NP-hardness of shop-scheduling problems with three jobs

Design of a genetic algorithm for bi-objective flow shop scheduling problems with re-entrant jobs

This paper presents a simulated genetic algorithm (GA) model of scheduling the flow shop problem with reentrant jobs. The objective of this research is to minimize the weighted tardiness and makespan. The proposed model considers that the jobs with non-identical due dates are processed on the machines in the same order. Furthermore, the re-entrant jobs are stochastic as only some jobs are requi...

On the NP-hardness of scheduling with time restrictions

In a recent paper, Braun, Chung and Graham [1] have addressed a single-processor scheduling problem with time restrictions. Given a fixed integer B ≥ 2, there is a set of jobs to be processed by a single processor subject to the following B-constraint. For any real x, no unit time interval [x, x+1) is allowed to intersect more than B jobs. The problem has been shown to be NP-hard when B is part...

Makespan Minimization on Three-Machine Flow shop with deteriorating jobs

In this study, we consider a permutation flow shop scheduling problem on a three-machine with deteriorating jobs (a deteriorating job means that the job’s processing time is an increasing function of its starting time) so as to minimize the makespan. We model job deterioration as a function that is proportional to a linear function of time. For some special cases, we prove that the problem can ...

Flexible Job-Shop Scheduling Problems

Planning and scheduling problems in various industrial environments are combinatorial and very difficult. Generally, it is extremely hard to solve these types of problems in their general form. Scheduling can be formulated as a problem of determining the best sequence to execute a set of tasks on a set of resources, respecting specific constraints like precedence or disjunctive constraints (Car...

Two Stage Flow Shop Scheduling Problem Including Transportation Time and Weightage of Jobs with Branch and Bound Method