Exam timetabling with allowable conflicts within a time window

Omar Abou Kasm, Baraa Mohandes, Ali Diabat, Sameh El Khatib

    Research output: Contribution to journalArticle

    Abstract

    The exam timetabling problem is considered an NP-complete problem and its complexity depends on the different constraints and policies set by an institution's administration. The goal of this work is to facilitate exam timetabling for Masdar Institute (MI), which is a graduate level institution. Besides the renowned constraint on conflicts for students, MI's timetabling case includes the incorporation of venues’ limited capacities, special instructor requests, and the number of exams scheduled for one student within a preset window of days. To the best knowledge of the authors, the latter constraint is new to the literature. Moreover, it increases the problem's complexity since it requires cross-validation on both student and course levels. This contrasts with conventional exam timetabling which only deals with checks on a course level. We introduce an integer programming (IP) formulation that captures all the studied constraints. The proposed formulation can solve small problems using commercial software; however, this formulation's performance deteriorates as the problem size increases. Therefore, the paper proposes heuristics to solve medium and large sized problems in a timely manner. This study employs graph coloring algorithms that include a new approach, within the steps of the proposed exam timetabling heuristics. Four real-case studies from MI are solved to illustrate the feasibility and competitiveness of the proposed heuristic. Finally, a computational study is presented to benchmark the proposed heuristics against the IP formulation. The results show that the proposed heuristics are capable of obtaining optimal and near-optimal solutions in smaller computational time.

    Original languageEnglish (US)
    Pages (from-to)263-273
    Number of pages11
    JournalComputers and Industrial Engineering
    Volume127
    DOIs
    StatePublished - Jan 1 2019

    Fingerprint

    Integer programming
    Students
    Coloring
    Computational complexity

    Keywords

    • Case studies
    • Exam timetabling
    • Graph theory
    • Integer programming
    • Largest box algorithm
    • NP-complete problem

    ASJC Scopus subject areas

    • Computer Science(all)
    • Engineering(all)

    Cite this

    Exam timetabling with allowable conflicts within a time window. / Abou Kasm, Omar; Mohandes, Baraa; Diabat, Ali; El Khatib, Sameh.

    In: Computers and Industrial Engineering, Vol. 127, 01.01.2019, p. 263-273.

    Research output: Contribution to journalArticle

    Abou Kasm, Omar ; Mohandes, Baraa ; Diabat, Ali ; El Khatib, Sameh. / Exam timetabling with allowable conflicts within a time window. In: Computers and Industrial Engineering. 2019 ; Vol. 127. pp. 263-273.
    @article{2eb2f2db166a4039aa1e695e7755a660,
    title = "Exam timetabling with allowable conflicts within a time window",
    abstract = "The exam timetabling problem is considered an NP-complete problem and its complexity depends on the different constraints and policies set by an institution's administration. The goal of this work is to facilitate exam timetabling for Masdar Institute (MI), which is a graduate level institution. Besides the renowned constraint on conflicts for students, MI's timetabling case includes the incorporation of venues’ limited capacities, special instructor requests, and the number of exams scheduled for one student within a preset window of days. To the best knowledge of the authors, the latter constraint is new to the literature. Moreover, it increases the problem's complexity since it requires cross-validation on both student and course levels. This contrasts with conventional exam timetabling which only deals with checks on a course level. We introduce an integer programming (IP) formulation that captures all the studied constraints. The proposed formulation can solve small problems using commercial software; however, this formulation's performance deteriorates as the problem size increases. Therefore, the paper proposes heuristics to solve medium and large sized problems in a timely manner. This study employs graph coloring algorithms that include a new approach, within the steps of the proposed exam timetabling heuristics. Four real-case studies from MI are solved to illustrate the feasibility and competitiveness of the proposed heuristic. Finally, a computational study is presented to benchmark the proposed heuristics against the IP formulation. The results show that the proposed heuristics are capable of obtaining optimal and near-optimal solutions in smaller computational time.",
    keywords = "Case studies, Exam timetabling, Graph theory, Integer programming, Largest box algorithm, NP-complete problem",
    author = "{Abou Kasm}, Omar and Baraa Mohandes and Ali Diabat and {El Khatib}, Sameh",
    year = "2019",
    month = "1",
    day = "1",
    doi = "10.1016/j.cie.2018.11.037",
    language = "English (US)",
    volume = "127",
    pages = "263--273",
    journal = "Computers and Industrial Engineering",
    issn = "0360-8352",
    publisher = "Elsevier Limited",

    }

    TY - JOUR

    T1 - Exam timetabling with allowable conflicts within a time window

    AU - Abou Kasm, Omar

    AU - Mohandes, Baraa

    AU - Diabat, Ali

    AU - El Khatib, Sameh

    PY - 2019/1/1

    Y1 - 2019/1/1

    N2 - The exam timetabling problem is considered an NP-complete problem and its complexity depends on the different constraints and policies set by an institution's administration. The goal of this work is to facilitate exam timetabling for Masdar Institute (MI), which is a graduate level institution. Besides the renowned constraint on conflicts for students, MI's timetabling case includes the incorporation of venues’ limited capacities, special instructor requests, and the number of exams scheduled for one student within a preset window of days. To the best knowledge of the authors, the latter constraint is new to the literature. Moreover, it increases the problem's complexity since it requires cross-validation on both student and course levels. This contrasts with conventional exam timetabling which only deals with checks on a course level. We introduce an integer programming (IP) formulation that captures all the studied constraints. The proposed formulation can solve small problems using commercial software; however, this formulation's performance deteriorates as the problem size increases. Therefore, the paper proposes heuristics to solve medium and large sized problems in a timely manner. This study employs graph coloring algorithms that include a new approach, within the steps of the proposed exam timetabling heuristics. Four real-case studies from MI are solved to illustrate the feasibility and competitiveness of the proposed heuristic. Finally, a computational study is presented to benchmark the proposed heuristics against the IP formulation. The results show that the proposed heuristics are capable of obtaining optimal and near-optimal solutions in smaller computational time.

    AB - The exam timetabling problem is considered an NP-complete problem and its complexity depends on the different constraints and policies set by an institution's administration. The goal of this work is to facilitate exam timetabling for Masdar Institute (MI), which is a graduate level institution. Besides the renowned constraint on conflicts for students, MI's timetabling case includes the incorporation of venues’ limited capacities, special instructor requests, and the number of exams scheduled for one student within a preset window of days. To the best knowledge of the authors, the latter constraint is new to the literature. Moreover, it increases the problem's complexity since it requires cross-validation on both student and course levels. This contrasts with conventional exam timetabling which only deals with checks on a course level. We introduce an integer programming (IP) formulation that captures all the studied constraints. The proposed formulation can solve small problems using commercial software; however, this formulation's performance deteriorates as the problem size increases. Therefore, the paper proposes heuristics to solve medium and large sized problems in a timely manner. This study employs graph coloring algorithms that include a new approach, within the steps of the proposed exam timetabling heuristics. Four real-case studies from MI are solved to illustrate the feasibility and competitiveness of the proposed heuristic. Finally, a computational study is presented to benchmark the proposed heuristics against the IP formulation. The results show that the proposed heuristics are capable of obtaining optimal and near-optimal solutions in smaller computational time.

    KW - Case studies

    KW - Exam timetabling

    KW - Graph theory

    KW - Integer programming

    KW - Largest box algorithm

    KW - NP-complete problem

    UR - http://www.scopus.com/inward/record.url?scp=85058777890&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=85058777890&partnerID=8YFLogxK

    U2 - 10.1016/j.cie.2018.11.037

    DO - 10.1016/j.cie.2018.11.037

    M3 - Article

    AN - SCOPUS:85058777890

    VL - 127

    SP - 263

    EP - 273

    JO - Computers and Industrial Engineering

    JF - Computers and Industrial Engineering

    SN - 0360-8352

    ER -