Machine Flow Shop Research Articles

An improved algorithm for the two machine flow shop problem with several availability constraints

In this paper we deal with the two-machine flow shop scheduling problem with several availability constraints on the first machine, under the resumable scenario. We first develop an improved algorithm with a relative worst-case error bound of 4/3. We then present a polynomially solvable case.

An empirical analysis of the optimality rate of flow shop heuristics

Abstract If a certain optimization problem is NP-hard or even harder, one could expect that the chances of solving it optimally should rather decrease with an increase of the problem size. We reveal, however, that the opposite occurs for a strongly NP-hard problem, which requires sequencing n jobs through an m machine flow shop so as to minimize the makespan. In particular, we empirically examine optimality rates (the probability of being optimal) of the famous NEH heuristic of Nawaz et al. [Nawaz, M., Enscore, Jr., E., Ham, I., 1983. A heuristic algorithm for the m-machine, n-job flow-shop sequencing problem. Omega, The International Journal of Management Science 11, 91–95] and two improved versions of NEH. By using millions of simulation trials and a new effective lower bound on the shortest makespan, we observe relatively high optimality rates of the three heuristics for small values of m. Rather surprisingly, for larger values of n, the heuristics become more frequently optimal as n increases. Neither theoretical nor empirical studies of optimality rates of flow shop heuristics have been conducted so far, and – to the best of our knowledge – no similar studies are known in the field of operations research.

A $${(\frac 4 3) -}$$ approximation algorithm for a special case of the two machine flow shop problem with several availability constraints

In this paper, we deal with a special case of the two-machine flow shop scheduling problem with several availability constraints on the second machine, under the resumable scenario. We develop an improved algorithm with a relative worst-case error bound of 4/3.

Proposed method for solving the flow shop scheduling problem for n-jobs on m-machines

This research suggested a new heuristic method for solving the n-jobs, m- machines flow shop scheduling problem to minimize total completion time. This method was compared with The (NEH) method for data generated by using (matlab) and showed high efficiency and easy to use.

Johnson's algorithm: A key to solve optimally or approximately flow shop scheduling problems with unavailability periods

Johnson's algorithm ( JA) is perhaps the most classical algorithm in the scheduling area. JA gives the optimal solution to the two machine flow shop to minimize the makespan in polynomial time. Researchers have tried to extend this notorious result to obtain polynomial time algorithms for more general cases. Such importance motivated us to devote this paper to JA applied to three flow shop problems with unavailability periods to minimize the makespan. First we focus on the optimality condition of JA. Then we propose a modification of JA. After we calculate new performances of JA as a heuristic. Last we deal with an extension of JA.

Batch Scheduling on Two-Machine Flowshop with Machine-Dependent Setup Times

We study a batch scheduling problem on a 2-machine flowshop. We assume unit processing time jobs, batch availability, and machine-dependent setup times. The objective is to find a job allocation to batches of integer size and a batch schedule that minimize makespan. We introduce a very efficient closed form solution for the problem.

A note on a greedy heuristic for flow-shop makespan minimization with no machine idle-time

We study makespan minimization on an m machine flowshop. No idle time is allowed between consecutive operations on each machine. We introduce an efficient (O( n 2)) greedy algorithm, which is shown numerically to perform better than a recently published heuristic.

Two machine flow shop scheduling problem with weighted WIP costs

This paper considers two new machine flow shop scheduling problems where the objective is to minimize the total WIP (work-in-process) cost. In this type of problems, the unit time WIP cost increases or decreases as a job passes through a series of stages in the production process. We first introduce this relatively new class of flow shop scheduling problems. Then, we establish the complexity of several problems with different types of job restrictions and weighted cost characteristics. For some tractable cases, we propose optimal solution procedures. Finally, a heuristic is introduced for a class of problem instances, and we find upper bounds on the relative errors.

Tabu Search and Simulated Annealing Algorithms for Scheduling in Flow Shops with Lot Streaming

This paper addresses the problem of making sequencing and scheduling decisions for n Jobs in m-machine flow shops with a lot sizing constraint. Lot streaming (lot sizing) is the process of creating sublots to move the completed portion of a production sublot to downstream machines. The planning decisions become more complex when lot streaming is allowed. There is scope for efficient metaheuristics for scheduling problems in an m machine flow shop with lot streaming. In recent years, much attention has been given to heuristics and search techniques. This paper proposes two metaheuristics, namely a simulated annealing algorithm (SA) and a tabu search algorithm (TABU), to evolve the optimal sequence for makespan and total flow time criteria in an m-machine flow shop with lot streaming. The algorithms are evaluated by means of comparison with Baker's algorithm for 2 m/c cases and the makespan criterion, which proves the capability of both of them.

Minimizing makespan on an [formula omitted]-machine re-entrant flowshop

This paper focuses on an m -machine re-entrant flowshop scheduling problem with the objective of minimizing makespan. In the re-entrant flowshop considered here, routes of all jobs are identical as in ordinary flowshops, but the jobs must be processed multiple times on the machines. We present heuristic algorithms, which are modified from well-known existing algorithms for the general m -machine flowshop problem or newly developed in this research. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems and results are reported.

Modified drum–buffer–rope scheduling mechanism for a non-identical parallel machine flow shop with processing-time variation

The drum–buffer–rope (DBR) is a scheduling mechanism under the Theory of Constraints (TOC) philosophy. In DBR, ‘drum’ is a production schedule on the capacity-constrained resources (CCRs), which controls the speed of production for the whole system; ‘rope’ is a mechanism to release the required material to the CCRs; and ‘buffer’ is used to protect the CCRs from starvation due to statistical fluctuations. For a non-identical parallel machine flow-shop environment, estimating an efficient rope and time buffer for DBR implementation is not an easy task because of the complexity of non-identical parallel machine loading. This paper proposes a new scheduling method, which is called the modified DBR (MOD-DBR). It applies a backward finite capacity scheduling technique, including machine loadings and detail scheduling, instead of the rope mechanism in DBR. The scheduling performances of MOD-DBR are evaluated under variable processing time situations. The experimental results indicate that the MOD-DBR without a time buffer outperformed the DBR with a considerable level of buffer on the average flow time, while they have the same performance on tardiness, constraint resource utilization, and throughput.

Applying machine based decomposition in 2-machine flow shops

The shifting bottleneck (SB) heuristic is among the most successful approximation methods for solving the job shop problem. It is essentially a machine based decomposition procedure where a series of one machine sequencing problems (OMSPs) are solved. However, such a procedure has been reported to be highly ineffective for the flow shop problems. In particular, we show that for the 2-machine flow shop problem, the SB heuristic will deliver the optimal solution in only a small number of instances. We examine the reason behind the failure of the machine based decomposition method for the flow shop. An optimal machine based decomposition procedure is formulated for the 2-machine flow shop, the time complexity of which is worse than that of the celebrated Johnson’s rule. The contribution of the present study lies in showing that the same machine based decomposition procedures which are so successful in solving complex job shops can also be suitably modified to optimally solve the simpler flow shops.

USING JOHNSON'S ALGORITHM TO APPROXIMATE SOME FLOW SHOP SCHEDULING PROBLEMS WITH UNAVAILABILITY PERIODS

Johnson’ algorithm (JA) is perhaps the most classical algorithm in the scheduling area. JA gives the optimal solution to the two machine flow shop to minimize the makespan in a polynomial time. Researchers have tried to extend this celebrated result to obtain polynomial time algorithms for more general cases. Such importance motivated us to devote this paper to JA applied to three flow shop problems with unavailability periods to minimize the makespan. First we focus on the optimality condition of JA. Then we propose an extension of JA. Last we calculate new performances of JA as a heuristic.

Sequencing of an M machine flow shop with setup, processing and removal times separated

In this research, a flow shop scheduling problem in which setup, processing and removal times are separated, with the objective of minimizing makespan, is considered. A tabu search based heuristic is presented for solving the addressed problem. The proposed heuristic begins with the construction of artificial processing times for each operation; then a modified NEH algorithm is used to generate an initial solution, followed by a designed tabu search procedure applied for further improvement of the solution. The proposed heuristic, as well as the existing one, is evaluated in a large number of randomly generated problems. The results of the experimental investigations of the proposed heuristic algorithm and the existing heuristic in meeting the objective of makespan are also reported. It is found that the solution quality of the proposed tabu search heuristic is better than that of the existing heuristic, but for large size problems more computational efforts are needed; however, the CPU time is still acceptable.

The [formula omitted]-machine flowshop problem with unit-time operations and intree precedence constraints

We consider the flowshop problem with unit-time operations and intree precedence constraints, with the objective to minimize the total completion time. We present a polynomial-time algorithm assuming that the number of machines is fixed. This proves a recently stated conjecture.

Stochastic group scheduling problems on single and multiple machines

This paper considers two types of stochastic group scheduling problems, one involves a single machine, and the other involves an m -machine flow shop. In both problems, jobs are classified into groups. The jobs of the same group are to be processed one after another, and a sequence independent setup time is incurred between each two consecutively scheduled groups. The job processing times are independent random variables and group setup times are functions of the job processing times. The objective is to find both a group sequence and a job sequence that minimizes the expected total flow time. An optimal group sequence and an optimal job sequence are obtained by processing jobs in increasing stochastic order of their mean processing times and group setup times for a single machine problem. A precedence relationship is derived for the m -machine flow shop problem.

A contribution to the stochastic flow shop scheduling problem

This paper deals with performance evaluation and scheduling problems in m machine stochastic flow shop with unlimited buffers. The processing time of each job on each machine is a random variable exponentially distributed with a known rate. We consider permutation flow shop. The objective is to find a job schedule which minimizes the expected makespan. A classification of works about stochastic flow shop with random processing times is first given. In order to solve the performance evaluation problem, we propose a recursive algorithm based on a Markov chain to compute the expected makespan and a discrete event simulation model to evaluate the expected makespan. The recursive algorithm is a generalization of a method proposed in the literature for the two machine flow shop problem to the m machine flow shop problem with unlimited buffers. In deterministic context, heuristics (like CDS [Management Science 16 (10) (1970) B630] and Rapid Access [Management Science 23 (11) (1977) 1174]) and metaheuristics (like simulated annealing) provide good results. We propose to adapt and to test this kind of methods for the stochastic scheduling problem. Combinations between heuristics or metaheuristics and the performance evaluation models are proposed. One of the objectives of this paper is to compare the methods together. Our methods are tested on problems from the OR-Library and give good results: for the two machine problems, we obtain the optimal solution and for the m machine problems, the methods are mutually validated.

Two–machine flowshop minimum–length scheduling problem with random and bounded processing times

We address the two–machine flowshop scheduling problem to minimize makespan where jobs have random and bounded processing times. The probability distributions of job processing times are unknown and only the lower and upper bounds of processing times are given before scheduling. In such cases there may not exist a unique schedule that remains optimal for all possible realizations of processing times, and therefore, a set of schedules has to be considered which dominates all other schedules. In this paper, we find some sufficient conditions for the considered problem.

An Ant Colony Optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem

Consider the 2-machine flowshop scheduling problem with the objective of minimizing both the total completion time and the makespan criteria. The latter is assumed to be optimized prior to the former. In view of the NP -hardness of the problem an Ant Colony Optimization approach is proposed to solve it. The heuristic also uses feature of Simulated Annealing search and local search algorithms. Computational experiments show its effectiveness compared to existing heuristics. The extension to the total completion time problem is also studied.

Stability of Johnson's schedule with respect to limited machine availability

The paper deals with the scheduling problem of minimizing the makespan in the two -machine n -job flow-shop with w non-availability intervals on each of the two machines. This problem is binary NP-hard even if there is only one non-availability interval ( w = 1) either on the first machine or on the second machine. If there are no non-availability intervals on any machine ( w = 0), the two-machine flow-shop problem may be easily solved using Johnson's permutation of n jobs. We derived sufficient conditions for optimality of Johnson's permutation in the case of the given w S 1 non-availability intervals. The instrument we use is stability analysis, which answers the question of how stable an optimal schedule is if there are independent changes in the processing times of the jobs. The stability analysis is demonstrated on a huge number of randomly generated two -machine flow-shop problems with 5 h n h 10 000 and 1 h w h 1000.