General mathematical model and timetabling problems: Expansion and application to real-time timetabling

Abstract

In this study, we illustrate two additional main requirements needed in a general model developed previously for scheduling problems. These two constraints are mutual constraints that can be found mostly in problems such as maritime crew scheduling, course timetabling and others related. The extended general model is then verified with six different timetabling problems with randomly generated data and further verified its applicability towards a real problem of examination course timetabling of a public university in Malaysia. The mathematical model is tested with a specific range of preferences value that represents their preferred assignments to slots and venues. We used Mixed-Integer Linear Programming (MILP) to formulate the whole idea and results reported are analysed with Advanced Interactive Multimedia Modelling System (AIMMS) mathematical software and CPLEX as the solver. Optimised solutions were gained for the various problems, which includes the application to the real problem of examination timetabling using the general model constructed. These indicate the assignments were allocated to where it is most desired. The study has proven its applicability to one of the most complicated scheduling problems. We aim for more application to other real problems thus therefore could be classified as a standard model used for all type of scheduling problems.