Approximation schemes for two-machine flow shop scheduling with two agents

In this paper we consider two-machine flow shop scheduling with two agents. Two models are investigated. One is the weighted-sum optimization model and the other is the constrained optimization model. For the former, we show that it is weakly NP-hard and propose a fully polynomial time approximation scheme. For the latter, we also show the problem is weakly NP-hard. With violating the constraint a factor of ?? a fully polynomial time approximation scheme is provided.     

Particle swarm optimization based-algorithms to solve the two-machine cross-docking flow shop problem: just in time scheduling

Cross-docking is an innovative logistical strategy which provides less inventory holding costs, less transportation costs and fast customer deliveries without storage in between or less than 24 hours. In this paper, we address the two-machine cross-docking scheduling problem within a Just-In-Time (JIT) context. This latter requires the punctuality and exactness of product deliveries. To satisfy this target, we aim to minimize the total earliness and tardiness, then early or tardy deliveries are discouraged. This study presents a great contribution in solving such NP-hard problem while applying different versions of the PSO (Particle Swarm Optimization) algorithm. One of them is hybridized with the Genetic Algorithm (GA). This latter is then shown to be the best one over computational experiments using different sized instances and by determining a percentage deviation from a developed lower bound.

     

Energy-efficient no-wait permutation flow shop scheduling by adaptive multi-objective variable neighborhood search

This paper considers an energy-efficient no-wait permutation flow shop scheduling problem to minimize makespan and total energy consumption, simultaneously. The processing speeds of machines can be dynamically adjusted for different jobs. In general, lower processing speeds require less energy consumption but result in longer processing times, while higher speeds take the opposite effect. To reach the Pareto front of the problem, we propose an adaptive multi-objective variable neighborhood search (AM-VNS) algorithm. Specifically, we first design two basic speed adjusting heuristics which can reduce the energy consumption of a given solution without worsening its makespan. Two widely used neighborhood-generating operations, i.e., insertion and swap, are adapted and integrated into the variable neighborhood descent phase. With respect to their executing order, two variable neighborhood descent structures can be designed. We adopt an adaptive mechanism to dynamically determine which structure will be selected to handle the current solution. To further improve the performance of the algorithm, we develop a novel problem-specific shake procedure. We also introduce accelerating techniques to speed up the algorithm. Computational results show that the AM-VNS algorithm outperforms multi-objective evolutionary algorithms NSGA-II and SPEA-II.     

The permutation flow shop problem with blocking. A tabu search approach

This paper develops a fast tabu search algorithm to minimize makespan in a flow shop problem with blocking. Some properties of the problem associated with the blocks of jobs have been presented and discussed. These properties allow us to propose a specific neighbourhood of algorithms. Also, the multimoves are used that consist in performing several moves simultaneously in a single iteration and guide the search process to more promising areas of the solutions space, where good solutions can be found. It allow us to accelerate the convergence of the algorithm. Besides, a dynamic tabu list is proposed that assists additionally to avoid being trapped at a local optimum. The proposed algorithms are empirically evaluated and found to be relatively more effective in finding better solutions than attained by the leading approaches in a much shorter time. The presented ideas can be applied in many local search procedures.     

A multi-objective particle swarm for a flow shop scheduling problem

Flow shop problems as a typical manufacturing challenge have gained wide attention in academic fields. In this paper, we consider a bi-criteria permutation flow shop scheduling problem, where weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a flow shop scheduling problem has been proved to be NP-hard in strong sense, an effective multi-objective particle swarm (MOPS), exploiting a new concept of the Ideal Point and a new approach to specify the superior particle's position vector in the swarm, is designed and used for finding locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm, i.e. SPEA-II. The computational results show that the proposed MOPS performs better than the genetic algorithm, especially for the large-sized problems.     

The permutation flow shop problem with just in time production considerations

This research presents a variation to the permutation flow shop problem where Just In Time (JIT) production requirements are taken into account. The model developed in this research employs dual objectives. In addition to the traditional objective of minimizing the production makespan, minimization of Miltenburg's material usage rate is also incorporated. In this model, multiple units of any product are permitted in the production sequence. However, the minimization of material usage rates attempts to prevent batch scheduling of products and allows unit flow of products as required in demand flow manufacturing. A solution method is proposed for determining an optimal production sequence via an efficient frontier approach and Simulated Annealing (SA). Test problems and specific performance criteria are used to assess the solutions generated by the proposed method. Experimental results presented in this paper show that the use of the efficient frontier and SA provide solutions that approach the optimal solution for the performance measures used in this research.     

Designing a tabu search algorithm for the two-stage flow shop problem with secondary criterion

This paper discusses the process of desigining a tabu search-based heuristic for the two-stage flow shop problem with makespan minimization as the primary criterion and the minimization of total flow time as the secondary criterion. A factorial experiment is designed to analyse thoroughly the effects of four different factors, i.e. the initial solution, type of move, size of neighbourhood and the list size, on the performance of the tabu search-based heuristic. Using the techniques of evolution curves, and response tables and response graphs, coupled with the Taguchi method, the best combination of the factors for the tabu search-based heuristic is identified, and the effectiveness of the heuristic algorithm in finding an optimal solution is evaluated by comparing its performance with the best known heuristic to solve this problem.     

Solving hybrid flow shop problem using energetic reasoning and global operations

This paper shows that the use of satisfiability tests and time-bound adjustments based on energetic reasoning and global operations can enhance the efficiency of branch and bound procedures for optimally solving the hybrid flow shop scheduling problem. Procedures to use energetic reasoning and extended forms of global adjustment techniques are described and are empirically evaluated. Computational results show that the proposed approaches outperform the best known procedures to optimally solve the hybrid flow shop problem.     

The no-wait job shop with regular objective: a method based on optimal job insertion

The no-wait job shop problem (NWJS-R) considered here is a version of the job shop scheduling problem where, for any two operations of a job, a fixed time lag between their starting times is prescribed. Also, sequence-dependent set-up times between consecutive operations on a machine can be present. The problem consists in finding a schedule that minimizes a general regular objective function. We study the so-called optimal job insertion problem in the NWJS-R and prove that this problem is solvable in polynomial time by a very efficient algorithm, generalizing a result we obtained in the case of a makespan objective. We then propose a large neighborhood local search method for the NWJS-R based on the optimal job insertion algorithm and present extensive numerical results that compare favorably with current benchmarks when available.     

A heuristic to minimize total flow time in permutation flow shop

In this paper, we address an n-job, m-machine permutation flow shop scheduling problem for the objective of minimizing the total flow time. We propose a modification of the best-known method of Framinan and Leisten [An efficient constructive heuristic for flowtime minimization in permutation flow shops. Omega 2003;31:311–7] for this problem. We show, through computational experimentation, that this modification significantly improves its performance while not affecting its time-complexity.     

Multi-objective permutation flow shop scheduling problem: Literature review,classification and current trends

The flow shop scheduling problem is finding a sequence given n jobs with same order at m machines according to certain performance measure(s). The job can be processed on at most one machine; meanwhile one machine can process at most one job. The most common objective for this problem is makespan. However, many real-world scheduling problems are multi-objective by nature. Over the years there have been several approaches used to deal with the multi-objective flow shop scheduling problems (MOFSP). Hence, in this study, we provide a brief literature review of the contributions to MOFSP and identify areas of opportunity for future research.     

一种求解柔性工作车间调度问题的混合遗传算法

针对柔性工作车间调度问题(Flexible job-shop scheduling problem, FJSP),提出了一种基于混合遗传算法的求解方案,在初始种群中引入基于启发式规则生成的优良个体,并使用有效的交叉、变异算子避免不可行个体的产生,同时利用混沌序列的随机性和遍历性特点,在遗传进化的过程中增加基于混沌序列的邻域搜索功能,以提高遗传算法的执行效率.通过仿真实验验证了该算法的可行性和有效性.     

一种求解双目标flow shop排序问题的进化算法

提出一种求解双目标flow shop排序的递进多目标进化算法.算法采用改进的精英复制策略,在实现精英保留的前提下降低了计算复杂性;通过递进进化模式增加群体多样性,改善了算法收敛性;通过群体进化过程中对非劣解集进行竞争型可变邻域启发式搜索,增强了算法局部搜索性能.采用新算法和参照算法NSGA-II对31个标准双目标flow shop算例进行优化.研究结果表明,新算法在所有算例的求解中均获得了优于NSGA-II的非劣解集,验证了算法的有效性.     

The flow refueling location problem with load flow control

Battery electric vehicles as well as renewable energy are two key factors that can contribute significantly to sustainable development within the transportation and the energy sector. However, the market introduction of these technologies results in new challenges, especially with regard to the interaction between both sectors. So far, neither location models for charging stations nor load flow models for the electrical grid consider these interactions sufficiently. Thus, an integration of planning problems from both sectors is needed in order to exploit potential synergies and to avoid negative impacts.In this paper, we present such an integrated planning approach to locate charging infrastructure for battery electric vehicles considering interactions with the electrical grid. Herein, we combine a charging station location model and a power flow model with integrated energy stores. We aim at determining a network configuration that satisfies the charging demand of battery electric vehicles, herein maximizing the benefits and minimizing the negative impacts resulting from the interactions of the two sectors. To demonstrate the benefit of our integrated planning approach, we apply it to an illustrative case and present results of a sensitivity analysis. We derive managerial insights regarding the interdependencies of the number of sited charging stations and the installed storage capacity based on renewable energy generation and charging demand.     

Minimizing makespan in an ordered flow shop with?machine-dependent processing times

We consider a generalization of the proportionate flow shop problem with the makespan objective. Each job has a processing requirement and each machine has a characteristic value. In our case, we assume that the time a job occupies a machine is equal to the processing requirement of the job plus a setup time that is equal to the characteristic value of that machine. In this paper, we consider permutation schedules and show that the problem is solvable in polynomial time when the number of machines is fixed.     

A comparative analysis of due date based job sequencing rules in a flow shop with multiple processors

The literature on job scheduling recognizes the importance of due date performance criteria such as mean tardiness and maximum tardiness. A number of studies test a large number of sequencing rules for these criteria in job shop and flow shop settings. The object of this present research is to examine the performance of some well-known priority rules in a flow shop with multiple processors. This study investigates the performance of ten priority rules in terms of mean and maximum tardiness. It examines the effects of problem characteristics, such as number of jobs, number of machines stages and number of parallel processors at each stage, and the performance of priority rules using regression analysis. The findings of the study suggest that the primary determinants of tardiness-based criteria are problem characteristics. In addition, both the regression analysis and the analysis of variance provide strong evidence of the strategy-effect. Finally, a detailed performance review of examined priority rules for various problem characteristics is presented.     

The maximum flow problem with disjunctive constraints

We study the maximum flow problem subject to binary disjunctive constraints in a directed graph: A negative disjunctive constraint states that a certain pair of arcs in a digraph cannot be simultaneously used for sending flow in a feasible solution. In contrast to this, positive disjunctive constraints force that for certain pairs of arcs at least one arc has to carry flow in a feasible solution. It is convenient to represent the negative disjunctive constraints in terms of a so-called conflict graph whose vertices correspond to the arcs of the underlying graph, and whose edges encode the constraints. Analogously we represent the positive disjunctive constraints by a so-called forcing graph. For conflict graphs we prove that the maximum flow problem is strongly $\mathcal{NP}$ -hard, even if the conflict graph consists only of unconnected edges. This result still holds if the network consists only of disjoint paths of length three. For forcing graphs we also provide a sharp line between polynomially solvable and strongly $\mathcal{NP}$ -hard instances for the case where the flow values are required to be integral. Moreover, our hardness results imply that no polynomial time approximation algorithm can exist for both problems. In contrast to this we show that the maximum flow problem with a forcing graph can be solved efficiently if fractional flow values are allowed.     

An estimation of distribution algorithm for lot-streaming flow shop problems with setup times

Lot-streaming flow shops have important applications in different industries including textile, plastic, chemical, semiconductor and many others. This paper considers an n-job m-machine lot-streaming flow shop scheduling problem with sequence-dependent setup times under both the idling and no-idling production cases. The objective is to minimize the maximum completion time or makespan. To solve this important practical problem, a novel estimation of distribution algorithm (EDA) is proposed with a job permutation based representation. In the proposed EDA, an efficient initialization scheme based on the NEH heuristic is presented to construct an initial population with a certain level of quality and diversity. An estimation of a probabilistic model is constructed to direct the algorithm search towards good solutions by taking into account both job permutation and similar blocks of jobs. A simple but effective local search is added to enhance the intensification capability. A diversity controlling mechanism is applied to maintain the diversity of the population. In addition, a speed-up method is presented to reduce the computational effort needed for the local search technique and the NEH-based heuristics. A comparative evaluation is carried out with the best performing algorithms from the literature. The results show that the proposed EDA is very effective in comparison after comprehensive computational and statistical analyses.