WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 1 Introduction to Operations Research.
-
Upload
norma-turner -
Category
Documents
-
view
223 -
download
1
Transcript of WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 1 Introduction to Operations Research.
WOOD 492 MODELLING FOR DECISION SUPPORT
Lecture 1
Introduction to Operations Research
Wood 492 - Saba Vahid 2
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
Sept 5, 2012
Wood 492 - Saba Vahid 3
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
Sept 5, 2012
Wood 492 - Saba Vahid 4
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.
Sept 5, 2012
Wood 492 - Saba Vahid 5
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.
Sept 5, 2012
Wood 492 - Saba Vahid 6
Example: cutting pattern optimization
Sept 5, 2012
Wood 492 - Saba Vahid 7
Example: Road network design
Sept 5, 2012
Wood 492 - Saba Vahid 8
Example: A forest company’s value chain
Sept 5, 2012
Forest
Bucking/merchandising Transportation
Sawmill/Pulp mill
TransportationDistribution center
Wood 492 - Saba Vahid 9
OR methods and techniques
• Linear programming
• Non-linear programming
• Integer programming
• Inventory theory
• Dynamic programming
• Queuing theory
Sept 5, 2012
• Game theory
• Transportation problems
• Network optimization
• Simulation
• Heuristics
• …
Wood 492 - Saba Vahid 10
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
Sept 5, 2012
Wood 492 - Saba Vahid 11
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 function
3. A set of constraints
4. A set of parameters
Sept 5, 2012
Wood 492 - Saba Vahid 12
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,…
Sept 5, 2012
Wood 492 - Saba Vahid 13
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
Sept 5, 2012
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
Wood 492 - Saba Vahid 14
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
Sept 5, 2012
Wood 492 - Saba Vahid 15
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
Sept 5, 2012
Wood 492 - Saba Vahid 16
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)
Sept 5, 2012
Wood 492 - Saba Vahid 17
Next Class
• Learn about Linear programming• Example of LP formulation• Graphical solution method for LP
Sept 5, 2012