Minimising Makespan in the Two-Machine Flow-Shop with Release Times (original) (raw)
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Minimizing Makespan with Start Time-Dependent Jobs in a Two-Machine Flow Shop
International Journal of Engineering, 2016
The purpose of this paper is to consider the problem of scheduling a set of start time-dependent jobs in a two-machine flow shop, in which the actual processing times of jobs increase linearly according to their starting time. The objective of this problem is to minimize the makespan. The problem is known to be NP-hardness; therefore, there is no polynomial-time algorithm to solve it optimally in a reasonable time. So, a branch-and-bound algorithm is proposed to find the optimal solution by means of dominance rules, upper and lower bounds. Several easy heuristic procedures are also proposed to derive near-optimal solutions. To evaluate the performance of the proposed algorithms, the computational experiments are extracted based on the recent literature. Deteriorating jobs lead to an increase in the makespan of the problems; therefore, it is important to obtain the optimal or near-optimal solution. Considering the complexity of the problem, the branch-and-bound algorithm is capable of solving problems of up to 26 jobs. Additionally, the average error percentage of heuristic algorithms is less than 1.37%; therefore, the best one is recommended to obtain a near-optimal solution for large-scale problems.
International Journal of Production Research, 2011
In this paper, we consider the two-machine no-wait flow-shop scheduling problem, when every machine is subject to one non-availability constraint and jobs have different release dates. The nonavailability intervals of the machines overlap and they are known in advance. We aim to find a nonresumable schedule that minimizes the makespan. We propose several lower bounds and upper bounds. These bounding procedures are used in a branch-and-bound algorithm. Computational experiments are carried out on a large set of instances and the obtained results show the effectiveness of our method.
Minimizing makespan in a two-machine flow shop with effects of deterioration and learning
Optimization Letters, 2012
We consider a two-machine flow shop scheduling problem with effects of deterioration and learning. By the effects of deterioration and learning, we mean that the processing time of a job is a function of its execution starting time and its position in a sequence. The objective is to find a sequence that minimizes the makespan. Several dominance properties and two lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm proposed to solve the problem. Two heuristic algorithms are also proposed to obtain near-optimal solutions. Computational results are presented to evaluate the performance of the proposed algorithms.
Scheduling three-operation jobs in a two-machine flow shop to minimize makespan
This paper considers a variant of the classical problem of minimizing makespan in a two-machine flow shop. In this variant, each job has three operations, where the first operation must be performed on the first machine, the second operation can be performed on either machine but cannot be preempted, and the third operation must be performed on the second machine. The NP-hard nature of the problem motivates the design and analysis of approximation algorithms. It is shown that a schedule in which the operations are sequenced arbitrarily, but without inserted machine idle time, has a worst-case performance ratio of 2. Also, an algorithm that constructs four schedules and selects the best is shown to have a worst-case performance ratio of 3/2. A polynomial time approximation scheme (PTAS) is also presented.
2012
This paper considers a two-stage hybrid flow shop scheduling problem. The objective is the minimizing of maximum completion time of all the jobs. There exist two dedicated machines at stage 1 and one machine at stage 2. Each job is defined by two operations processed on the two-stages in series. Depending on the job type, the job is processed on either of the two machines at stage1 and must be processed on the single machine at stage2. the jobs are transported between the stages by a robot or a conveyor. After the problem formulation, we present lower bounds for the objective function. We then discuss a few polynomially solvable cases of the problem and present the solution algorithms. Since a general case of the problem is strongly NP-hard, we propose two heuristics to find approximate solutions to the general case. Computational experiments are done on a number of randomly generated test problems, and the test results are reported.
Minimizing total flow time in a two-machine flowshop problem with minimum makespan
International Journal of Production …, 2001
This paper considers the two-machine flowshop scheduling problem where it is desired to find a minimum total flow time schedule subject to the condition that the makespan of the schedule is minimum. Based on the analysis of the problem characteristics, several existing results are extended to develop two optimization algorithms for the problem. In view of the NP-hardness of the problem, two polynomially solvable cases are identified and solved. Further, several polynomial heuristic solution algorithms are developed and empirically evaluated as to their effectiveness in finding an optimal schedule for the problem.
Sustainability
This paper is aimed at studying a two-machine flowshop scheduling where the processing times are linearly dependent on the waiting times of the jobs prior to processing on the second machine. That is, when a job is processed completely on the first machine, a certain delay time is required before its processing on the second machine. If we would like to reduce the actual waiting time, the processing time of the job on the second machine increases. The objective is to minimize the makespan. When the processing time is reduced, it implies that the consumption of energy is reduced. It is beneficial to environmental sustainability. We show that the proposed problem is NP-hard in the strong sense. A 0-1 mixed integer programming and a heuristic algorithm with computational experiment are proposed. Some cases solved in polynomial time are also provided.
Approximation algorithms for two-machine flow shop scheduling with batch setup times
Mathematical Programming, 1998
In many practical situations, batching of similar jobs to avoid setups is performed while constructing a schedule. This paper addresses the problem of non-preemptively scheduling independent jobs in a two-machine flow shop with the objective of minimizing the makespan. Jobs are grouped into batches. A sequence independent batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. Besides its practical interest, this problem is a direct generalization of the classical two-machine flow shop problem with no grouping of jobs, which can be solved optimally by Johnson's well-known algorithm. The problem under investigation is known to be NP-hard. We propose two O(n log n) time heuristic algorithms. The first heuristic, which creates a schedule with minimum total setup time by forcing all jobs in the same batch to be sequenced in adjacent positions, has a worst-case performance ratio of 3/2. By allowing each batch to be split into at most two sub-batches, a second heuristic is developed which has an improved worst-case performance ratio of 4/3.
2020
Abstract: Flow shop scheduling problems as a typical manufacturing challenge have gained wide attention in academic fields. In this paper, we consider two stage flow shop scheduling problem in which a job block for a group job and the interval of non-availability of machine has been taken with an objective to minimize the make span. This paper provides a branch and bound technique to find optimal or near optimal sequence. This approach is very simple and easy to understand and, also provide an important tool for decision makers to design a schedule for two stage flowshop scheduling problems. The method is clarified with the help of numerical illustration. I.INTRODUCTION A flow shop is characterized by unidirectional flow of work with a variety of jobs being processed sequentially in a one-pass manner. The processing time of all the jobs are assumed to be known and all the jobs are processed in the same order in various machines. Scheduling in a manufacturing system is necessary to m...
Two-machine flow shop scheduling problems with minimal and maximal delays
4OR, 2006
In this paper we provide a fairly complete complexity classification of various versions of the two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. For some version, we offer a fully polynomial-time approximation scheme and a 4 3 -approximation algorithm.