Ateneo - UPO

Linear programming, project management, inventory management, introduction to programming in R.

- Bellenzier L., Grassi R., Stefani S., Torriero A., Metodi quantitativi per il Management, Esculapio, 2012. - Hillier S., Lieberman G.J., Ricerca Operativa, 9/ed., McGraw Hill, 2010 (please follow the instructions published on the DIR site). - Garrett Grolemund, Hands-On Programming with R: Write Your Own Functions and Simulations, O'Reilly Media, 2014 (also available online. Please follow the instructions published on the DIR site)

At the end of the course, the student should know the technical instruments of operation management, in order to solve simple management problems using a quantitative approach. They should learn concepts and terminology of some optimization procedure techniques and project management. They should also be able to apply quantitative methods to simple problems also using R programming (or Excel) and to justify in a sufficiently rigorous way the implemented solutions.

The course is worth 8 ECTS credits, corresponding to 60 hours of face-to-face teaching. Overall, approximately 40 hours are delivered as direct instruction (DE) and 20 hours as interactive teaching (DI). The allocation between these two teaching modes is flexible and may vary across individual class sessions.

Solution of Linear Algebraic systems. Notions of random variable and probability distribution. Basic differential calculus in one or more variables.

Lectures and practise exercise and computer laboratory.
The course is worth 8 ECTS credits, corresponding to 60 hours of face-to-face teaching. Overall, approximately 40 hours are delivered as direct instruction (DE) and 20 hours as interactive teaching (DI). The allocation between these two teaching modes is flexible and may vary across individual class sessions.

Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The exam consists of a written test and an oral test, both compulsory. The oral test may only be taken after passing the written test.

Written test (duration: 90 minutes) covers the modules on Linear Programming, Project Management and Inventory Management. It consists of 3 exercises, one for each of the following topics:

● formulation and solution of a linear programming problem including elements of sensitivity analysis;
● construction of a project graph and application of CPM/PERT techniques (calculation of the critical path and slacks) and optimization of the trade-off duration/costs;
● application of an inventory management model (with deterministic or random demand) to calculate the economic order quantity or the reorder level.

Each exercise assesses the ability to translate a management problem into a quantitative model, to correctly apply the solving technique, and to argue the result. Each exercise, if completed fully and correctly, is awarded up to 10 points (30 points total). The written test is considered passed with a score of no less than 18/30, and this score is the starting grade for the oral test.

Oral test (covers the introductory module on programming in R, as well as any clarifications on the written test). The candidate must:

● demonstrate knowledge of the basic syntax of R and the functions used to implement the techniques covered in class;
● solve or comment on a short script/applied problem in R, connecting the software tool to the quantitative models studied;
● argue, using appropriate technical language, the modelling choices made in the written test, showing the ability to self-correct if prompted.

Overall assessment criteria
Pass (18/30): written test passed and, in the oral test, knowledge of the fundamental concepts of R and of the functions essential to implementing the models, albeit with some uncertainty.
Good (24-27/30): command of the written topics and the ability to use R independently on problems similar to those covered in class, identifying and correcting any errors.
Excellent (30 cum laude): full autonomy in the use of R, the ability to tackle non-standard variants of the proposed problems, and a clear, rigorous and well-argued presentation of conclusions.

The final grade is a single grade: the oral test may raise or lower the score obtained in the written test, depending on performance.

To prepare for the written test, students are advised to consult Bellenzier et al. and Hillier-Lieberman (chapters on the simplex method, PERT/CPM, inventory management). For the oral test, the Grolemund textbook and the R lab materials published on the DIR website.

Linear programming: examples, definitions, simplex algorithm and its implementation in Excel. Duality, sensitivity analysis with exemplifications in Excel, Integer Linear Programming (HINT). Project management: project graphs, Gantt chart, CPM and PERT. Inventory management: Economic order quantity model with deterministic demand, one period model with random demand, basic idea of the dynamic programming technique. Introduction to R programming, with practical examples based on the first three topics of the course.

By the end of the course, students will have achieved the following learning outcomes, structured according to the Dublin Descriptors.

Knowledge and understanding.
Knowledge of the theoretical foundations and terminology of the main optimization techniques covered: linear programming (the graphical method and sensitivity analysis), network-based project management techniques (CPM/PERT) and inventory management models, as well as the basic elements of the R programming language.

Applying knowledge and understanding.
Ability to apply the techniques studied to solve practical problems of resource and project planning and management, including through the use of the R language (or a spreadsheet), arguing the implemented solutions with sufficient rigour.

Making judgements.
Ability to identify, among the quantitative techniques presented, the one most suitable for a given management problem, and to critically assess the plausibility and consistency of the results obtained with respect to the application context.

Communication skills.
Ability to present, both in written and oral form, the model's assumptions, the solution method adopted and the results obtained, using appropriate technical language and clear, well-structured arguments.

Learning skills.
Ability to independently apply the R programming tools learned during the course to new problems not explicitly covered in class, identifying and correcting any errors on their own.