Related papers: Revisiting Johnson's rule for minimizing makespan …
In the present scenario the recent engineering and industrial built-up units are facing hodgepodge of problems in a lot of aspects such as machining time, electricity, man power, raw material and customers constraints. The job-shop…
We consider the following special case of minimizing makespan. A set of jobs $J$ and a set of machines $M$ are given. Each job $j \in J$ can be scheduled on a machine from a subset $M_j$ of $M$. The processing time of $j$ is the same on all…
This paper studies a combinatorial optimization problem which is obtained by combining the flow shop scheduling problem and the shortest path problem. The objective of the obtained problem is to select a subset of jobs that constitutes a…
We consider some flow-time minimization problems in the unrelated machines setting. In this setting, there is a set of $m$ machines and a set of $n$ jobs, and each job $j$ has a machine dependent processing time of $p_{ij}$ on machine $i$.…
We consider a special case of the ordinary NP-hard two-machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs. In [S. S. Panwalkar, C. Koulamas, An O(n^2)…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job…
We consider the routing flow shop problem with two machines on an asymmetric network. For this problem we discuss properties of an optimal schedule and present a polynomial time algorithm assuming the number of nodes of the network to be…
Linear programming is a powerful method in combinatorial optimization with many applications in theory and practice. For solving a linear program quickly it is desirable to have a formulation of small size for the given problem. A useful…
We consider the problem of scheduling $n$ jobs to minimize the makespan on $m$ unrelated machines, where job $j$ requires time $p_{ij}$ if processed on machine $i$. A classic algorithm of Lenstra et al. yields the best known approximation…
The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a…
We consider the problem of minimizing the makespan in a flowshop involving maximal and minimal time lags. Time lag constraints generalize the classical precedence constraints between operations. We assume that such constraints are only…
We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give linear-time algorithms to compute all non-dominated…
We consider a 1-machine scheduling problem where the temperature of a job rises during processing, and cools down when not being processed according to given linear heating and cooling rates. No job's temperature is allowed to rise above a…
In this paper, we consider an NP-hard problem of scheduling a set of jobs of equal processing time on two machines, given a partial precedence order on the set of jobs, with an objective to minimize the makespan. An approximation algorithm…
Since its development in the early 90's, parameterized complexity has been widely used to analyze the tractability of many NP-hard combinatorial optimization problems with respect to various types of problem parameters. While the generic…
We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in…
The minimization of makespan in open shop with time lags has been shown NP-hard in the strong sense even for the case of two machines and unit-time operations. The minimization of total completion time however has remained open for that…
The open shop problem is to find a minimum makespan schedule to process each job $J_i$ on each machine $M_q$ for $p_{iq}$ time such that, at any time, each machine processes at most one job and each job is processed by at most one machine.…
We study the problem of preemptive scheduling n jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. We show that when all jobs have equal processing times then the problem can…