Solving Discrete-Continuous Scheduling Problems by Tabu Search

In this paper we consider discrete-continuous scheduling problems defined in [7], where general results and methodology have been presented as well. These problems are characterized by the fact that each job simultaneously requires for its processing at a time discrete and continuous (i.e. continuouslydivisible) resources. We deal with a class of these problems where there are: one discrete resource, which is a set of parallel, identical machines, and one continuous, renewable resource whose total amount available at a time is limited. Jobs are independent and nonpreemptable and their ready times are equal to 0. The processing rate of each job depends on the amount of the continuous resource assigned to this job at a time. The makespan, the mean flow time and the maximum lateness are considered as the scheduling criteria. The tabu search (TS) metaheuristic to solve the considered problems is discussed. A performance analysis of tabu search for discrete-continuous scheduling problems is presented. Results obtained by tabu search are compared to optimal solutions as well as to results produced by other two metaheuristics: simulated annealing (SA) and genetic algorithms (GA). Moreover, three tabu list management methods: the Tabu Navigation Method (TNM), the Cancellation Sequence Method (CSM) and the Reverse Elimination Methods (REM) are compared. Several computational experiments are described and some conclusions and final remarks are included.