Scheduling for parallel dedicated machines with a single server

Abstract

This paper examines scheduling problems in which the setup phase of each operation needs to be attended by a single server, common for all jobs and different from the processing machines. The objective in each situation is to minimize the makespan. For the processing system consisting of two parallel dedicated machines we prove that the problem of finding an optimal schedule is NP -hard in the strong sense even if all setup times are equal or if all processing times are equal. For the case of m parallel dedicated machines, a simple greedy algorithm is shown to create a schedule with the makespan that is at most twice the optimum value. For the two machine case, an improved heuristic guarantees a tight worst-case ratio of 3/2. We also describe several polynomially solvable cases of the later problem. The two-machine flow shop and the open shop problems with a single server are also shown to be NP -hard in the strong sense. However, we reduce the two-machine flow shop no-wait problem with a single server to the Gilmore-Gomory traveling salesman problem and solve it in polynomial time.

Flow shop scheduling to minimize the total completion time with a permanently present operator: Models and ant colony optimization metaheuristic

“…Constraints (18) show that each job should exactly be assigned to a position on each machine. Constraints (19) mean that each position must be assigned with a job exactly. Constraints (20) require that position on each machine must be associated with a rank.…”

Scheduling jobs with equal processing times and a single server on parallel identical machines

“…But immediately after it is finished, the server becomes released and the machine has to process the job till completion without preemption. The problem is interesting because it occurs in many scenarios of production environments, like the network computing [5], the textile industry [1], the third-party logistics [11] and so on.…”

“…Kravchenko and Werner settled the complexity of one open problem (the existence of pseudopolynomial algorithms for minimizing the makespan with unit setup times) and the problem of minimizing the forced idle times [9]. Glass et al [5] considered the single server scheduling on dedicated machines, where both the complexity and the approximation results for problems of minimizing the makespan are provided. The two-machine flow shop scheduling problem is studied in [3,4,12,13], where quite a number of complexity results are obtained.…”

Parallel machine scheduling with additional resources: Notation, classification, models and solution methods

“…PMS problems with input/output resources are dealt with in Blazewicz et al (2004), Hall et al (2000) and Glass et al (2000). Comprehensive studies on continuous resources can be found in Jozefowska and Weglarz (2004) and Blazewicz et al (2007), while an example study related to non-renewable resources is given by Shabtay and Kaspi (2006), and a doubly constrained project scheduling problem is presented by Ozdamar and Ulusoy (1994).…”