Solving Discrete-Continuous Scheduling Problems by Tabu Search

In this paper we consider discrete-continuous scheduling problems defined in [7], where general resultsand methodology have been presented as well. These problems are characterized by the fact that eachjob simultaneously requires for its processing at a time discrete and continuous (i.e. continuously-divisible) resources. We deal with a class of these problems where there are: one discrete resource,whichisasetofparallel,identicalmachines,andonecontinuous,renewableresourcewhosetotalamountavailableat atime is limited. Jobsareindependent and nonpreemptable and their readytimes areequalto 0. The processing rate of each job depends on the amount of the continuous resource assigned tothis job at a time. The makespan, the mean flow time and the maximum lateness are considered as theschedulingcriteria. The tabusearch(TS)metaheuristictosolvetheconsideredproblemsisdiscussed. Aperformance analysis of tabu search for discrete-continuous scheduling problems is presented. Resultsobtained by tabu search are compared to optimal solutions as well as to results produced by othertwo metaheuristics: simulated annealing (SA) and genetic algorithms (GA). Moreover, three tabu listmanagementmethods: theTabuNavigationMethod(TNM),theCancellationSequenceMethod(CSM)and the Reverse Elimination Methods (REM) are compared. Several computational experiments aredescribed and some conclusions and final remarks are included.