WOOD 492 MODELLING FOR DECISION SUPPORT

Lecture 1 Introduction to Operations Research

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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

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Forest

Bucking/merchandising Transportation

Sawmill/Pulp mill

TransportationDistribution center

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OR methods and techniques

• Linear programming

• Non-linear programming

• Integer programming

• Inventory theory

• Dynamic programming

• Queuing theory

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• Game theory

• Transportation problems

• Network optimization

• Simulation

• Heuristics

• …

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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. A set of decision variables,2. An objective function3. A set of constraints4. 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 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 generate the highest profits

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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

Objective

Decision variableConstraints

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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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