16:00 May 12, 2023

Poster Presentation: 1 pm-5 pm May 17, 2023

Tentative plan：

• Time: 1 pm - 5 pm, Wednesday, May 17th

• Venue: Entrance of MB Building

• Each group should prepare a poster

• Printing options:

  • We print it for you (send the file to our TA [email protected] by May 14th)

  • Print it out yourself and bring it to the poster presentation

Each group (not each person) should submit a report:

• Hard copy (A4 size) to the mailbox (Min's or Ruonan's) on the 5th floor MB building
• 1000-1500 words (including tables & figures,excluding references and appdendix).
• Include a cover page, specifying your team name and which topic you choose

Search or designed by yourself to investigate a real-life MIP problem. Formulate the general model for the problem and solve it using existing solvers, such as Excel, LINGO, CPLEX, etc.

CPLEX download: https://www.ibm.com/products/ilog-cplex-optimization-studio

LINGO download: https://lindo.com/

Report outline sample for Topic 3:

• Introduction(the background of your problem, the story)

• Problem description(what are the inputs, the assumptions, the objective, and the constraints; a toy example, figure illustrations if possible; etc.)

• MIP Model(Notations for sets, parameters, variables; explain how to model each constraint, present the entire model)

• Computational Results(data, software/solver used to solve the MIP model, sensitivity analysis and other interesting results, etc)

• Conclusion

• References

• Appendix (snapshot of models and results in the solver, etc)

Report

(15%) Structure

(10%) Creativity

(30%) Methodology

(20%) Coherent account in own words

(15%) Ease of reading and grammar

(10%) Word count

Poster presentation

(40%) Preparation of poster

(20%) Clarity of voice and spoken language

(40%) Logic and structure of the contents

Lecturer’s marks will be given to the entire team (same for all the members) considering report and presentation, each with 50%

Minimize: $$\sum_{(u, v) \in E} c(u, v) \cdot x(u, v)$$

Subject to: $$\sum_{(u, v) \in \delta(S)} x(u, v) \geq 1 \quad \forall S \subseteq V, S \neq \emptyset, V$$ $$\sum_{v \in V} x(u, v) = 1 \quad \forall u \in V$$ $$\sum_{u \in V} x(u, v) = 1 \quad \forall v \in V$$

In this formulation:

• 'c(u, v) ' is the cost (e.g., distance) between nodes 'u' and 'v'.
• ' $x(u, v)$ ' is a binary variable, equal to 1 if the edge ' $(u, v)$ ' is included in the solution, and $O$ otherwise.
• ' $\delta(\mathbf{S})$ ' is the set of edges with one endpoint in the subset ' $\mathbf{S}$ ' and the other endpoint outside of ' $\mathbf{S}$ '.
• The first constraint ensures that at least one edge enters and leaves every subset ' $\mathbf{S}^{\text {' }}$ of nodes.
• The second and third constraints ensure that exactly one edge enters and leaves each node.