Week 1: Introduction to Supply
Chain and Linear Programming
Brett Smith & Huashan (Jason) Li
Department of Management & Organizations
UWA Business School
INMT5518 Supply Chain Analytics
• Subject overview
• Introduction to supply chain analytics
• Introduction to linear programming
This week
3Subject overview
Subject introduction
4
• Brett Smith:
• Subject coordinator
• Expertise: logistics and modelling
• Email: Brett.Smith@uwa.edu.au
• Jason Li:
• Tutor
• Expertise: supply chain management and statistics
• Email: Jason.Li@uwa.edu.au
Teaching Team
Notes: Consultation by appointment.
Subject introduction
5
• Linear programming (Week 1-4)
• Introduction to Linear Programming
• Linear Programming Applications
• Transportation and Network Optimisation Models
• Integer Programming
• Forecasting and Inventory management (Week 6-9)
• Forecasting for Logistics Planning
• Inventory Management I
• Inventory Management II (Public Holiday)
• Simulation for logistics
• Simulation using AnyLogistix (Week 11-12)
• Facility Location Decisions using Any Logistics
• Simulation for Supply Chain Resilience
• Case studies (Week 5 and Week 10)
• Case Study I (Visagio)
• Case Study II (Visagio)
Structure
Jason
Brett
Brett & Jason
Visagio
Class structure
6
Each week
One hour pre-recorded lecture (Friday)
Theories, principles, etc.
Two-hour workshop (Tuesday)
Practicing (in the Trading room [BUSN: 124])
Requirements
Watch the videos and materials before you go to workshop
Textbook
7
Subject introduction
8
Assessments
Assessment Weights Due
Lab Assignments
(four quizzes)
35% Weeks 2, 4, 6, 8 (detailed in
the outline)
Case study I 30% Week 6
Case Study II 35% Week 11
No exam!!!
9What is supply chain?
Supply chain
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• A chain including all parties, directly or indirectly, in fulfilling a
customer request
• Includes manufacturers, suppliers, transporters, warehouses,
retailers, and customers
• Within each organization, the supply chain includes all functions
involved in receiving and fulfilling a customer request (new product
development, marketing, operations, distribution, finance, customer
service)
What is a supply chain
Supply chain
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Automotive supply chain
Supply chain
12
Supply chain
13
Automotive supply chain
Supply chain
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• Customer is an integral part of the supply chain
• Includes movement of products from suppliers to manufacturers to
distributors and information, funds, and products in both directions
• May be more accurate to use the term “supply network”
• Typical supply chain stages: customers, retailers, wholesalers,
distributors, manufacturers, suppliers
What is a supply chain
Supply chain
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Flows in a supply chain
Supply chain
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• Maximize net value generated
The Objective of a Supply Chain
Supply Chain Surplus = Customer Value −
Supply Chain Cost
Supply chain
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Framework for Supply Chain Decisions
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What is business
analytics?
Business Analytics
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Elements
Business Analytics
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• Descriptive: categorize, characterize, consolidate and classify data to
convert it into useful information for the purposes of understanding and
analysing past and current business performance and make informed
decisions.
• Predictive: analyze past performance in an effort to predict the future
by examining historical data, detecting patterns or relationships in
these data, and then extrapolating these relationships forward in time.
• Prescriptive: use optimization to identify the best alternatives to
minimize or maximize a single or multiple objective. The mathematical
and statistical techniques of predictive analytics can also be combined
with optimization to make decisions that take into consideration the
uncertainty in the data.
Types
Supply chain analytics
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Linear Programming
Linear Programming
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• In the world of management science or operations research,
programming refers to modelling and solving a problem
mathematically.
• Linear programming (LP) is widely used mathematical technique
designed to help managers plan and make the decisions necessary
to allocate resources.
• Many business decisions involve trying to make the most effective
use of an organization’s resources. Resources typically include
machinery, labour, money, time, and raw materials. These resources
may be used to produce products or services.
Introduction
Linear Programming
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• A set of decision variables: which are used to stand for
the quantity of each product or service to be produced.
• An objective function: which measures the extent to
which alternative feasible decisions achieve the aim
being pursued.
• A set of constraints: which define in mathematical terms
the values of the decision variables that are feasible.
Elements
Linear Programming
25
General Form
Max or Min c1x1 + c2x2 + … + cnxn
Subject to: a11x1 + a12x2 + … + a1nxn  b1
a21x1 + a22x2 + … + a2nxn  b2
………………………………………
am1x1 + am2x2 + … + amnxn  bm
All x1, …, xn  0.
c1, …, cn: Objective function coefficients
a11, …, amn: Technical coefficients
b1, …, bm: Right-hand-sides (RHS)
Objective function
Constraints
Left-hand side (LHS) Righ-hand side (RHS)
x1, …, xn: Decision variables Decision variables
Linear Programming
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Assumptions
• Deterministic model
– All ci, aij, bj (for i = 1, …, n; j = 1, …, m) are known with certainty.
• Implications of linearity
– Proportionality: Value of the function is in direct proportion to the
values of the decision variables. For example, if we increase the
cost per unit shipped by 10%, then we will increase the total cost
of the shipments by 10% .
Question
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Which of the following is a valid objective function for a linear
programming problem?
A. Minimize (1/2)x1 + x2 + (3/2) x3
B. Minimize x1x2
C. Minimize x1 / x2
D. Maximize 0.5x1x2 + 1.5x3 + x4
Linear Programming
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• Step 1: Fully understand the managerial or optimization problem
being faced
• Step 2: Define the decision variables
• Step 3: Identify the objective function
• Step 4: Identify the constraints
• Step 5: Solve the model and make a recommendation
Steps
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Linear Programming
Maximization example
Linear Programming
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Maximization example
The Shader Electronics Company produces two products: (1) the Shader x-
pod, a portable music player, and (2) the Shader BlueBerry, an internet-
connected colour telephone. The production process for each product is
similar in that both require a certain number of hours of electronic work and
a certain number of labour-hours in the assembly department. Each x-pod
takes 4 hours of electronic work and 2 hours in the assembly shop. Each
BlueBerry requires 3 hours in electronics and 1 hour in assembly. During
the current production period, 240 hours of electronic time are available,
and 100 hours of assembly department time are available. Each x-pod
produced yields a profit of $7; each BlueBerry produced can get a $5 profit.
Shader’s problem is to determine the best possible combination of x-pods
and BlueBerrys to manufacture to reach the maximum profit.
Linear Programming
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Maximization example
The Shader Electronics Company produces two products: (1) the Shader x-
pod, a portable music player, and (2) the Shader BlueBerry, an internet-
connected colour telephone. The production process for each product is
similar in that both require a certain number of hours of electronic work and
a certain number of labour-hours in the assembly department. Each x-pod
takes 4 hours of electronic work and 2 hours in the assembly shop. Each
BlueBerry requires 3 hours in electronics and 1 hour in assembly. During
the current production period, 240 hours of electronic time are available,
and 100 hours of assembly department time are available. Each x-pod
produced yields a profit of $7; each BlueBerry produced can get a $5 profit.
Shader’s problem is to determine the best possible combination of x-pods
and BlueBerrys to manufacture to reach the maximum profit.
Linear Programming – Formulation
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Step 1: Fully understand the managerial or optimization problem
being faced
Hours required to produce one unit
Department x-pods BlueBerrys Available hours
Electronic 4 3 240
Assembly 2 1 100
Profit per unit $7 $5
How many x-pods and BlueBerrys should Shader manufacture
to reach the maximum profit, while not exceeding the limited
amount of electronic and assembly time?
Linear Programming – Formulation
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Step 2: Define the decision variables
x1 = number of x-pods to be produced
x2 = number of BlueBerrys to be produced
Step 3: Identify the objective function
Maximize profit or z = 7x1 + 5x2
Step 4: Identify the constraints
4x1 + 3x2 ≤ 240 (Electronic department resource constraint)
2x1 + 1x2 ≤ 100 (Assembly department resource constraint)
x1 and x2 ≥ 0 (Non-negativity)
Linear Programming – Formulation
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Maximize profit or z = 7x1 + 5x2
Subject to 4x1 + 3x2 ≤ 240
2x1 + 1x2 ≤ 100
x1 and x2 ≥ 0
This is a linear programming model:
• Objective function is linear
• All functions on left-hand side of the constraints are linear
Linear Programming – Solution
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• Graphical Solution Method:
– Plot the solution on a two-dimensional graph
• MS Excel:
– Solver add-in is needed.
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Lab activities
Lab activities
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• Quick recap
• Graphical solution for the example
• Excel basics
• Excel solution for the example
• Formulating the LP model for the minimization example
• Graphical solution for the minimization example
• Excel solution for the minimization example
Plan
Lab activities
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• Familiar yourself with Excel
• Try to solve the LP model for the maximization example using
graphical approach
• Try to solve the LP model for the maximization example using the
Excel approach
• Read the minimization question and formulate the LP model by
yourself
Preparation list
Linear Programming
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Minimization example
As part of a quality improvement initiative, Consolidated Electronics
employees complete a 3-day training program on teaming and a 2-day
training program on problem solving. The manager of quality improvement
has requested that at least 8 training programs on teaming and at least 10
training programs on problem solving be offered during the next 3 months.
In addition, senior-level management has specified that at least 25 training
programs must be offered during this period. Consolidated Electronics uses
a consultant to teach the training programs. During the next 3 months, the
consultant has 84 days of training time available. Each training program on
teaming costs $10,000 and each training program on problem solving costs
$8,000.
Consolidated Electronics’s problem is to determine the number of training
programs on teaming and the number of training programs on problem
solving that should be offered in order to minimize the total cost.