Heuristic algorithms for a military training timetabling problem

Abstract

We suggest several algorithms for a military training timetabling problem (MTTP) that occurs in the Korea army. The MTTP is a generalized version of the professor-lecturer model that was considered for the first time in 1980. Professor-lecturer model is composed of several elements: classes, groups, professors that have only group-lectures and lecturers that have only individual-lectures. Unlike the typical professor-lecturer model, one needs to consider additional constraints to reflect restrictions in real situation, such as those for lunch time, duration of each lecture (2 hours and 4 hours), set-up time occurs between the lectures have different place for lecture (indoor and outdoor) and so on. Since this type of problem is known to be NP-hard, in this research, we propose heuristic algorithms to obtain a reasonably good solution in a reasonable amount of computation time. Since the MTTP is closely related with the edge-coloring problem of a bipartite graph, which is the problem of minimizing the number of colors to color all edges in such a way that adjacent edges receive different colors, we use results of previous research on the graph theory. We present three algorithms including four edge-ordering rules for finding a solution on a bipartite graph, and each edge-ordering rule has weight factors concerned about types of teachers and places for lectures. Results of a series of computational experiments show that the suggested algorithms give good schedules in a reasonably short time and that they can be applied to the real situation.