The simplex method, the big M method, duality: Exercises.

Answer and sensitivity reports displayed by Solver and sensitivity analysis with the graphical approach: shadow price for each constraint and its range of feasibility. Exercises.

The dual problem. The relationship between primal and dual problems. Economic intuition behind duality.
Reading the optimal dual solution from the optimal simplex tableau. Duality and shadow prices. Complementary slackness.

Answer and sensitivity reports displayed by Solver and sensitivity analysis with the graphical approach: binding constraints; range of optimality for the objective function coefficient for each variable. Exercises.

Linear programming problems. The simplex method - revisions. Starting basic feasible solution - the Big M Method.

Revisions: formulating linear programming models; the graphical approach for solving these models. Using Solver from EXCEL to solve linear programming models. Exercises.

The class was scheduled to take place in another date

The class was scheduled to take place in another date

Test

Sensitivity Analysis: Right side vector, non basic costs, basic costs, interpretation. Examples and Exercises.

Review for the exam (LP, Simplex, Graphical Method and Sensitivity analysis examples)

Simplex: Special cases, interpretation, examples, exercises, “tableau” version. Model a LP and then solve it using Simplex. Exercises

Solving Methods: Simplex (Augmented Polyhedron, Standard form, Intuition of the algorithm, theory, properties, special cases, steps) Examples and Exercises

Properties and Geometry of LP. Solving Methods: Graphical Method. Special Cases. Exercises

OR Introduction. Linnear Programming. How to Model a LP. Exercises

The class was scheduled to take place in another date

The class was scheduled to take place in another date

The class was scheduled to take place in another date

The class was scheduled to take place in another date

Test

Spatially explicit forest harvest scheduling models with integer programming. Modeling harvest opening size restrictions.

Modeling connectivity in reserve design using integer programming. Linearization techniques for cross products of binary and continuous variables.

Integer programming fundamentals. Examples from reserve design: modeling reserve size, connectivity, shape (perimeter-area ratio), proximity and contiguity. Species representation models.

Future directions in development of spatial decision support systems for forest management. In the first part, a brief recap of system features is presented that have made the EMDS system successful for the past 20 years. Most of the lecture looks at ways in which the power of contemporary decision support systems can be enhanced through implementation of various components that support features such as web services, provenance tracking, and workflow management for automation and customization, etc. The lecture concludes with a quick introduction to the FORSYS COST action and its follow-on community of practice.

Forest management with linear programming. The concept of regulated forests and analysis areas. Formulating cost minimizing and profit maximizing harvest scheduling models. Formulating area constraints, harvest target and harvest flow constraints, and ending age constraints. Modeling non-timber objectives with LP-based harvest scheduling models. Modeling extended rotations, wildlife openings and streamside management zones.

Major applications of the EMDS system are presented, including decision support applications for

a.       Watershed analysis

b.      National criteria and indicators for forest sustainability

c.       National forest fuels analysis (broad scale, simple models)

Mid-scale forest fuels analysis (fine scale, more complex models)

 Basic linear programming concepts. Defining the decision variables and formulating the objective functions and constraints. Graphical solutions to linear programs. LP solution outputs. Reduced costs, shadow prices, slack and surplus values. The fundamental assumptions of linear programming.

Introduction to logic (knowledge-based) modeling with NetWeaver. Concepts and principles behind logic modeling were addressed in lectures 2 and 3. In this lecture, the emphasis is on the mechanics of building logic models, which is done in a computer lab.

The role of models in making forest and natural resource management decisions, classification of model, model types and model building fundamentals. Multi-objective optimization.

Introduction to multi-criteria decision analysis (MCDA). Concepts and principles of structured decision making are presented first. Students learn the mechanics of how to build decision models based on the analytic hierarchy process and multi-attribute rating technique, using the Criterium DecisionPlus software in a computer lab.

Model building 1

An in-depth look at the Ecosystem Management Decision Support (EMDS) system. EMDS is presented as a general framework for building decision support applications. Major topics discussed are 1) use of knowledge-based modeling for environmental assessment, 2) use of multi-criteria decision models for planning, 3) the complementarity of the two methods, and 4) spatial decision support for multi-scale management problems that can be large, abstract, and complex.

The first part of the lecture traces the origins of decision support, presents a fundamental model for decision making, and defines what is meant by a decision support system. The balance of the lecture introduces a broad array of modeling approaches (both historical and contemporary) used in decision support systems. For each approach, basic concepts and principles are described, methods are briefly illustrated, and advantages and disadvantages are summarized.

Sets the context for contemporary decision support in forest management by reviewing social, economic, environmental, and science trends in North America and Europe, starting in the late 1800s. Concepts and principles of ecosystem management, adaptive management, and sustainable forest management are presented, put in historical context.

Introduction

The class was postponed to another date