Minimizing total completion time on a single machine with step improving jobs

Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming (MIP) model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions

Minimizing total completion time on a single machine with step improving jobs

Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming (MIP) model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions

A common framework and taxonomy for multicriteria scheduling problems with Interfering and competing Jobs: Multi-agent scheduling problems

Most classical scheduling research assumes that the objectives sought are common to all jobs to be scheduled. However, many real-life applications can be modeled by considering different sets of jobs, each one with its own objective(s), and an increasing number of papers addressing these problems has appeared over the last few years. Since so far the area lacks a uni ed view, the studied problems have received different names (such as interfering jobs, multi-agent scheduling, mixed-criteria, etc), some authors do not seem to be aware of important contributions in related problems, and solution procedures are often developed without taking into account existing ones. Therefore, the topic is in need of a common framework that allows for a systematic recollection of existing contributions, as well as a clear de nition of the main research avenues. In this paper we review multicriteria scheduling problems involving two or more sets of jobs and propose an uni ed framework providing a common de nition, name and notation for these problems. Moreover, we systematically review and classify the existing contributions in terms of the complexity of the problems and the proposed solution procedures, discuss the main advances, and point out future research lines in the topic

Competitive two-agent scheduling with deteriorating jobs on a single parallel-batching machine

We consider a scheduling problem in which the jobs are generated by two agents and have time-dependent proportional-linear deteriorating processing times. The two agents compete for a common single batching machine to process their jobs, and each agent has its own criterion to optimize. The jobs may have identical or different release dates. The batching machine can process several jobs simultaneously as a batch and the processing time of a batch is equal to the longest of the job processing times in the batch. The problem is to determine a schedule for processing the jobs such that the objective of one agent is minimized, while the objective of the other agent is maintained under a fixed value. For the unbounded model, we consider various combinations of regular objectives on the basis of the compatibility of the two agents. For the bounded model, we consider two different objectives for incompatible and compatible agents: minimizing the makespan of one agent subject to an upper bound on the makespan of the other agent and minimizing the number of tardy jobs of one agent subject to an upper bound on the number of tardy jobs of the other agent. We analyze the computational complexity of various problems by either demonstrating that the problem is intractable or providing an efficient exact algorithm for the problem. Moreover, for certain problems that are shown to be intractable, we provide efficient algorithms for certain special cases

Simple assembly line balancing problem under task deterioration

This paper introduces the effect of task deterioration in simple assembly line balancing problem. In many realistic assembly lines, a deterioration task is considered when a task is started earlier than the assigned time since the station time is constant and the earliness of the task does not reduce the cycle time. This phenomenon is known as deteriorating tasks. Therefore, we seek an optimal assignment and schedule of tasks in workstations, in order to minimize the number of stations for a given cycle time, which is known as SALBP-1. For this purpose, a mathematical model is proposed. Since the pure SALBP-1 is proved to be NP-hard and considering task deterioration complicates problem further, we propose a genetic algorithm for solving such problem. Several well-known test problems are solved to study the performance of the proposed approach

Serial-batch scheduling – the special case of laser-cutting machines

The dissertation deals with a problem in the field of short-term production planning, namely the scheduling of laser-cutting machines. The object of decision is the grouping of production orders (batching) and the sequencing of these order groups on one or more machines (scheduling). This problem is also known in the literature as "batch scheduling problem" and belongs to the class of combinatorial optimization problems due to the interdependencies between the batching and the scheduling decisions. The concepts and methods used are mainly from production planning, operations research and machine learning

A single-machine scheduling problem with multiple unavailability constraints: A mathematical model and an enhanced variable neighborhood search approach

AbstractThis research focuses on a scheduling problem with multiple unavailability periods and distinct due dates. The objective is to minimize the sum of maximum earliness and tardiness of jobs. In order to optimize the problem exactly a mathematical model is proposed. However due to computational difficulties for large instances of the considered problem a modified variable neighborhood search (VNS) is developed. In basic VNS, the searching process to achieve to global optimum or near global optimum solution is totally random, and it is known as one of the weaknesses of this algorithm. To tackle this weakness, a VNS algorithm is combined with a knowledge module. In the proposed VNS, knowledge module extracts the knowledge of good solution and save them in memory and feed it back to the algorithm during the search process. Computational results show that the proposed algorithm is efficient and effective