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 Sept 5, 2012Wood Saba Vahid2

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: Sept 5, 2012Wood Saba Vahid3

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, 2012Wood Saba Vahid4

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, 2012Wood Saba Vahid5

Example: cutting pattern optimization Sept 5, 2012Wood Saba Vahid6

Example: Road network design Sept 5, 2012Wood Saba Vahid7

Example: A forest company’s value chain Sept 5, 2012Wood Saba Vahid8 Forest Bucking/merchandising Transportation Sawmill/Pulp mill TransportationDistribution center

OR methods and techniques Linear programming Non-linear programming Integer programming Inventory theory Dynamic programming Queuing theory Sept 5, 2012Wood Saba Vahid9 Game theory Transportation problems Network optimization Simulation Heuristics …

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, 2012Wood Saba Vahid10

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, 2012Wood Saba Vahid11

What is a mathematical model? – Cont’d Decision variables: –the quantifiable decisions to be made (variables whose respective values should be determined) e.g. x 1, x 2, … Objective function: –The identified measure of performance that is to be improved, expressed by using the decision variables e.g. 2x x 2, … Constraints: –Any restrictions to be applied to the values of decision variables e.g. x 1 >0, x 1 +x 2 <20, … Parameters: –The constants in the equations, the right hand sides and the multipliers e.g. 0,20, 6.5,… Sept 5, 2012Wood Saba Vahid12

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, 2012Wood Saba Vahid13 DepartmentCapacity per unitAvailable capacity per week Pine deskAlder hutch Solid wood Panel00.25 Finishing Profit per unit $40$50 Objective Decision variableConstraints

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 km 2 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, 2012Wood Saba Vahid14

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, 2012Wood Saba Vahid15

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, 2012Wood Saba Vahid16

Next Class Learn about Linear programming Example of LP formulation Graphical solution method for LP Sept 5, 2012Wood Saba Vahid17