Heuristic algorithms for preemptive scheduling in a two-stage hybrid flowshop with additional renewable resources at each stage

This paper deals with the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines and renewable resources at both the stages. The resource requirements are of a 0–1 type. The objective is the minimization of makespan. The problem is NP-hard. Four heuristic algorithms using linear programming are proposed for solving this problem. Performance of the algorithms is analyzed experimentally by comparing heuristic solutions with the lower bound on the optimal makespan. Statistical comparative analysis of the developed algorithms is carried out. The results of a computational experiment show that the proposed algorithms are able to produce good quality solutions in a small amount of computation time.     

Heuristic algorithms for preemptive scheduling in a two-stage hybrid flowshop with additional renewable resources at each stage

This paper deals with the problem of preemptive scheduling in a two-stage flowshop with parallel unrelated machines and renewable resources at both the stages. The resource requirements are of a 0–1 type. The objective is the minimization of makespan. The problem is NP-hard. Four heuristic algorithms using linear programming are proposed for solving this problem. Performance of the algorithms is analyzed experimentally by comparing heuristic solutions with the lower bound on the optimal makespan. Statistical comparative analysis of the developed algorithms is carried out. The results of a computational experiment show that the proposed algorithms are able to produce good quality solutions in a small amount of computation time.     

A genetic algorithm and a simulated annealing algorithm combined with column generation technique for solving the problem of scheduling in the hybrid flowshop with additional resources

In this paper, a heuristic is proposed for solving the problem of scheduling in a two-stage flowshop with parallel unrelated machines and additional renewable resources at the first stage and a single machine at the second stage. Resource requirements are arbitrary integers. The availability of additional resources is limited at every moment. The objective is the minimization of makespan. The problem is NP-hard. The proposed heuristic combines column generation technique with a genetic algorithm (the heuristic algorithm HG) or a simulated annealing algorithm (the heuristic algorithm HS). The performance analysis is performed experimentally by comparing heuristic solutions to the lower bound on the optimal makespan. Results of the computational experiment show that both the heuristic algorithms yield good quality solutions using reasonable computation time and that HS outperforms HG for the most difficult problems.     

A Constructive Genetic Algorithm for permutation flowshop scheduling

The general flowshop scheduling problem is a production problem where a set of n jobs have to be processed with identical flow pattern on m machines. In permutation flowshops the sequence of jobs is the same on all machines. A significant research effort has been devoted for sequencing jobs in a flowshop minimizing the makespan. This paper describes the application of a Constructive Genetic Algorithm (CGA) to makespan minimization on flowshop scheduling. The CGA was proposed recently as an alternative to traditional GA approaches, particularly, for evaluating schemata directly. The population initially formed only by schemata, evolves controlled by recombination to a population of well-adapted structures (schemata instantiation). The CGA implemented is based on the NEH classic heuristic and a local search heuristic used to define the fitness functions. The parameters of the CGA are calibrated using a Design of Experiments (DOE) approach. The computational results are compared against some other successful algorithms from the literature on Taillard’s well-known standard benchmark. The computational experience shows that this innovative CGA approach provides competitive results for flowshop scheduling problems.     

Bi-criteria minimization for the permutation flowshop scheduling problem with machine-based learning effects

In traditional scheduling problems, the processing time for the given job is assumed to be a constant regardless of whether the job is scheduled earlier or later. However, the phenomenon named “learning effect” has extensively been studied recently, in which job processing times decline as workers gain more experience. This paper discusses a bi-criteria scheduling problem in an m-machine permutation flowshop environment with varied learning effects on different machines. The objective of this paper is to minimize the weighted sum of the total completion time and the makespan. A dominance criterion and a lower bound are proposed to accelerate the branch-and-bound algorithm for deriving the optimal solution. In addition, the near-optimal solutions are derived by adapting two well-known heuristic algorithms. The computational experiments reveal that the proposed branch-and-bound algorithm can effectively deal with problems with up to 16 jobs, and the proposed heuristic algorithms can yield accurate near-optimal solutions.     

A generalized two-machine flowshop scheduling problem with processing time linearly dependent on job waiting-time

We consider a two-machine flowshop scheduling problem where the processing times are linearly dependent on the waiting times of the jobs. The objective is to minimize the makespan. A 0–1 mixed integer program and a heuristic algorithm are proposed. Some cases solved in polynomial time and computational experiments are also provided.     

A two-machine flowshop makespan scheduling problem with deteriorating jobs

In traditional scheduling problems, the job processing times are assumed to be known and fixed from the first job to be processed to the last job to be completed. However, in many realistic situations, a job will consume more time than it would have consumed if it had begun earlier. This phenomenon is known as deteriorating jobs. In the science literature, the deteriorating job scheduling problems are relatively unexplored in the flowshop settings. In this paper, we study a two-machine flowshop makespan scheduling problem in which job processing times vary as time passes, i.e. they are assumed as increasing functions of their starting times. First, an exact algorithm is established to solve most of the problems of up to 32 jobs in a reasonable amount of time. Then, three heuristic algorithms are provided to derive the near-optimal solutions. A simulation study is conducted to evaluate the performances of the proposed algorithms. In addition, the impact of the deterioration rate is also investigated.     

The three-stage assembly flowshop scheduling problem

We consider the three-stage assembly flowshop scheduling problem with the objective of minimizing the makespan. The three-stage assembly problem generalizes both the serial three machine flowshop problem and the two-stage assembly flowshop scheduling problem and is therefore strongly NP-hard. We analyze the worst-case ratio bound for several heuristics for this problem. We also analyze the worst-case absolute bound for a heuristic based on compact vector summation techniques and we point out that, for a large number of jobs, this heuristic becomes asymptotically optimal.Scope and purposeThe three-stage assembly flowshop scheduling problem models situations which arise frequently in manufacturing when various fabrication operations are performed concurrently and then collected and transported into an assembly area for a final assembly operation. The main criterion for this problem is the minimization of the maximum job completion time (makespan). The objective of this paper is to derive algorithms for minimizing the makespan. In doing so, we also demonstrate the reduction of assembly flowshop problems to their embedded serial flowshop problems.     

Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects

In this paper, we study the problem of minimizing the weighted sum of makespan and total completion time in a permutation flowshop where the processing times are supposed to vary according to learning effects. The processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in the sequence. We present heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound. We also adopt an existing algorithm as well as a branch-and-bound algorithm for the general m-machine permutation flowshop problem. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems.     

Algorithms for a realistic variant of flowshop scheduling

This paper deals with a realistic variant of flowshop scheduling, namely the hybrid flexible flowshop. A hybrid flowshop mixes the characteristics of regular flowshops and parallel machine problems by considering stages with parallel machines instead of having one single machine per stage. We also investigate the flexible version where stage skipping might occur, i.e., not all stages must be visited by all jobs. Lastly, we also consider job sequence dependent setup times per stage. The optimization criterion considered is makespan minimization. While many approaches for hybrid flowshops have been proposed, hybrid flexible flowshops have been rarely studied. The situation is even worse with the addition of sequence dependent setups. In this study, we propose two advanced algorithms that specifically deal with the flexible and setup characteristics of this problem. The first algorithm is a dynamic dispatching rule heuristic, and the second is an iterated local search metaheuristic. The proposed algorithms are evaluated by comparison against seven other high performing existing algorithms. The statistically sound results support the idea that the proposed algorithms are very competitive for the studied problem.     

Flowshop scheduling with a general exponential learning effect

This paper investigates flowshop scheduling problems with a general exponential learning effect, i.e., the actual processing time of a job is defined by an exponent function of the total weighted normal processing time of the already processed jobs and its position in a sequence, where the weight is a position-dependent weight. The objective is to minimize the makespan, the total (weighted) completion time, the total weighted discounted completion time, and the sum of the quadratic job completion times, respectively. Several simple heuristic algorithms are proposed in this paper by using the optimal schedules for the corresponding single machine problems. The tight worst-case bound of these heuristic algorithms is also given. Two well-known heuristics are also proposed for the flowshop scheduling with a general exponential learning effect.     

Minimizing makespan subject to minimum flowtime on two identical parallel machines

We consider the problem of scheduling jobs on two parallel identical machines where an optimal schedule is defined as one that gives the smallest makespan (the completion time of the last job) among the set of schedules with optimal total flowtime (the sum of the completion times of all jobs). We propose an algorithm to determine optimal schedules for the problem, and describe a modified multifit algorithm to find an approximate solution to the problem in polynomial computational time. Results of a computational study to compare the performance of the proposed algorithms with a known heuristic shows that the proposed heuristic and optimization algorithms are quite effective and efficient in solving the problem.Scope and purposeMultiple objective optimization problems are quite common in practice. However, while solving scheduling problems, optimization algorithms often consider only a single objective function. Consideration of multiple objectives makes even the simplest multi-machine scheduling problems NP-hard. Therefore, enumerative optimization techniques and heuristic solution procedures are required to solve multi-objective scheduling problems. This paper illustrates the development of an optimization algorithm and polynomially bounded heuristic solution procedures for the scheduling jobs on two identical parallel machines to hierarchically minimize the makespan subject to the optimality of the total flowtime.     

Efficient non-population-based algorithms for the permutation flowshop scheduling problem with makespan minimisation subject to a maximum tardiness

This paper focuses on the problem of scheduling jobs in a permutation flowshop with the objective of makespan minimisation subject to a maximum allowed tardiness for the jobs, a problem that combines two desirable manufacturing objectives related to machine utilisation and to customer satisfaction. Although several approximate algorithms have been proposed for this NP-hard problem, none of them can use the excellent speed-up method by Taillard (1990) [22] for makespan minimisation due to the special structure of the problem under consideration. In this paper, several properties of the problem are defined in order to be able to partly apply Taillard׳s acceleration. This mechanism, together with a novel feasible tabu local search method, allows us to further exploit the structure of solutions of the problem, and are incorporated in two proposed algorithms: a bounded-insertion-based constructive heuristic and an advanced non-population-based algorithm. These algorithms are compared with state-of-the-art algorithms under the same computer conditions. The results show that both algorithms improve existing ones and therefore, constitute the new state-of-art approximate solution procedures for the problem.     

A two-machine flowshop scheduling problem with a separated maintenance constraint

This paper considers a two-machine flowshop scheduling problem with a separated maintenance constraint. This means that the machine may not always be available during the scheduling period. It needs a constant time to maintain the machine after completing a fixed number of jobs at most. The objective is to find the optimal job combinations and the optimal job schedule such that the makespan is minimized. The proposed problem has some practical applications, for example, in electroplating process, the electrolytic cell needs to be cleaned and made up a deficiency of medicine. In this paper, we propose a heuristic algorithm to solve this problem. Some polynomially solvable cases and computational experiments are also provided.     

Evolutionary algorithms for scheduling a flowshop manufacturing cell with sequence dependent family setups

This paper considers the problem of scheduling part families and jobs within each part family in a flowshop manufacturing cell with sequence dependent family setups times where it is desired to minimize the makespan while processing parts (jobs) in each family together. Two evolutionary algorithms—a Genetic Algorithm and a Memetic Algorithm with local search—are proposed and empirically evaluated as to their effectiveness in finding optimal permutation schedules. The proposed algorithms use a compact representation for the solution and a hierarchically structured population where the number of possible neighborhoods is limited by dividing the population into clusters. In comparison to a Multi-Start procedure, solutions obtained by the proposed evolutionary algorithms were very close to the lower bounds for all problem instances. Moreover, the comparison against the previous best algorithm, a heuristic named CMD, indicated a considerable performance improvement.     

Setting a common due date in a constrained flowshop: A variable neighbourhood search approach

In this paper we study a due date setting problem in a flowshop layout. The problem consists of scheduling a set of jobs arriving to the system together with jobs already present (denoted as old jobs), in order to set a common due date for the new jobs. Since the old jobs have a common due date that must not be violated, our problem is a rescheduling problem with the objective of minimising the makespan of the new jobs (thus obtaining the tightest possible due date for the new jobs) and a constraint since the maximum tardiness of the old jobs must be equal to zero. This approach leads to an interesting scheduling problem in which two different objectives are considered, each one for a subset of the jobs that must be scheduled. To the best of our knowledge, this type of problems have been scarcely considered in the literature, and only for very specific purposes. Since our problem is clearly NP-hard, a new heuristic based on variable neighbourhood search (VNS) has been designed. The computational results show that our proposed heuristic outperforms two existing heuristic methods for similar problems in the literature.     

Production scheduling for blocking flowshop in distributed environment using effective heuristics and iterated greedy algorithm

Production scheduling plays an important role in the intelligent decision support system and intelligent optimization decision technology. In the context of the globalization trend, the current production and management may extend from a single factory to a distributed production network. In this paper, we study the distributed blocking flowshop scheduling problem (DBFSP) that is an important generalization of the traditional blocking flowshop scheduling problem in the distributed environment. Six constructive heuristics and an iterated greedy (IG) algorithm are proposed to minimize the makespan, which provides procedures for obtaining efficient and effective solutions to make decision-making sounder. The first five heuristics are developed based on the well-known NEH2 heuristic [B. Naderi, R. Ruiz, The distributed permutation flowshop scheduling problem, Computers & Operations Research, 37 (4) (2010) 754–768.] and the last heuristic is presented by extending the PW heuristic [Q.K. Pan, L. Wang, Effective heuristics for the blocking flowshop scheduling problem with makespan minimization, Omega, 40 (2) (2012) 218–229.] to DBFSP in an effective way. The composite heuristics that combining constructive heuristics and local searches are also studied. The proposed composite heuristics are chosen to generate an initial solution with a high level of quality. Keeping the simplicity of the IG algorithm, three local search procedures, two destruction procedures, an improved reconstruction procedure, and a simulated annealing-like acceptance criterion are well designed based on the problem-specific knowledge to enhance the IG algorithm. The computational experiments are carried out based on the 720 benchmark instances from the literature. The results show that the proposed heuristics are very effective for solving the problem under consideration and the presented IG algorithm performs significantly better than the other state-of-the-art metaheuristics from the literature.     

Minimizing makespan and total flowtime in permutation flowshops by a bi-objective multi-start simulated-annealing algorithm

In this study, a bi-objective multi-start simulated-annealing algorithm (BMSA) is presented for permutation flowshop scheduling problems with the objectives of minimizing the makespan and total flowtime of jobs. To evaluate the performance of the BMSA, computational experiments were conducted on the well-known benchmark problem set provided by Taillard. The non-dominated sets obtained from each of the existing benchmark algorithms and the BMSA were compared, and then combined to form a net non-dominated front. The computational results show that more than 64% of the solutions in the net non-dominated front are contributed by the proposed BMSA. It is believed that these solutions can serve as new benchmarks for future research.     

Group scheduling problem: Key to flexible manufacturing systems

We present an efficient heuristic algorithm for determining the sequence which minimizes the makespan of a group scheduling problem at the first level. The problem, therefore, focuses on scheduling of parts (jobs) in a part family. In the generation of partial schedules at each iteration, a job with a high mean total processing time is given a higher priority than others. An example problem, chosen from a real world application, is used to implement, the algorithmic steps. For this example, it has also been shown that the makespan determine by the proposed heuristic is smaller than that determined previously by two documented algorithms.     

Worst-case and numerical analysis of heuristic algorithms for flowshop scheduling problems with a time-dependent learning effect

In this paper, we investigate a time-dependent learning effect in a flowshop scheduling problem. We assume that the time-dependent learning effect of a job was a function of the total normal processing time of jobs scheduled before the job. The following objective functions are explored: the makespan, the total flowtime, the sum of weighted completion times, the sum of the kth power of completion times, and the maximum lateness. Some heuristic algorithms with worst-case analysis for the objective functions are given. Moreover, a polynomial algorithm is proposed for the special case with identical processing time on each machine and that with an increasing series of dominating machines, respectively. Finally, the computational results to evaluate the performance of the heuristics are provided.