worst case time.

Thus the expected duration of a path (t_path) is the sum of activity expected times.

The variance of each activity time is $\sigma^2=(\frac{b - a}{6})^2$

The variance of a path is then the sum of activity variances, and the variance of the critical path is also known as the project variance.

Like always, the standard deviation of anything is the square root of the variance.

As for calculation probabilities, the probability of completing a project by a certain time isw

$z=\frac{deadline - t_path}{\sigma}$

Use z-table to get a probability representing p(x < deadline) where sigma is the std of the critical path.

To calculate the deadline given a probability, use the z-table to get a z value, and then use the z formula to calculate.

### Crashing

With CPM and PERT some activities can be crashed. For crashing to have an effect on the project duration, the crashes must reduce the time of the critical path or paths. A single crash might not have an affect on the project duration if there was an equivalent critical path that didn’t need that activity.

Crashing information is stated as cost to crash completely (additional cost) as well as how many weeks can be crashed. Thus, implicitly, activities can be crashed by a single week rather than the entire allowable crash time.

## Demand Forecasting

Projections of demand for products/services underlies strategic planning when it comes to plant or service design.

• often inaccurate
• forecasts of similar goods is more accurate than individual items
• forecast horizons increases uncertainty

### Decision Based on Forecasts

• Production and Operations
• aggregate planning
• inventory control
• scheduling
• Finance
• plant/equipment investment
• budgetery planning
• Marketing
• new product introduction
• sales-force allocation
• promotions
• Human Resources
• workforce planning
• hiring, layoff

### Making Forecasts Useful

• long enough to make it relevant
• typically for daily, weekly, or monthly sales demand for up to approximately two years into the future, depending on the company and the type of industry.
• limitations on accuracy must be clearly stated
• forecasting method should be reliable
• operations forecasts should be expressed in units

### Quantitative Forecasting Methods

• Time-Series methods
• use historical data to project into the future
• naive method, moving average, weighted moving average, exeponential smoothing
• Associative models
• independent casual variables

#### Naive Method

Assumes the demand for the next period will be the same as the previous period

#### Moving Average

As the MA-window increases, so too will the lag.

For MA-2, do

$F_t=MA_t=\frac{D_{t-1}+D_{t-2}}{2}$

#### Weighted Moving Average

$F_t=WMA_t=\sum_{i \in periods} w_i \times D_i$

#### Exponential Smoothing

$F_t=\alpha D_{t-1} + (1-\alpha)F_{t-1}$

Incorporates a trend factor on top of exponential smoothing

$F_{a_t}=F_t+T_t$ $T_t=\beta(F_t-F_{t-1})+(1-\beta)T_{t-1}$

Where beta is a smoothing constant for the overall trend

Example

For the data given below, generate a forecast using adjusted exponential smoothing. Assume alpha = 0.5 and beta = 0.3.

An adjusted exponential smoothing forecast requires T2 to start the computational process. For this case, assume T2 = 0.

Period Month Demand Forecast Ft Trend Ti Adjusted Forecast AFt
1 JAN 37 37.00 - -
2 FEB 40 37.00 0 37.00
3 MAR 41 38.50 0.45 38.95
4 APR 37 39.75 0.69 40.44
5 MAY 45 38.37 0.07 38.44

Sample calculation

F3 = alpha(D2) + (1 - alpha) F2 = 38.5

T3 = Beta(F3 - F2) + T2(1 - Beta) = 0.45

AF3 = F3 + T3

Course specific: seasonal adjustment factor (Sq) relative to the total demand for some period. Use factor after a forecast to get each quarter’s demand forecast.

$S_q=\frac{D_q}{\sum D}$

#### Forecast Accuracy

et = Dt - Ft

MAD = sum of | et | / n

mean squared error = sum (e_t^2) / n

mean absolute percentage deviation = sum (e_t) / sum (D_t)

## Inventory Management

### What is Inventory?

• raw materials
• work in progress
• finished products
• packaging
• replacement parts
• goods-in-transit

Important because assets are tied up in inventory. Too much inventory can increase costs and reduce efficiency while too

### Inventory Control Systems

#### Continuous System

• economic [fixed] order quantity (EOQ) whenever the reorder point is reached
• inventory is continually monitored (costly)

#### Periodic System

• orders are placed on a fixed time interval
• order quantity = desired inventory level - inventory on hand
• less level of control

### Economic Order Quantity (EOQ)

• single product
• constant annual demand is known
• single delivery with constant lead time smaller than the order cycle
• no discounts

Average inventory = Q / 2

Average inventory cost = Q / 2 * Cc [holding cost per unit]

Purchase orders per year = D / Q

Annual order costs = D / Q * CO

TC = Q/2 * Cc + D/Q * CO = Holding Cost + Ordering cost

$EOQ = Q_{opt}=\sqrt{\frac{2DC_O}{C_C}}$

Slope = dTC / dQ = CC/2 - DC_O / Q2 = 0

#### Quantity Discounts

Add PD to total cost where price is per unit and D is demand.

If quantity is feasible done, otherwise compare with the minimum for each proce discount level larger than EOQ.

### Economic Production Quantity

Receive quantity incremetally while inventory is being depleted.

$EPQ = Q_{opt} = EOQ * \sqrt{\frac{p}{p-d}}$

Where p is the production rate per day and d is the demand rate per day.

Inventory max = (Q/p)(p-d)

TC = I/2 * Cc + D/Q * CS = Holding Cost + Setup cost per run

### Reorder Point (Constant Demand)

Ensure that the time unit is the same.

### Reorder Point (Variable Demand)

R = demand rate * lead time + Safety Stock

$z\sigma_d\sqrt{L}$

Use table for z depending on % service level. e.g. 95% -> z = 1.65. Service level is the probability that demand won’t be greater than quantity of goods in stock.

### Periodic Order Quantities (Variable Demand)

Q = average demand rate * (time between orders + lead time) + z sigma (sqrt (t + L)) - I

### Single Period Inventory Model

Shortage Costs = revenue per unit - cost per unit

Excess Costs = cost per unit - salvage value

SL = C_S / (C_E + C_S) (round up to closest cumulative probability in table)