An improved on-line algorithm for scheduling on two unrestrictive parallel batch processing machines

Abstract

Abstract.We consider the problem of on-line scheduling a set of n jobs on two parallel batch processing machines. Each machine can handle an infinite number of jobs as a batch simultaneously. The processing time of a batch is the time required for processing the longest job in the batch. Each job becomes available at its release date, which is not known in advance, and its processing time only becomes known at its arrival. We deal with the problem of minimizing the makespan. We provide an algorithm for the problem that is better than one given in the literature, improving the competitive ratio from

Online scheduling on unbounded parallel-batch machines to minimize the makespan

“…Consequently, we have C max (σ ) S k + p k + p n C max (σ ). (9) Claim 5. For every job J x ∈ I with S x < S 1 , p x < p 1 .…”

“…(See Nong et al [9].) Without decreasing the ratio of C max (σ )/C max (π ), we can assume that there is only one job in each batch of σ .…”

“…Specifically, they gave a lower bound √ 2 on the competitive ratio, and presented a dense-algorithm with a competitive ratio √ 5+1 2 . When all the jobs have equal processing times, Zhang et al [15] established two best possible online algorithms with competitive ratios 1 + ξ m and Nong et al [9] and Tian et al [5] provided different online algorithms with the same competitive ratio √ 2; and the latter authors also provided a lower bound √ 2 on the competitive ratio. So both algorithms provided in [9] and [5] are best possible.…”

The openshop batch processing problem with non-identical processing times, using simulated annealing and genetic algorithms approaches

“…Melouk et al [2] and Kashan et al [3] used metaheuristic algorithms, including simulated annealing (SA) and hybrid genetic algorithms (GA) to solve the single batch processing problem with makespan objective, respectively; Wang and Chou [4] used SA and GA simultaneously to solve the problem. Ridouard et al [5] studied online scheduling problem on a BPM and Nong et al [6] and Liu et al [7] studied online scheduling problem on two parallel BPMs. All the three recent papers considered makespan objective and offered some algorithms to solve the problems.…”

Online scheduling on two parallel-batching machines with limited restarts to minimize the makespan

“…For the bounded case, they proposed a √ 5+1 2 -competitive best possible online algorithm. Nong et al [8] investigated online scheduling on two unbounded parallel-batching machines and proposed an online algorithm that is √ 2-competitive; for m (an input number) unbounded parallel-batching machines, Liu et al [6] and Tian et al [10] independently proposed two different but best possible online algorithms with a competitive ratio 1 + α m , where α m is the positive solution of the equation α 2 m + mα m − 1 = 0.…”