Scheduling batches with simultaneous job processing for two-machine shop problems

We consider the problem of scheduling independent jobs on two machines in an open shop, a job shop and a flow shop environment. Both machines are batching machines, which means that several operations can be combined into a batch and processed simultaneously on a machine. The batch processing time is the maximum processing time of operations in the batch, and all operations in a batch complete at the same time. Such a situation may occur, for instance, during the final testing stage of circuit board manufacturing, where burn-in operations are performed in ovens. We consider cases in which there is no restriction on the size of a batch on a machine, and in which a machine can process only a bounded number of operations in one batch. For most of the possible combinations of restrictions, we establish the complexity status of the problem.

Two-Machine Shop Scheduling with an Uncapacitated Interstage Transporter

In this paper we study the two-machine flow shop and open shop problems to minimize the makespan with a single interstage transporter that may carry any number of jobs between the machines at a time. For each of these problems we present a best possible approximation algorithm within a class of schedules with at most two shipments. As a by-product of this research, for the problem of minimizing the makespan on parallel identical machines we analyze the ratio of the makespan for a non-preemptive schedule over the makespan of a preemptive schedule.

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.

Two-stage no-wait scheduling models with setup and removal times separated

This paper studies two models of two-stage processing with no-wait in process. The first model is the two-machine flow shop, and the other is the assembly model. For both models we consider the problem of minimizing the makespan, provided that the setup and removal times are separated from the processing times. Each of these scheduling problems is reduced to the Traveling Salesman Problem (TSP). We show that, in general, the assembly problem is NP-hard in the strong sense. On the other hand, the two-machine flow shop problem reduces to the Gilmore-Gomory TSP, and is solvable in polynomial time. The same holds for the assembly problem under some reasonable assumptions. Using these and existing results, we provide a complete complexity classification of the relevant two-stage no-wait scheduling models.

Scheduling for parallel dedicated machines with a single server

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. (c) 2000 John Wiley & Sons, Inc.

Two-machine flowshop scheduling problems with no-wait jobs

We study a two-machine flow shop scheduling problem with no-wait in process, in which one of the machines is not available during a specified time interval. We consider three scenarios of handing the operation affected by the nonavailability interval. Its processing may (i) start from scratch after the interval, or (ii) be resumed from the point of interruption, or (iii) be partially restarted after the interval. The objective is to minimize the makespan. We present an approximation algorithm that for all these scenarios delivers a worst-case ratio of 3/2. For the second scenario, we offer a 4/3-approximation algorithm.