In this paper we study two generalizations of the well known unrelated parallel machines scheduling problem under makespan (Cmax) minimization. First, a situation in which not every available parallel machine should be used and it is desirable to employ only a subset of the parallel machines. This is referred to as “Not all Machines” or NAM in short. This environment applies frequently in produ...

In this paper we propose a tabu search implementation to solve the unrelated parallel machines scheduling problem with sequenceand machinedependent setup times to minimize the schedule’s makespan. The problem is NP-hard and finding an optimal solution efficiently is unlikely. Therefore, heuristic techniques are more appropriate to find near-optimal solutions. The proposed tabu search algorithm...

A new hybrid flow shop scheduling problem with blocking is studied. The problem is characterized by multistage unrelated parallel machines and no intermediate buffer. Firstly, the math model of the hybrid scheduling problem is constructed. And then the computation method of production period is given. Due to there is no intermediate buffer, and there are unrelated parallel machines in multi-sta...

We discuss scheduling problems with m identical machines and n jobs where each job has to be assigned to some machine. The goal is to optimize objective functions that solely depend on the machine completion times. As a main result, we identify some conditions on the objective function, under which the resulting scheduling problems possess a polynomial time approximation scheme. Our result cont...

In classical shop scheduling, the tasks corresponding to a job may not be executed in parallel, i.e., their processing times may not overlap. In case these tasks are processes , independent of each other, this assumption is no longer justified. We consider corresponding scheduling problems where each job splits into a number of pairwise independent processes that have to be executed on dedicate...

We consider preemptive machine scheduling problems on identical parallel machines. It is shown that every such problem with chain-like precedence constraints, release dates and a regular unit-concave objective function has the following integer preemption property : for any problem instance with integral input data there exists an optimal schedule where all interruptions (as well as starting an...

We consider an online version of the classical problem of preemptive scheduling on uniformly related machines. We are given m machines with speeds s 1 ≥ s 2 ≥. .. ≥ s m and a sequence of jobs, each described by its processing time (length). The actual time needed to process a job with length p on a machine with speed s is p/s. In the preemptive version, each job may be divided into several piec...

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tr...

We address a generalization of the classical multiprocessor scheduling problem with non simultaneous machine availability times, release dates, and delivery times. We develop new lower and upper bounds as well as a branching strategy which is based on a representation of a schedule as a permutation of jobs. We show that embedding a semi-preemptive lower bound based on max-flow computations in a...

We consider scheduling a batch of jobs with stochastic processing times on parallel machines. We derive various new formulae for the expected flowtime and weighted flowtime under general scheduling rules. Smith's Rule, which orders job starts by decreasing ratio of weight to expected processing time provides a natural heuristic for this problem. We obtain a bound on the worst case difference be...