An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects

The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a stable matching of students to projects (and lecturers). However, these stable matchings can have different sizes, and the problem of finding a maximum stable matching (MAX-SPA-P) is NP-hard. There are two known approximation algorithms for MAX-SPA-P, with performance guarantees of 2 and 32 . In this paper, we describe an Integer Programming (IP) model to enable MAX-SPA-P to be solved optimally. Following this, we present results arising from an empirical analysis that investigates how the solution produced by the approximation algorithms compares to the optimal solution obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. Our main finding is that the 32 -approximation algorithm finds stable matchings that are very close to having maximum cardinality

Artificial intelligence tools for academic management: assigning students to academic supervisors

[EN] In the last few years, there has been a broad range of research focusing on how learning should take place both in the classroom and outside the classroom. Even though academic dissertations are a vital step in the academic life of both students, as they get to employ all their knowledge and skills in an original project, there has been limited research on this topic. In this paper we explore the topic of allocating students to supervisors, a time-consuming and complex task faced by many academic departments across the world. Firstly, we discuss the advantages and disadvantages of employing different allocation strategies from the point of view of students and supervisors. Then, we describe an artificial intelligence tool that overcomes many of the limitations of the strategies described in the article, and that solves the problem of allocating students to supervisors. The tool is capable of allocating students to supervisors by considering the preferences of both students and supervisors with regards to research topics, the maximum supervision quota of supervisors, and the workload balance of supervisors.Sanchez-Anguix, V.; Chalumuri, R.; Alberola Oltra, JM.; Aydogan, R. (2020). Artificial intelligence tools for academic management: assigning students to academic supervisors. IATED. 4638-4644. https://doi.org/10.21125/inted.2020.1284S4638464

Super-stability in the Student-Project Allocation Problem with Ties

The Student-Project Allocation problem with lecturer preferences over Students ( Open image in new window ) involves assigning students to projects based on student preferences over projects, lecturer preferences over students, and the maximum number of students that each project and lecturer can accommodate. This classical model assumes that preference lists are strictly ordered. Here, we study a generalisation of Open image in new window where ties are allowed in the preference lists of students and lecturers, which we refer to as the Student-Project Allocation problem with lecturer preferences over Students with Ties ( Open image in new window ). We investigate stable matchings under the most robust definition of stability in this context, namely super-stability. We describe the first polynomial-time algorithm to find a super-stable matching or to report that no such matching exists, given an instance of Open image in new window . Our algorithm runs in O(L) time, where L is the total length of all the preference lists. Finally, we present results obtained from an empirical evaluation of the linear-time algorithm based on randomly-generated Open image in new window instances. Our main finding is that, whilst super-stable matchings can be elusive, the probability of such a matching existing is significantly higher if ties are restricted to the lecturers’ preference lists

Student-project allocation with preferences over projects: algorithmic and experimental results

We study the Student-Project Allocation problem with lecturer preferences over Projects (spa-p). In this context it is known that stable matchings can have different sizes and the problem of finding a maximum size stable matching is NP-hard. There are two known approximation algorithms for max-spa-p, with performance guarantees 2 and . We show that max-spa-p is polynomial-time solvable if there is only one lecturer involved, and NP-hard to approximate within some constant if there are two lecturers involved. We also show that this problem remains NP-hard if each preference list is of length at most 3, with an arbitrary number of lecturers. We then describe an Integer Programming (IP) model to enable max-spa-p to be solved optimally in the general case. Following this, we present results arising from an empirical evaluation that investigates how the solutions produced by the approximation algorithms compare to optimal solutions obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets

Optimizing the preference of student-lecturer allocation problem using analytical hierarchy process and integer programming

This paper focuses on solving a student-lecturer allocation problem by optimizing declared preferences. Typically, many students undertake an internship program every semester and many preferences need to be taken when assigning students to lecturer for supervision. The aim is to maximize student’s total preference. Analytic Hierarchy Process (AHP) technique is used in ranking the preference criteria and alternatives to form a preference matrix. Then, an Integer Programming (IP) model is developed by considering related constraints, which involves lecturer capacity according to academic position and matching gender of student to lecturer. This study demonstrates the effectiveness of using AHP technique in prioritizing preference criteria and facilitates finding the best solutions in the context of multiple criteria by using preference matrix. The IP model shows that all constraints are satisfied, and students’ total preferences is maximized. The study demonstrates that the proposed method is efficient and avoids biased assignment. The satisfaction of the gender related constraint and preferences toward lecturers contributes significantly to satisfaction among students and staff

A Three-Phase Multiobjective Mechanism for Selecting Retail Stores to Close

To operate a successful and growing business, a retail store manager has to make tough decisions about selectively closing underperforming stores. In this paper, we propose using a three-phase multiobjective mechanism to help retail industry practitioners determine which stores to close. In the first phase, a geographic information system (GIS) and k-means clustering algorithm are used to divide all the stores into clusters. In the second phase, stores can be strategically selected according to the requirements of the company and the attributes of the stores. In the third phase, a neighborhood-based multiobjective genetic algorithm (NBMOGA) is utilized to determine which stores to close. To examine the effectiveness of the proposed three-phase mechanism, a variety of experiments are performed, based partly on a real dataset from a stock-list company in Taiwan. Results from the experiments show that the proposed three-phase mechanism can help efficiently decide which store locations to close. In addition, the neighborhood radius has a considerable influence on the results

ÖĞRENCİ-PROJE ATAMA PROBLEMİNDE FARKLI GRUP KARARLARININ DEĞERLENDİRİLMESİ

Öğrenci-Proje Atama (ÖPA), genel olarak, çeşitli kriterlerin dikkate alınmasıyla öğrenci-proje gruplarının oluşturmasını ve bu gruplara projelerin atanmasını içeren çok-kriterli bir problem olarak tanımlanabilir. Bu çalışmada, problemin çözümü için üç aşamadan oluşan bir yaklaşım önerilmektedir. Yakın tarihli başka bir çalışmada geliştirilmiş olan bir 0-1 tamsayılı-hedef programlama formülasyonundan adapte edilmiş olan matematiksel programlama modeliyle, çalışmanın ilk aşamasında çeşitli kriterler dikkate alınarak öğrenci-proje gruplarının oluşturulması gerçekleştirilmektedir. Söz konusu kriterler ise (i) bir gruptaki öğrenci sayısı, (ii) genel akademik not ortalaması (GANO) değeri, (iii) yabancı dil, (iv) bilgisayar programlama, (v) genel ofis yazılımları ve (vi) veri tabanı yönetimi yetenekleridir. Sonraki aşamada, grup-proje eşleştirmeleri gerçekleştirilmeden önce, oluşturulan grupların proje tercihleri için grup üyelerinin farklı bakış açılarını yansıtan grup kararları belirlenmektedir. Son olarak, öğrenci-proje gruplarının proje tercihlerine yönelik olarak oluşturulan grup kararları kullanılarak bir 0-1 tamsayılı program ile grup-proje atamaları gerçekleştirilmektedir. Çalışmanın literatüre olan katkısı, önerilen üç aşamalı yaklaşımla, grup kararlarının dikkate alınarak ÖPA probleminin çözülmesi şeklinde özetlenebilir. Böylelikle, farklı bakış açılarına sahip çok sayıdaki öğrencinin tercihleri, ÖPA sürecinde önemli bir kriter olan tercih kriteri için yansız ve tek bir grup kararı olarak ele alınabilmektedir. Önerilen yaklaşım, akademik bir kurumdaki gerçek bir ÖPA problemine uygulanmıştır. Elde edilen sonuçlar, ilgili literatürde bulunan diğer atama yaklaşımlarının sonuçları ile çeşitli performans parametreleri açısından karşılaştırılmıştır ve kriterlerin performans skorlarında ortalama %9 oranında iyileşme olduğu gözlenmiştir