Two-machine Permutation Flowshop Research Articles

A distributionally robust approach for the two-machine permutation flow shop scheduling

A distributionally robust approach for the two-machine permutation flow shop scheduling

A branch-and-bound approach to minimise the value-at-risk of the makespan in a stochastic two-machine flow shop

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments.

Minimizing Total Tardiness in a Two-Machine Flowshop Scheduling Problem with Availability Constraints

In this paper, we consider the problem of minimizing the total tardiness in a deterministic two-machine permutation flowshop scheduling problem subject to release dates of jobs and known unavailability periods of machines. The theoretical and practical importance of minimizing tardiness in flowshop scheduling environment has motivated us to investigate and solve this interested two-machine scheduling problem. Methods that solve this important optimality criterion in flowshop environment are mainly heuristics. In fact, despite the -hardness in the strong sense of the studied problem, to the best of our knowledge there are no approximate algorithms (constructive heuristics or metaheuristics) or an algorithm with worst case behavior bounds proposed to solve this problem. Thus, the design of new promising algorithms is desirable. We develop five metaheuristics for the problem under consideration. These metaheuristics are: the Particle Swarm Optimization (PSO), the Differential Evolution (DE), the Genetic Algorithm (GA), the Ant Colony Optimization (ACO) and the Imperialist Competitive Algorithm (ICA). All the proposed metaheuristics are population-based approaches. These metaheuristics have been improved by integrating different local search procedures in order to provide more satisfactory, especially in term of quality solutions. Computational experiments carried out on a large set of randomly generated instances provide evidence that the Imperialist Competitive Algorithm (ICA) records the best performances.

Exact method to optimize the total electricity cost in two-machine permutation flow shop scheduling problem under Time-of-use tariff

This study investigates the minimization of total electricity cost in a two-machine permutation flow shop scheduling problem under the most common electricity tariff, Time-of-Use (ToU). We provide a new property and solution approach to enhance existing methods in the literature. First, we provide an overview of the optimal cases for some specific ToU pricing structures that consist of only two pricing intervals. When the electricity price decreases, Johnson’s rule and dynamic programming give rise to an optimal solution. On the other hand, when the electricity price increases, we provide a condition of optimality for Johnson’s rule. Second, we develop a property based on Johnson’s rule to determine the optimal sequence for general ToU pricing structures. Third, we propose a new mixed-integer linear programming. Then, we design an exact method based on “Logic-based Benders decomposition” to solve the problem. Finally, the numerical tests show that our proposed approach significantly improves the quality of existing results in the literature.

Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine.

The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant c. This case is interesting because it occurs in various applications, for example, when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant c is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in O(nlogn) steps. Two heuristics for solving the NP-hard flow shop problems are proposed: (i) a modification of the commonly used NEH heuristic (mNEH) and (ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.

Flowshop scheduling with machine deterioration based on job sequences

This paper addresses the two-machine permutation flowshop problem with deterioration. The objectives are minimizing the makespan and the average tardiness. Jobs have a baseline process time in each machine and have a due date. The actual time to process a job depends on the machine performance level at the start of each job, which is a function of the previously processed jobs and their wear/deterioration effect on the machine. The article proposes multiple heuristics and a comprehensive set of experiments. The results indicate that as a group, the heuristics generate solutions that are very close to the optimal for both criteria. Furthermore, no heuristic approach is dominant for all experimental conditions, thus heuristic selection to solve practical problems should be based on the specific problem characteristics.

Multi-state two-machine permutation flow shop scheduling optimisation with time-dependent energy costs

This paper studies a multi-state two-machine flowshop scheduling problem with variable electricity tariffs. The objective is to process a set of jobs in the available time slots with different energy costs to minimise the total energy consumption costs. For this purpose, two different 0-1 linear programs are proposed for the problem.Computational experiments are presented and numerical results are discussed and analyzed in order to evaluate their efficiencies.

MILP models and valid inequalities for the two-machine permutation flowshop scheduling problem with minimal time lags

In this paper, we consider the problem of scheduling on two-machine permutation flowshop with minimal time lags between consecutive operations of each job. The aim is to find a feasible schedule that minimizes the total tardiness. This problem is known to be NP-hard in the strong sense. We propose two mixed-integer linear programming (MILP) models and two types of valid inequalities which aim to tighten the models’ representations. One of them is based on dominance rules from the literature. Then, we provide the results of extensive computational experiments used to measure the performance of the proposed MILP models. They are shown to be able to solve optimally instances until the size 40-job and even several larger problem classes, with up to 60 jobs. Furthermore, we can distinguish the effect of the minimal time lags and the inclusion of the valid inequalities in the basic MILP model on the results.

Genetic factors of chronic pancreatitis in Russian population

The two-machine permutation flow shop scheduling problem with the objective of minimizing total earliness and tardiness is addressed. Unforced idle time can be used to complete jobs closer to their due dates. It is shown that unforced idle time only needs to be considered on the second machine. This result is then used to extend a lower bound and dominance conditions for the single-machine problem to the two-machine permutation flow shop problem. Two branch-and-bound algorithms are developed for the problem utilizing the lower bound and dominance conditions. The algorithms are tested using instances that represent a wide variety of conditions.

Research on common due window assignment flowshop scheduling with learning effect and resource allocation

ABSTRACTIn this article, the two-machine no-wait permutation flowshop scheduling problem with common due window assignment, learning effect and resource allocation is considered, wherein learning effect and resource allocation mean that the processing time of a job is a function of its position in a sequence and its amount of resource allocation. According to the common due window assignment method, each job is associated with a common due window, which is a decision variable. The goal is to determine the sequence of jobs, common due window starting time, due window size and resource allocation such that the linear weighted sum of job earliness, tardiness, due window size and resource cost is minimized. This article shows that the scheduling problem can be solved in polynomial time.

Branch-and-bound algorithms for minimizing total earliness and tardiness in a two-machine permutation flow shop with unforced idle allowed

The two-machine permutation flow shop scheduling problem with the objective of minimizing total earliness and tardiness is addressed. Unforced idle time can be used to complete jobs closer to their due dates. It is shown that unforced idle time only needs to be considered on the second machine. This result is then used to extend a lower bound and dominance conditions for the single-machine problem to the two-machine permutation flow shop problem. Two branch-and-bound algorithms are developed for the problem utilizing the lower bound and dominance conditions. The algorithms are tested using instances that represent a wide variety of conditions.

Methods for Scheduling Problems Considering Experience, Learning, and Forgetting Effects

Workers with different levels of experience and knowledge have different effects on job processing times. By taking into account 1) the sum-of-processing-time; 2) the job-position; and 3) the experience of workers, a more general learning model is introduced for scheduling problems. We show that this model generalizes existing ones and brings the consideration of learning and forgetting effects closer to reality. We demonstrate that some single machine scheduling problems are polynomially solvable under this general model. Considering the forgetting effect caused by the idle time on the second machine, we construct a learning-forgetting model for the two-machine permutation flow shop scheduling problem with makespan minimization. A branch-and-bound method and four heuristics are presented to find optimal and approximate solutions, respectively. The proposed heuristics are evaluated over a large number of randomly generated instances. Experimental results show that the proposed heuristics are effective and efficient.

Scheduling on a two-machine permutation flow shop under time-of-use electricity tariffs

We consider a two-machine permutation flow shop scheduling problem to minimise the total electricity cost of processing jobs under time-of-use electricity tariffs. We formulate the problem as a mixed integer linear programming, then we design two heuristic algorithms based on Johnson’s rule and dynamic programming method, respectively. In particular, we show how to find an optimal schedule using dynamic programming when the processing sequence is fixed. In addition, we propose an iterated local search algorithm to solve the problem with problem-tailored procedures and move operators, and test the computational performance of these methods on randomly generated instances.

No-wait two-machine permutation flow shop scheduling problem with learning effect, common due date and controllable job processing times

We consider a two-machine no-wait permutation flow shop common due date assignment scheduling problem where the processing time of a job is given as a function of its position in the sequence and its amount of resource allocated to this job. The common due date (CON) assignment method means that all the jobs are given a common due date. We need to make a decision on the common due date, resource allocation and the sequence of jobs to minimise total earliness, tardiness, common due date cost and total resource cost. We show that the problem remains polynomially solvable under the proposed model.

A branch-and-bound algorithm for the two-machine total completion time flowshop problem subject to release dates

We consider the problem of minimizing the sum of completion times in a two-machine permutation flowshop problem subject to release dates. We derive several lower bounds as well as a branch-and-bound algorithm for the problem under consideration. Computational experiments, on a large set of randomly generated instances, provide evidence that the proposed procedure performs consistently well.

Minimizing the total completion time in a two-machine flowshop problem with time delays

This article proposes to solve the problem of minimizing the total completion time in a two-machine permutation flowshop environment in which time delays between the machines are considered. For this purpose, an enumeration algorithm based on the branch-and-bound framework is developed, which includes new lower and upper bounds as well as dominance rules. The computational study shows that problems with up to 40 jobs can be solved in a reasonable amount of time.

Two-agent two-machine flowshop scheduling with learning effects to minimize the total completion time

We study a two-agent scheduling problem in a two-machine permutation flowshop with learning effects. The objective is to minimize the total completion time of the jobs from one agent, given that the maximum tardiness of the jobs from the other agent cannot exceed a bound. We provide a branch-and-bound algorithm for the problem. In addition, we present several genetic algorithms to obtain near-optimal solutions. Computational results indicate that the algorithms perform well in either solving the problem or efficiently generating near-optimal solutions.

A branch and bound algorithm to minimise the total tardiness in the two-machine permutation flowshop scheduling problem with minimal time lags

In this paper, we consider the two-machine permutation flowshop scheduling problem with minimal time lags and the objective of minimising total tardiness. Dominance criteria are developed to establish precedence constraints between jobs in an optimal schedule and a lower bound on the total tardiness of the problem is derived. A branch and bound algorithm for this problem is developed to reach an optimal solution using lower bound and dominance criteria. Also, computationally efficient heuristics are proposed. Results of computational experiments on randomly generated problems are reported.

Minimizing the total completion time in a two-machine flowshop with sequence-independent setup times

We consider the problem of minimizing the sum of completion times in a two-machine permutation flowshop subject to setup times. We propose a new priority rule, several constructive heuristics, local search procedures, as well as an effective multiple crossover genetic algorithm. Computational experiments carried out on a large set of randomly generated instances provide evidence that a constructive heuristic based on newly derived priority rule dominates all the proposed constructive heuristics. More specifically, we show that one of our proposed constructive heuristics outperforms the best constructive heuristic in the literature in terms of both error and computational time. Furthermore, we show that one of our proposed local search-based heuristics outperforms the best local search heuristic in the literature in terms of again both error and computational time. We also show that, in terms of quality-to-CPU time ratio, the multiple crossover genetic algorithm performs consistently well.

２機械順列フローショップ問題に対するｄｙｎａｓｅａｒｃｈの拡張

The purpose of this study is to construct a solution algorithm for the two-machine permutation flowshop problem based on the dynasearch. The dynasearch is an efficient local search algorithm that employs a special neighborhood structure called dynasearch swap neighborhood. Its primary advantage is that the neighborhood of a solution can be explored in polynomial time although it is composed of an exponential number of solutions. The dynasearch for machine scheduling was originally developed for the single-machine total weighted tardiness problem. Then, it was extended to the problem with idle time and setup times. This study further extends the dynasearch to the two-machine permutation flowshop problem and its effectiveness is examined by numerical experiments for both total weighted tardiness and total weighted earliness-tardiness objectives.