Equilibrium Programming in Engineering
Market, Spatial, and Traffic Equilibrium Models
in Project Management
The course project is intended to give students first-hand experience with equilibrium and mixed integer nonlinear programming (MINLP) problems for a chosen topic. Equilibrium problems here means nonlinear complementarity or variational inequality problems (NCP or VI). There are three phases to this project as in the case of real-world projects. In particular, a proposal for the work to be done needs to be generated. Second, the actual analysis and data collection needs to be performed. And lastly, like real-world projects, there is the reporting stage. The project will analyze one or more equilibrium topics by implementing an appropriate model on a problem with real or realistic data.
Students are encouraged to talk with Professor Gabriel about possible topics prior to the proposal deadline. If desired, two students may work together on this course project with the understanding that both students must contribute significantly on all phases of the project (proposal, mid-project review, presentation, final report). In what follows, a “project team” therefore means either one or two students as appropriate.
The project is divided into the following four parts all contributing to the project grade:
- Written proposal for intended project due October 19 , 2009 at the start of class.
- Mid-project meeting to be arranged with Professor Gabriel in October or November , and
- Final presentation and report (due last day of class, December 7, 2009) no late reports accepted.
- The grade for the course project will be based on the depth of the analysis of the project under consideration, the professionalism of the work (e.g., clear arguments with ample documentation for data files, software used, etc.), as well as the overall quality of the project.
The written proposal is a “contract” in some sense between the project team and the instructor and should be thought out carefully. It will consist of 3-5 pages necessarily including the following sections:
- Overview of the project
- Objective of the project
- Description of the course concepts to be used
- Work plan, listing specific work tasks to be performed in support of the project objective, with key dates, for example
- Estimate the number of hours for each task and when these hours will be spent. This estimate will be compared with the actual number of hours expended when the project team meets for the mid-project review, the final presentation and perhaps at other times during the semester.
- List of possible problems (for example, lack of sufficient data for analysis) and back-up plan in order to perform the project on time.
- Distribution of work between the project members if two people make up the project team. This item could instead be included in the work plan if preferred.
a. Task 1: Collect relevant data, October 7- October 14
b. Task 2: Perform statistical analyses, October 14-October 21,
Note that each project will potentially have distinct tasks along with specific dates by when the work tasks should be completed.
The project team will meet with Professor Gabriel at least once during the semester to report on the progress of the project. In particular, items to be discussed will include how well the work plan is being followed, any problems encountered, any new tasks that need to be included. This meeting is important to the success of the project and is mandatory.
Format: Must be typed, specific sections required (see below), only GAMS models allowed.
|1. Overview and Significance of Problem (maximum of 1 page)||Total points: 3|
|2. Mathematical Formulation Must clearly define variables, constants, and all notation used (maximum of 3 pages)||Total points: 3|
|3. Data Sources Must clearly describe the source of the dataset as well as the data elements (maximum of 2 pages)||Total points: 3|
|4. Analysis Must clearly describe and present the results of an analysis of using the model: Key scenarios, assumptions, output, recommendations (maximum of 3 pages)||Total points: 3|
|5. Conclusions, Future Work, Course Concepts Used, Problems Encountered (maximum of 1 page)||Total points: 3|
|6. GAMS code and relevant data files (if any), this needs to be emailed as the GAMS code will be checked to see that it actually runs correctly||Total points: 3|
|Total points for project: 18, maximum number of pages (single-spaced): 10|
Final Presentation, last day of class, December 7, 2009
Details to be provided since it depends on the number of project teams.
Selected Previous Projects
(from a course on probabilistic optimization, ENCE 722)