Related papers: Arc-flow approach for single batch-processing mach…
In the classical interval scheduling type of problems, a set of $n$ jobs, characterized by their start and end time, need to be executed by a set of machines, under various constraints. In this paper we study a new variant in which the jobs…
This paper addresses the problem of scheduling a set of jobs that are released over the time on a set of identical parallel machines, aiming at the minimization of the total weighted completion time. This problem, referred to as $P|r_j|\sum…
In this paper, we study the following batch scheduling model: find a schedule that minimizes total flow time for $n$ uniform length jobs, with release times and deadlines, where the machine is only actively processing jobs in at most $k$…
The paper considers scheduling on parallel machines under the constraint that some pairs of jobs cannot be processed concurrently. Each job has an associated weight, and all jobs have the same deadline. The objective is to maximise the…
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…
This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the…
We consider the problem of scheduling multiprocessor jobs to minimize the total completion time under the given energy budget. Each multiprocessor job requires more than one processor at the same moment of time. Processors may operate at…
We consider online preemptive scheduling of jobs arriving one by one, to be assigned to two identical machines, with the goal of makespan minimization. We study the effect of selecting the best solution out of two independent solutions…
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are…
The problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in…
We consider the flow network model to solve the multiprocessor real-time task scheduling problems. Using the flow network model or its generic form, linear programming (LP) formulation, for the problems is not new. However, the previous…
Scheduling on dataflow graphs (also known as computation graphs) is an NP-hard problem. The traditional exact methods are limited by runtime complexity, while reinforcement learning (RL) and heuristic-based approaches struggle with…
Many academic disciplines - including information systems, computer science, and operations management - face scheduling problems as important decision making tasks. Since many scheduling problems are NP-hard in the strong sense, there is a…
This paper examines scheduling problem denoted as $P|seq, ser|C_{max}$ in Graham's notation; in other words, scheduling of tasks on parallel identical machines ($P$) with sequence-dependent setups ($seq$) each performed by one of the…
The minimum cost flow problem is one of the most studied network optimization problems and appears in numerous applications. Some efficient algorithms exist for this problem, which are freely available in the form of libraries or software…
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…
We study the computational complexity of scheduling jobs on a single speed-scalable processor with the objective of capturing the trade-off between the (weighted) flow time and the energy consumption. This trade-off has been extensively…
Network flow formulations are among the most successful tools to solve optimization problems. Such formulations correspond to determining an optimal flow in a network. One particular class of network flow formulations is the arc flow, where…
We deal with a challenging scheduling problem on parallel machines with sequence-dependent setup times and release dates from a real-world application of semiconductor work-shop production. There, jobs can only be processed by dedicated…
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…