DISCRETE-CONTINUOUS SCHEDULING TO MINIMIZE THE MEAN FLOW TIME — COMPUTATIONAL EXPERIMENTS

Problems of scheduling nonpreemptable jobs which require simultaneously a machine f rom a set of parallel, identical machines and a continuous, renewable resource to minimize the mean flow time are considered. For each job there are known: its processing speed as a continuous, concave function of a continuous resource allotted at a time and its processing demand. The problem can be decomposed into two interrelated subproblems: (i) to sequence jobs on machines, and (ii) to find an optimal (continuous) resource allocation among j o b s already sequenced. For some special cases the problem can be solved in polynomial time. For the general case we propose to use heuristic search methods defined on the space of feasible sequences. Three metaheuristics: Tabu Search, Simulated Annealing and Genetic Algori thm have been implemented and compared computationally. The computational experiment has been carried out on a SGI PowerChallenge XL computer with 12 RISC R8000 processors. Some directions for further research have been pointed out. 1 . P r o b l e m f o r m u l a t i o n T h e discrete-cont inuous s c h e d u l i n g p r o b l e m i s def ined as f o l l o w s ( J ó z e f o w s k a . W ę g l a r z , 1997) . Cons ider n independent, n o n p r e e m p t a b l e j o b s w h i c h s i m u l t a n e o u s l y require f o r their p r o c e s s i n g discrete (i.e. d i screte ly-div i s ib le) and cont inuous (i.e. cont inuous ly-div i s ib le) r e s o u r c e s . T h e discrete r e s o u r c e is a set of m paral le l , identical machines . T h e total amount of the r e n e w a b l e , cont inuous resource a v a i l a b l e at a t ime is l imited. J o b s a r e all a v a i l a b l e a t the s tar t o f the process . P r o c e s s i n g rate of j o b i , i=1,2,. . . ,n, depends on the a m o u n t of the cont inuous r e s o u r c e al lotted to this j o b at t ime t and is d e s c r i b e d by the equat ion: