Two-machine flow-shop scheduling to minimize total late work

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.

This paper is pertain to heuristic technique for n-jobs, 3-machines flowshop scheduling problem in which processing times and setup times are associated with their respective probabilities involving transportation time, break down interval and job block criteria is taken in to account. Further jobs are attached with weights to indicate their relative importance. The proposed method is very easy to understand and also provide an important tool for decision makers. A numerical illustration followed by a computer programme is also given to clarify the algorithm.

Lecture Notes in Computer Science, Vol. 3285, 2004, 68 - 75, 2004

In the paper, we analyze different solving methods for the two-machine flow shop scheduling problem with a common due date with the weighted late work criterion, i.e. F2 | di = d | Yw, which is known to be NP-hard. In computational experiments, we compared the practical efficiency of a dynamic programming approach, an enumerative method and heuristic procedures. Test results showed that each solving method has its advantages and it cannot be rejected from the consideration a priori.

2012

The paper deals with a specially structured n-jobs 2-machine flow shop scheduling problem under specified rental policy in which processing times are associated with their respective probabilities. Further jobs are attached with weights to indicate their relative importance. The objective of the paper is to obtain a optimal / near optimal sequence of jobs in order to minimize the rental cost of machines. A computer program followed by a numerical illustration is given to justify the algorithm.

The paper deals with n jobs, 3 machines flow shop production scheduling in which processing times and set up times are associated with their respective probabilities involving transportation time and jobs are processed in two disjoint job blocks in a string. A heuristic method with an objective to minimize the total time elapsed time/idle time of the jobs/machines is discussed. A computer program followed by numerical illustration is given to clarify the algorithm.

International Journal of Production Economics, 2009

This paper presents optimal scheduling in a two-machine flow shop, in which the objective function is to minimize the sum of maximum earliness and tardiness (n/2/P/ ET max ). Since this problem tries to minimize earliness and tardiness, the results can be useful for different production systems such as just in time (JIT). This objective function has already been considered for n jobs and m machines, but the proposed algorithms are not efficient to solve large scale problems. In this paper, neighborhood conditions are developed and the dominant set for any optimal solution is determined. The branchand-bound (B&B) method is used to solve the problem and the proper upper and lower bounds are also introduced. A number of effective lemmas are introduced to develop an algorithm which is more efficient than those already known. To show the effectiveness of the proposed algorithm, 380 problems of different sizes are randomly generated and solved. More than 82% of the problems are shown to reach optimal solutions.

In the field of scheduling, the flow shop problems have been thoroughly studied. In this paper we propose a concise overview of flow shop scheduling techniques evolved during the time period. We surveyed the exact and heuristics methods for solving various flow shop scheduling problems. As a result various optimization techniques, solution procedures are available to solve a variety of problems. We also present a brief glimpse of the evolution of flow shop scheduling problems and possible approaches for their solutions. This paper also concludes with some fruitful directions for the future research.

International Journal of Computer Integrated Manufacturing, 2013

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2012

The present paper is attempt to develop a new heuristic algorithm, an alternative to the traditional algorithm proposed by Johnson's (1954) to find the optimal sequence to minimize the utilization time of the machines and hence their rental cost for two stage specially structured flow shop scheduling under specified rental policy in which processing times and set up time are associated with their respective probabilities, including job block criteria. Further jobs are attached with weights to indicate their relative importance. The proposed method is very simple and easy to understand and also provide an important tool for the decision maker. Algorithm is justified by numerical illustration.

Computers & Industrial Engineering, Vol. 49, 2005, 611 - 624

In this paper, we analyze different solution procedures for the two-machine flow shop scheduling problem with a common due date and the weighted late work criterion, i.e. for problem F2 | d j = d | Y w , which is known to be binary NP-hard. In computational experiments, we compare the practical efficiency of a dynamic programming approach, an enumerative method and a heuristic list scheduling procedure. Test results show that each solution method has its advantages and none of them can be rejected from the consideration a priori.