No-wait Flow Shop Problem Research Articles

A Novel Evolutionary Algorithm for Scheduling Distributed No-Wait Flow Shop Problems

A Novel Evolutionary Algorithm for Scheduling Distributed No-Wait Flow Shop Problems

An efficient iterated greedy algorithm for a multi-objective no-wait flow shop problem with sequence dependent setup times

An efficient iterated greedy algorithm for a multi-objective no-wait flow shop problem with sequence dependent setup times

A Novel Parallel Simulated Annealing Methodology to Solve the No-Wait Flow Shop Scheduling Problem with Earliness and Tardiness Objectives

In this paper, the no-wait flow shop problem with earliness and tardiness objectives is considered. The problem is proven to be NP-hard. Recent no-wait flow shop problem studies focused on familiar objectives, such as makespan, total flow time, and total completion time. However, the problem has limited studies with solution approaches covering the concomitant use of earliness and tardiness objectives. A novel methodology for the parallel simulated annealing algorithm is proposed to solve this problem in order to overcome the runtime drawback of classical simulated annealing and enhance its robustness. The well-known flow shop problem datasets in the literature are utilized for benchmarking the proposed algorithm, along with the classical simulated annealing, variants of tabu search, and particle swarm optimization algorithms. Statistical analyses were performed to compare the runtime and robustness of the algorithms. The results revealed the enhancement of the classical simulated annealing algorithm in terms of time consumption and solution robustness via parallelization. It is also concluded that the proposed algorithm could outperform the benchmark metaheuristics even when run in parallel. The proposed algorithm has a generic structure that can be easily adapted to many combinatorial optimization problems.

Application of Non-Dominated Sorting Genetic Algorithm (NSGA-II) to Increase the Efficiency of Bakery Production: A Case Study

Minimizing the makespan is an important research topic in manufacturing engineering because it accounts for significant production expenses. In bakery manufacturing, ovens are high-energy-consuming machines that run throughout the production time. Finding an optimal combination of makespan and oven idle time in the decisive objective space can result in substantial financial savings. This paper investigates the hybrid no-wait flow shop problems from bakeries. Production scheduling problems from multiple bakery goods manufacturing lines are optimized using Pareto-based multi-objective optimization algorithms, non-dominated sorting genetic algorithm (NSGA-II), and a random search algorithm. NSGA-II improved NSGA, leading to better convergence and spread of the solutions in the objective space, by removing computational complexity and adding elitism and diversity strategies. Instead of a single solution, a set of optimal solutions represents the trade-offs between objectives, makespan and oven idle time to improve cost-effectiveness. Computational results from actual instances show that the solutions from the algorithms significantly outperform existing schedules. The NSGA-II finds a complete set of optimal solutions for the cases, whereas the random search procedure only delivers a subset. The study shows that the application of multi-objective optimization in bakery production scheduling can reduce oven idle time from 1.7% to 26% while minimizing the makespan by up to 12%. Furthermore, by penalizing the best makespan a marginal amount, alternative optimal solutions minimize oven idle time by up to 61% compared to the actual schedule. The proposed strategy can be effective for small and medium-sized bakeries to lower production costs and reduce CO2 emissions.

Distributed no-wait flow shop problem with sequence dependent setup time: Optimization of makespan and maximum tardiness

This paper investigates a multi-objective optimization distributed no-wait permutation flow shop scheduling problem under the constraint of sequence dependent setup time. Our optimization case is minimizing the makespan and maximum tardiness criteria. Therefore, our main objective will be to find the optimal jobs sequence that minimizes a function representing the two criteria of makespan and maximum tardiness. This function will be linearly dependent of these two criteria via a weighting parameter for each criterion. To solve this industrial problem, we propose the mixed integer linear programming (MILP) and a set of efficient metaheuristics solving different size instances. To this end, we suggest three inspired nature metaheuristics: The genetic algorithm (GA), the artificial bee colony (ABC) algorithm and migratory bird optimization (MBO) algorithm. We suggest a total of six new algorithms based on nature-inspired metaheuristics. Also, two constructive heuristics are used, the greedy randomized adaptive search procedure (GRASP) and Nawaz–Enscore–Ham (NEH) algorithms. It was revealed that GA algorithm with NEH initialization gives the best results comparing to the other metaheuristics.

A Two-Stage Cooperative Evolutionary Algorithm With Problem-Specific Knowledge for Energy-Efficient Scheduling of No-Wait Flow-Shop Problem.

Green scheduling in the manufacturing industry has attracted increasing attention in academic research and industrial applications with a focus on energy saving. As a typical scheduling problem, the no-wait flow-shop scheduling has been extensively studied due to its wide industrial applications. However, energy consumption is usually ignored in the study of typical scheduling problems. In this article, a two-stage cooperative evolutionary algorithm with problem-specific knowledge called TS-CEA is proposed to address energy-efficient scheduling of the no-wait flow-shop problem (EENWFSP) with the criteria of minimizing both makespan and total energy consumption. In TS-CEA, two constructive heuristics are designed to generate a desirable initial solution after analyzing the properties of the problem. In the first stage of TS-CEA, an iterative local search strategy (ILS) is employed to explore potential extreme solutions. Moreover, a hybrid neighborhood structure is designed to improve the quality of the solution. In the second stage of TS-CEA, a mutation strategy based on critical path knowledge is proposed to extend the extreme solutions to the Pareto front. Moreover, a co-evolutionary closed-loop system is generated with ILS and mutation strategies in the iteration process. Numerical results demonstrate the effectiveness and efficiency of TS-CEA in solving the EENWFSP.

A two-machine no-wait flow shop problem with two competing agents

A two-machine no-wait flow shop problem with two competing agents

A hybrid genetic local and global search algorithm for solving no-wait flow shop problem with bi criteria

This paper addresses the m-machine no-wait Flow Shop Scheduling with Setup Times (NW-FSSWST). Two performance measures: total flow time and makespan are considered. The objective is to find a sequence that minimizing total flow time (sum C_{j}) and makespan (C_{j}) simultaneously. A Hybrid Genetic Local and Global Search Algorithm (HGLGSA) is proposed to solve the NW-FSSWST for two performance criteria. The hybrid genetic algorithm is constructed by insert-search and self-repair algorithm with self-repair function. The proposed HGLGSA is tested on 192 benchmark problems of NW-FSSWST in the literature. A full factorial experimental design is made for determined the best parameter sets that improve the performance of the proposed algorithm. The computational results are compared with the benchmark solutions from the literature. The experimental results demonstrate the effectiveness and efficiency of the proposed HGLGSA for solving NW-FSSWST.

New results for minimising variation of flow time in two-machine proportionate no-wait flow shops

In this paper, the two-machine no-wait proportionate flow shop problem is analysed with the objective of minimising the total absolute deviation of job completion times. The optimality of V-shaped sequences is extended to problems with 12 jobs and it is shown that an optimal sequence may not be V-shaped with 13 jobs. For problems of larger size, the best V-shaped sequence is determined in linear time without resorting to dynamic programming. For larger size problems, it is shown that the number of non-dominated potentially optimal semi-V-shaped sequences increases rapidly. This indicates that derivation of optimal solutions in low order polynomial time is unlikely with a large number of jobs. Finally, the findings are extended to the corresponding problem with the objective of minimising the total absolute differences in waiting times.

Minimizing total completion time in the two-machine no-idle no-wait flow shop problem

We consider the two-machine total completion time flow shop problem with additional requirements. These requirements are the so-called no-idle constraint where the machines must operate with no inserted idle time and the so-called no-wait constraint where jobs cannot wait between the end of an operation and the start of the following one. We propose a matheuristic approach that uses an ILP formulation based on positional completion times variables and exploits the structural properties of the problem. The proposed approach shows very competitive performances on instances with up to 500 jobs in size.

A branch and bound algorithm to solve a two-machine no-wait flowshop scheduling problem with truncated learning function

ABSTRACTThis paper addresses a two-machine no-wait flowshop problem with the effect of the truncated learning function of jobs whose actual processing times depend on their positions in the sequence. By considering truncated learning effect, the actual processing time of a job is a function of its position index in the schedule and a control parameter. In a production scenario with truncated learning effect, the actual processing time of a job will not be lower than a threshold when the number of processed jobs increases. We develop a branch and bound algorithm to minimize the makespan. A lower bound and a dominance property have been proposed to increase the speed of elimination process in the branch and bound algorithm.

Integrating preventive maintenance activities to the no-wait flow shop scheduling problem with dependent-sequence setup times and makespan minimization

In this paper, preventive maintenance (PM) operations are incorporated as a constraint to the m-machine no-wait flow shop problem with dependent-sequence setup times and makespan minimization scheduling problem. PM are based on the concept of flexible and diverse maintenance levels (ML). Flexibility means that PM activities can be carried out in other periods besides the pre-determined. In order to ensure the diversity of each ML is determined according to different parameters of a PM policy based on Weibull distribution. A MILP is proposed to describe the problem. A procedure to assign PM activity in the sequence of jobs are proposed. As solution methods for the problem, the main constructive heuristics for the m-machine no-wait flow shop with makespan minimization are implemented in the original and adapted versions to solve small and large problem sizes. Computational results show that LWW and FCH are the best heuristics regarding the quality of solution in large problem sizes and generate the better results in small sizes, compared with the MILP solutions. In comparison with other procedures to scheduling PM operations to the sequence of jobs, the proposed procedure generates better results in all large problem sizes.

Incorporating preventive maintenance into the m-machine no-wait flow-shop scheduling problem with total flow-time minimization: a computational study

ABSTRACTIn this article, the impact of preventive maintenance policies on the constructive heuristics performance for the no-wait flow-shop problem with total flow-time minimization is evaluated. The main constructive heuristics for the m-machine no-wait flow-shop scheduling problem with total flow-time minimization are compared through computational experiments with a set of 5760 problems. The results show that the adopted parameters significantly affect the performance of the constructive heuristics; also, the computational effort required to solve the problems increases owing to the complexity of the function-objective calculation. Heuristics proposed by Laha and Sapkal (LSH) and Framinan, Nagano and Moccellin (FNMH) provide the best solutions for both evaluated policies.

An Iterated Greedy Heuristic for Mixed No-Wait Flowshop Problems.

The mixed no-wait flowshop problem with both wait and no-wait constraints has many potential real-life applications. The problem can be regarded as a generalization of the traditional permutation flowshop and the no-wait flowshop. In this paper, we study, for the first time, this scheduling setting with makespan minimization. We first propose a mathematical model and then we design a speed-up makespan calculation procedure. By introducing a varying number of destructed jobs, a modified iterated greedy algorithm is proposed for the considered problem which consists of four components: 1) initialization solution construction; 2) destruction; 3) reconstruction; and 4) local search. To further improve the intensification and efficiency of the proposal, insertion is performed on some neighbor jobs of the best position in a sequence during the initialization, solution construction, and reconstruction phases. After calibrating parameters and components, the proposal is compared with five existing algorithms for similar problems on adapted Taillard benchmark instances. Experimental results show that the proposal always obtains the best performance among the compared methods.

On the exact solution of the no-wait flow shop problem with due date constraints

This paper deals with the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, the jobs should be completed before their respective due dates; due date constraints are dealt with as hard constraints. The considered performance criterion is makespan. The problem is strongly NP-hard. This paper develops a number of distinct mathematical models for the problem based on different decision variables. Namely, a mixed integer programming model, two quadratic mixed integer programming models, and two constraint programming models are developed. Moreover, a novel graph representation is developed for the problem. This new modeling technique facilitates the investigation of some of the important characteristics of the problem; this results in a number of propositions to rule out a large number of infeasible solutions from the set of all possible permutations. Afterward, the new graph representation and the resulting propositions are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the mathematical models and to compare them with the developed exact algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.

A new hybrid ant colony algorithm for scheduling of no-wait flowshop

In this paper, the no-wait flow shop scheduling problem under makespan and flowtime criteria is addressed. The no-wait flowshop is a variant of the well-known flowshop scheduling problem where all processes follow the previous one without any interruption for operations of a job. Owing to the problem is known to be NP-hard for more than two machines, a hybrid meta-heuristic algorithm based on ant colony optimization (ACO) and simulated annealing (SA) algorithm is improved. First, at each step, due to the characteristic of ACO algorithm that include solution construction and pheromone trail updating, some different areas of search space are checked and best solution is selected. Then, to enhance the quality and diversity of the solution and finding best neighbor of this solution, a novel SA is presented. Moreover, a new principle is applied for global pheromone update based on the probability function like SA algorithm. The proposed approach solution is compared with several the state-of-the-art algorithms in the literature. The reported results show that the proposed algorithms are effective and the new approach for local search in ACO algorithm is efficient for solving the no-wait flow shop problem. Then, we employed another hybrid ACO algorithm based on hybridization of ACO with variable neighborhood search (VNS) and compare the results given by two proposed algorithms. These results show that our new hybrid provides better results than ACO-VNS algorithm.

No-Wait Flowshop Scheduling Is as Hard as Asymmetric Traveling Salesman Problem

In this paper, we study the classical no-wait flowshop scheduling problem with makespan objective (F|no-wait|Cmax in the standard three-field notation). This problem is well known to be a special case of the asymmetric traveling salesman problem (ATSP) and as such has an approximation algorithm with logarithmic performance guarantee. In this work, we show a reverse connection, we show that any polynomial time α-approximation algorithm for the no-wait flowshop scheduling problem with makespan objective implies the existence of a polynomial time α(1 + ɛ)-approximation algorithm for the ATSP for any ɛ > 0. This, in turn, implies that all nonapproximability results for the ATSP (current or future) will carry over to its special case. In particular, it follows that the no-wait flowshop problem is APX-hard, which is the first nonapproximability result for this problem.

Review and classification of constructive heuristics mechanisms for no-wait flow shop problem

Permutation flow shop scheduling has been studied since the 1950s. Due to practical applications and because of its complex nature, several constrains have been studied, for example the no-wait flow shop problem. Classified as non-deterministic polynomial-time hard (NP-hard), several constructive heuristics have been proposed to reach the best trade-off between quality of the solution and computational time. This paper aims to present a review and classification of constructive heuristics proposed for no-wait flow shop problem with additional constraints (setup times, machine unavailability, release dates, and due dates) and several criterion objectives (makespan, total flow time, due date consideration, and multi-criterion objectives). As a result of the literature review, constructive heuristics were classified according to its composition (initial sequence generation, constructive phase, and improvement phase) and category (simple or composite). Several different mechanisms from the considered phases could be identified. These mechanisms can be combined to develop new constructive heuristics and can be applied for other scheduling problems. Besides, final considerations highlight directions for future possible researches, mainly the development of new strategies, for each phase considered.

An Enumeration Algorithm for the No-Wait Flow Shop Problem with Due Date Constraints

This paper develops an enumeration algorithm for the no-wait flow shop scheduling problem with due date constraints. In this problem, waiting time is not allowed between successive operations of jobs. Plus, each job is accompanied by a due date which is dealt with as a hard constraint. The considered performance criterion is makespan. The problem is strongly NP-hard. In this research, a new modelling approach is developed for the problem. This new modelling technique and the resulting observations are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.

An enhanced greedy random adaptive search procedure with path-relinking for no-wait flowshop problem with setup times

In this paper, we consider the no-wait flowshop scheduling problem with sequence-dependent setup times to minimize makespan, which is widespread in industries. An enhanced greedy random adaptive search procedure is combined with the Path- Relinking and the GRPEP method is proposed for the problem under study. An evolutionary local search algorithm is integrated to improve the exploration of the search process. Two local search methods, with and without memory, are introduced to improve the intensification. An ageing strategy is developed to increase the diversification. The proposed algorithm is compared with existing approaches for the considered problem and some recent effective algorithms for flowshop scheduling problems with sequence-dependent setup times on benchmark instances. Experimental results show that GRPEP outperforms all the compared meta-heuristics with the same CPU-times. GRPEP obtains better solutions than the compared heuristics