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COURSEWORK DESCRIPTION

Refer to the Car Rental 1 and Car Rental 2 optimization problems described in sections 12.25 and 12.26 of the following book in the reading list:

Model Building in Mathematical Programming. H.P. Williams, Wiley, 5th edition, 2013.

Hard copies of the above book are available from the University libraries, but electronic copies of the relevant chapters are made available in Moodle.

The optimization models for these problems are given in sections 13.25 and 13.26, while the optimal solutions are described in sections 14.25 and 14.26 respectively. Study the descriptions, optimization models and optimal solutions for these problems to make sure you understand them well. In what follows, Car Rental refers to the integrated problem, that is, the model for Car Rental 1 then extended from Car Rental 2.

Develop an Excel spreadsheet model to solve the Car Retal optimization problem. The spreadsheet model should execute with no errors, even if the model is not complete or does not produce the correct optimal solution. Make sure to include appropriate labels and comments in the spreadsheet model to clarify the approach. Also include annotations and comments in the spreadsheet model to clearly illustrate the corresponding algebraic model being implemented, whether it follows the model given in the book or not. Good principles of spreadsheet modelling should be followed whenever possible.

Develop an LP-Solve model to solve the Car Rental optimization problem. The LP-Solve model should execute with no errors, even if the model is not complete or does not produce the correct optimal solution. Make sure to include appropriate comments in the LP-Solve model to clarify the algebraic formulation. Also include the algebraic compact notation as comments in the LP-Solve model to clearly illustrate the correspondence between each algebraic expression and the constraints implemented in the LP-Solve model. Explain the correspondence of your LP-Solve model to the algebraic model provided in the book and to the Excel spreadsheet model.

Develop a short demonstration video of maximum 15 minutes duration that describes the design and use of your spreadsheet model, the implementation of the LP-Solve model as well as the correspondence between the two models. The demonstration video should clearly explain in a logical and coherent way, the implementation of the spreadsheet and LP-Solve models with references to the algebraic model. The video should also describe how the spreadsheet model was designed (layout, calculations, solver settings, etc.) and how it can be used to understand the solution found. The video may also describe any issues, additional insights, reflections, and clarifications about your work. There is no need to describe the given optimization problem but references to it and the LP-Solve algebraic model might be needed. It is required that you appear in the video and holding your student ID card, even if for only a few seconds at the beginning, this is to confirm your identity as the person presenting the video. Any appropriate software may be used for producing the video, but please make sure the video file can be played in standard media players and/or Internet browsers. Also, please aim to keep the size of the file as small as possible while still ensuring good viewing quality. The maximum file size allowed for the video is 150MB. Make sure to select in advance suitable software to record your video without exceeding the maximum file size.3

MARKING CRITERIA FOR COURSEWORK SUBMISSION

The purpose of this coursework is to assess your ability to understand and interpret an optimization problem and to implement the corresponding optimization model. If there is any element of the problem that is not entirely clear to you, please attempt to interpret such element in the best way you can and explain your rationale in the demonstration video. The given algebraic model for the problem might not be described in full detail and hence you will have to achieve an understanding of the model. If your optimization model or optimal solution do not correspond to the ones given in the book, then please explain as appropriate. Although you should endeavour to provide the correct model, this does not mean that all marks will be lost because of your model not finding the correct optimal solution. Marks are awarded for correctness but also for quality of the work as follows:

Correct Spreadsheet Model (30 marks): this refers to the spreadsheet model being fully correct in terms of modelling and solving the optimization problem, any innovative modelling mechanisms implemented, and the correspondence to the LP-Solve model.

Quality of Spreadsheet Model (20 marks): this refers to layout and presentation of the spreadsheet model for clarity and usability, any additional features developed to enhance the visualisation of the model and the solution, any additional features developed to enhance the implementation and usability of the model.

Correct and Clear LP-Solve Model (20 marks): this refers to the LP-solve model being fully correct and clear in terms of modelling, the lp-solve model solving the optimization problem correctly, and the correspondence to the spreadsheet model.

Quality of Demonstration Video (30 marks): this refers to the effectiveness and the visual quality of the video in explaining the optimization models, the optimal solutions obtained, any issues/insights/reflections that enhance the demonstration, video following the given guidelines.

IMPORTANT: Please note that since the reference optimization model and optimal solution are already provided, not questions will be asked about the interpretation or understanding of the problem, the reference model, or the reference optimal solution. If you think there is any error in the book sections provided, you are welcome to implement fixes and describe them in your demonstration video.