WOOD 492
MODELLING FOR DECISION SUPPORT
Lecture 1
Introduction to Operations Research
What is this course about?
• Understanding the principles of linear programming and
its applications in forestry
• Understanding practical questions that managers have
about forestry and forest products
• Translating the “forest system” to a mathematical model
• Using the model to answer the questions
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What is the course format?
• Combination of lectures and labs
• Examples of mathematical models in class, posted on the
course website
• Weekly assignments in the computer lab: students develop or
complete their own decision support models
• Labs are posted each Thursday (starting next week) on the
course website
• Quizzes in class and two midterms
• Course website: http://courses.forestry.ubc.ca/wood492
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What is Operations Research (OR)?
• Involves “research” on “operations”
• Concerned with allocating resources and planning the
operations of various components within an organization in
the most effective way
• Goes back many decades (WWII), started with military
applications
• Is used in : manufacturing, transportation, health care,
military, financial services, natural resource management, etc.
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OR in forestry
• Cutting pattern optimization
• Cut-block selection
• Wood processing facility location
• Road network design
• Log bucking and merchandising at the stump
• Production planning in wood processing facilities
• Supply chain planning for forest companies
• etc.
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Example: cutting pattern optimization
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Example: Road network design
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Example: A forest company’s value chain
Bucking/merchandising
Transportation
Sawmill/Pulp mill
Forest
Distribution center
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Transportation
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OR methods and techniques
• Linear programming
• Game theory
• Non-linear programming
• Transportation problems
• Integer programming
• Network optimization
• Inventory theory
• Simulation
• Dynamic programming
• Heuristics
• Queuing theory
• …
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OR modelling approach
• Define the problem and gather data
• Formulate a mathematical model
• Develop an algorithm to find solutions to the model
• Test and verify the model
• Analyze the results and make recommendations to
eliminate the problem and improve the operations
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What is a mathematical model?
• quantitative representation of a system, showing the
inter-relationships of its different components
• Is used to show the essence of a business/economic
problem
• A mathematical model has 4 components:
1.
2.
3.
4.
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A set of decision variables,
An objective function
A set of constraints
A set of parameters
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What is a mathematical model? – Cont’d
• Decision variables:
– the quantifiable decisions to be made (variables whose
respective values should be determined) e.g. x1, x2, …
• Objective function:
– The identified measure of performance that is to be improved,
expressed by using the decision variables e.g. 2x1+6.5x2, …
• Constraints:
– Any restrictions to be applied to the values of decision variables
e.g. x1>0, x1+x2 <20, …
• Parameters:
– The constants in the equations, the right hand sides and the
multipliers e.g. 0,20, 6.5,…
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Example 1: Custom Cabinets company
• Use excess capacity for 2 new products: Pine desks & Alder hutches
• Has three departments that are partially committed to producing
Constraints
Decision variable
existing products
• Wants to determine how many units of each new product can be
produced each week by using the excess capacity of departments to
Objective
generate the highest profits
Department
Capacity per unit
Available capacity per week
Pine desk
Alder hutch
Solid wood
0.25
0
12
Panel
0
0.2
5
Finishing
0.25
0.5
18
Profit per unit
$40
$50
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Examples: decision variables and objectives
• In a road network design problem:
– Decision variables: which roads to build (binary variable)
– Objective: minimize the construction costs
• In a land-use planning problem:
– Decision variables: how many km2 to assign to each purpose
– Objective: maximize the total revenues
• In a cutting pattern selection problem:
– Decision variables: Which cutting pattern to use on incoming
logs
– Objective: maximize the profits or product volumes
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Solutions to the mathematical model
• Many different algorithms for different types of models
(linear, non-linear, integer, etc.)
• the “optimal” solution: the values of the decision
variables for which the objective function reaches its best
value, while all the constraints are satisfied
• “near optimal” solutions: when the optimal solution can
not be mathematically calculated, but a close solution is
found which satisfies all the constraints
• Sensitivity analysis: shows what would happen to the
optimal solution if value of some variables or parameters
are modified
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Importance of mathematical models
• Help us better understand a system
• To determine best practices
• To study cause and effect relationships in the model
• To ask “what-if” questions and answer them (you can’t
try many different scenarios in real systems because it
would be costly)
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Next Class
• Learn about Linear programming
• Example of LP formulation
• Graphical solution method for LP
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