Supply Chain Management

Course FacilitatorKashif Mahmood

Session 7

My Expectations from Students

HonestyHard WorkResponsible Attitude

Contents of session 6Lean Manufacturing

• Basic elements in lean manufacturing

• Benefits of lean manufacturing

• Integration of lean manufacturing into SCM

• Success factors for leanness

Role of distribution in supply chain

Structure of distribution channel

Designing distribution channel

Distribution network in practice

Logistical requirement of channel partners

Distribution Decisions

Review of Previous Session

What we will cover today ?

Contents of session 7

Different QTs used in decision making in SCLinear programmingModellingQueuing theoryGame theorySimulation

Chapter 23

Quantitative Techniques in Supply Chain

Quantitative Forecasting Methods• Correlation analysis• Time series forecasting models• Cross-impact matrix method• Scenario method

Correlation Analysis• Measure strength of association

between quantitative variables.• For example, we could measure the

degree of relationship between sales(y) and the corresponding ad spent(x).

• Strength of relationship between two sets of data is usually measured by the correlation coefficient.

CorrelationYear Promotional

expensesSales Year Promotion

al expensesSales

2001 19 70 2006 44 1192002 22 76 2007 49 1322003 25 80 2008 51 1442004 29 89 2009 54 1552005 40 102 2010 60 161

The correlation coefficient with the above formula works out to be 0.96, which means two variables highly correlated.

Time Series Forecasting Models

• Historical data is explored to find out its cyclic nature or trends.

• Mathematical techniques are then used to extrapolate to find out the future value/trends.

Naive Forecasts

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

The forecast for any period equals the previous period’s actual value.

Simple to useVirtually no costQuick and easy to prepareData analysis is nonexistentEasily understandableCannot provide high accuracyCan be a standard for accuracy

Naïve Forecasts

Stable time series data◦F(t) = A(t-1)

Seasonal variations◦F(t) = A(t-n)

Data with trends◦F(t) = A(t-1) + (A(t-1) – A(t-2))

Uses for Naïve Forecasts

Techniques for AveragingMoving averageWeighted moving averageExponential smoothing

Moving AveragesMoving average – A technique that

averages a number of recent actual values, updated as new values become available.

Weighted moving average – More recent values in a series are given more weight in computing the forecast.

Ft = MAn= n

At-n + … At-2 + At-1

Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1

Example of Moving AverageMonth Attendance Month Attendance

1 47 13 442 51 14 573 54 15 604 55 16 555 49 17 516 46 18 487 38 19 428 32 20 309 25 21 2810 24 22 2511 30 23 3512 35 24 38

Compute 3 Months, 5 Months and 7 Months Moving Average and forecast the attendance for next 6 months.

Simple Moving Average

35373941434547

1 2 3 4 5 6 7 8 9 10 11 12

Actual

MA3

MA5

Ft = MAn= nAt-n + … At-2 + At-1

Exponential Smoothing

Weighted averaging method based on previous forecast plus a percentage of the forecast error

A-F is the error term, is the % feedback

Ft = Ft-1 + (At-1 - Ft-1)

Time (t) Demand (y)1 422 403 434 405 416 397 468 449 4510 3811 40

Example 3 Exponential Smoothing

• Forecast demand for 12th period by using smoothing factor or 0.1 and 0.4• Calculate Error term for both cases and select the best smoothing factor

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92

Example 3 Exponential Smoothing

Picking a Smoothing Constant

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Dem

and .1

.4

Actual

Linear Trend Equation

Ft = Forecast for period tt = Specified number of time

periodsa = Value of Ft at t = 0b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

Ft

Calculating a and b

b = n (ty) - t y

n t2 - ( t)2

a = y - b tn

Linear Trend Equation Example

Week (t) Sales (y)

1 150

2 157

3 162

4 166

5 177

Linear Trend Equation Example

t yW e e k t 2 S a l e s t y

1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5

t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5

Linear Trend Calculation

y = 143.5 + 6.3t

a = 812 - 6.3(15)5

=

b = 5 (2499) - 15(812)5(55) - 225

= 12495-12180275 -225

= 6.3

143.5

Linear Model

A straight line is fitted to a set of sample points.

0

10

20

30

40

50

0 5 10 15 20 25

X Y7 152 106 134 15

14 2515 2716 2412 2014 2720 4415 347 17

Computedrelationship

Forecast AccuracyError - difference between actual value

and predicted valueMean Absolute Deviation (MAD)

◦ Average absolute errorMean Squared Error (MSE)

◦ Average of squared errorMean Absolute Percent Error (MAPE)

◦ Average absolute percent errorRoot Mean Square Error (RMSE)

◦ Square root of average squared errors

MAD, MSE, and MAPE

MAD =Actual forecast

n

MSE = Actual forecast)

2

n

(

MAPE = Actual forecast

n

/ Actual*100)(

Cross-impact Matrix Method• Occurrence of an event can effect the likelihoods

of other events.• Probabilities are assigned to reflect the likelihood

of an event in the presence and absence of other events.

• Helps decision makers to look at the relationships between system components, rather than viewing any variable as working independently of the others.

Scenario Method • Describes interrelationships of all system

components • Scenarios are new technology, population shifts

and changing consumer preferences• Expected to forecast that is likely to happen• Enables the decision makers to organize

resources and decide course of action in advance

Linear Programming• It’s a mathematical method for determining a way

to achieve the best outcome (such as maximum profit or lowest cost).

• Describe many realistic problems arising in modern industry.

• Largely used in logistics, transportation, finance, warehousing, etc.

• Single and well-defined objective with a set of decision variables (i.e. maximum profit or minimum cost)

• Set of constraints including non-negative constraints (i.e., representations of a limited supply of resources)

• There exist more than one solution to the problem (there are infinite number of solutions)

• Objective and constraints are in the form of linear equations or inequalities

Linear Programming Structure

• Product mix problem

• Investment problem

• Scheduling problem

• Transportation problem

• Assignment problem

Applications of LP Models

Mathematical Models• Mathematical modelling is most useful for tactical

decision-making, with a certain time horizon and where certain level of aggregation of data is possible.

• In modelling, the quantification of certain key elements of cost, or quantifying the attributes of various scenarios, is often very useful in strategic decision-making process.

• Models are useful to describe the inter-relationships between different quantities of interest and sometimes to derive certain optimal or good policies.

Mathematical Models• Inventory Model

• Square Root Law

• Warehouse-Cost vs. Area

Limitations of Mathematical Models• Input data may be uncertain.

• Apparent precision of model forecasts may be

misleading.

• Usefulness of a model may be limited by its

original purpose.

Queuing Theory• Queue – a line of people or vehicles waiting for

something• Queuing Theory – Mathematical study of waiting

lines, using models to show results, and show opportunities, within arrival, service, and departure processes

Queuing Problem• Queuing model is relevant in service-oriented

industry such as logistics, transportation, shipping, hospitality and banking.

• Customer arrives randomly to avail the service.• Service time is a random variable. • Typical queuing situation: customers arrive to avail

the service at a service system, enter a waiting line, receive service, and then leave.

Key Elements of Queuing Process

• Source population

• Arrival process

• Waiting time

• Queuing discipline

• Service process

• Departure

Game Theory• Powerful tool for analyzing situations in which

the decisions of multiple agents effects each payoff.

• Game theory focuses on how groups of people interact.

• Game theory provides a mathematical background for modelling the system and generating solutions in competitive or conflicting situations.

“Simulation is a numerical technique for conducting

experiments on digital computers, which involves

certain types of mathematical and logical relationships

necessary to describe the behaviour and structure of a

complex real world system over extended period of

time”.

Simulation

…….T.H.Taylor

• System

• Decision variables

• Environmental variables

• Endogenous variables

• Criteria function

Simulation – Basic Concepts

• A Monte Carlo method is a technique that involves using random numbers and probability to solve problems.

• The term Monte Carlo Method was coined by S.Ulam and Nicholas Metropolis in reference to games of chance, a popular attraction in Monte Carlo.

• Monte Carlo simulation is a method for evaluating a deterministic model using sets of random numbers as inputs.

• This method is often used when the model is complex, nonlinear or involves more than just a couple uncertain parameters.

Monte Carlo Simulation Technique

Contents of session 7

Different QTs used in decision making in SCLinear programmingModellingQueuing theoryGame theorySimulation

Review of Today’s Session

Next Class AssignmentWritten Quiz of Topics Covered

today

Any Question?