An improved approximation algorithm for two-machine flow shop scheduling with an availability constraint

We study the problem of scheduling n jobs in a two-machine flow shop where the second machine is not available for processing during a given time interval. A resumable scenario is assumed, i.e., if a job cannot be finished before the down period it is continued after the machine becomes available again. The objective is to minimize the makespan. The best fast approximation algorithm for this problem guarantees a relative worst-case error bound of 4/3. We present an improved algorithm with a relative worst-case error bound of 5/4.     

An approximation scheme for two-machine flowshop scheduling with setup times and an availability constraint

This paper studies the two-machine permutation flowshop scheduling problem with anticipatory setup times and an availability constraint imposed only on the first machine. The objective is to minimize the makespan. Under the assumption that interrupted jobs can resume their operations, we present a polynomial-time approximation scheme for this problem.     

Heuristics for two-machine no-wait flowshop scheduling with an availability constraint

In this paper we study the two-machine no-wait flowshop problem with an availability constraint. The problem has been shown to be NP-hard, and some heuristics with a worst-case error bound of 2 have been developed for it. We provide two improved heuristics for the problem, and show that each has a worst-case error bound of 5/3.     

Minimizing total flow time for the non-permutation flow shop scheduling problem with learning effects and availability constraints

The flow shop scheduling problem is an attractive subject in the field of scheduling, which has attracted the attention of many researchers in the past five decades. In this paper, the non-permutation flow shop scheduling problem with the learning effects and machine availability constraints has been studied for minimizing the total flow time as a performance measure. First, a mixed integer linear programming model has been proposed for the modeling of the problem and then, an effective improving heuristic method, which is able to find proper non-permutation solutions, has been presented. Finally, the computational results are used for evaluation the performance and effectiveness of the proposed heuristic.     

求解作业排序问题的一种改进修复约束满足算法

修复约束满足算法(修复法)是在完整初始解的基础上不断对变量进行修复,最终得到可行解.对此,提出一种求解flow shop排序问题的改进修复法(IRCS_WT),通过采用新的变量表达方式,设计了一种以启发式优化规则为指导的变量选择算法(LWT),并采用一种变量互换算法(LTEE)保证算法的全局搜索性能.将新算法应用于31个标准算例,与传统算法及遗传算法的优化结果进行比较,结果表明在相同运算时问下改进算法具有明显的优越性.     

Variable neighborhood search for two-agent flow shop scheduling problem

Multi-agent scheduling in flow shop environment is seldom considered. In this paper flow shop scheduling problem with two agents is studied and its feasibility model is considered, in which the goal is to minimize the makespan of the first agent and the total tardiness of the second agent simultaneously under the given upper bounds. A simple variable neighborhood search (VNS) algorithm is proposed, in which a learning neighborhood structure is constructed to produce new solutions and a new principle is applied to decide if the current solution can be replaced with the new one. VNS is tested on a number of instances and the computational results show the promising advantage of VNS when compared to other algorithms of the problem.     

A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem

In this paper, a discrete artificial bee colony (DABC) algorithm is proposed to solve the lot-streaming flow shop scheduling problem with the criterion of total weighted earliness and tardiness penalties under both the idling and no-idling cases. Unlike the original ABC algorithm, the proposed DABC algorithm represents a food source as a discrete job permutation and applies discrete operators to generate new neighboring food sources for the employed bees, onlookers and scouts. An efficient initialization scheme, which is based on the earliest due date (EDD), the smallest slack time on the last machine (LSL) and the smallest overall slack time (OSL) rules, is presented to construct the initial population with certain quality and diversity. In addition, a self adaptive strategy for generating neighboring food sources based on insert and swap operators is developed to enable the DABC algorithm to work on discrete/combinatorial spaces. Furthermore, a simple but effective local search approach is embedded in the proposed DABC algorithm to enhance the local intensification capability. Through the analysis of experimental results, the highly effective performance of the proposed DABC algorithm is shown against the best performing algorithms from the literature.     

A branch-and-bound algorithm for solving a two-machine flow shop problem with deteriorating jobs

In this paper we consider a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job we mean that the job's processing time is an increasing function of its starting time. We model job deterioration as a function that is proportional to a linear function of time. The objective is to find a sequence that minimizes the total completion time of the jobs. For the general case, we derive several dominance properties, some lower bounds, and an initial upper bound by using a heuristic algorithm, and apply them to speed up the elimination process of a branch-and-bound algorithm developed to solve the problem.     

Approximation algorithms for shop scheduling problems with minsum objective: A correction

We present a correction to the paper, “Approximation algorithms for shop scheduling problems with minsum objective” (Journal of Scheduling 2002; 5:287–305) by Queyranne and Sviridenko. This correction provides a correct derivation of its 2eρ approximation result. Wenhua Li and Jinjiang Yuan: Project supported by NNSFC (Grant 10371112) and NSFHN (Grant 0411011200). Maurice Queyranne: Supported by research grants from NSERC, the Natural Sciences and Engineering Research Council of Canada.     

MIP formulation and heuristics for multi-stage capacitated lot-sizing and scheduling problem with availability constraints

In this paper, the problem of lot-sizing and scheduling of multiple product types in a capacitated flow shop with availability constraints for multi-period planning horizon is considered. In many real production systems, machines may be unavailable due to breakdowns or preventive maintenance activities, thus integrating lot-sizing and scheduling with maintenance planning is necessary to model real manufacturing conditions. Two variants are considered to deal with the maintenance activities. In the first, the starting times of maintenance tasks are fixed, whereas in the second one, maintenance must be carried out in a given time window. A new mixed-integer programming (MIP) model is proposed to formulate the problem with sequence-dependent setups and availability constraints. The objective is to find a production and preventive maintenance schedule that minimizes production, holding and setup costs. Three MIP-based heuristics with rolling horizon framework are developed to generate the integrated plan. Computational experiments are performed on randomly generated instances to show the efficiency of the heuristics. To evaluate the validity of the solution methods, problems with different scales have been studied and the results are compared with the lower bound. Computational experiments demonstrate that the performed methods have good-quality results for the test problems.     

Complexity and algorithms for two-stage flexible flowshop scheduling with availability constraints

This paper considers the two-stage flexible flowshop scheduling problem with availability constraints. We discuss the complexity and the approximability of the problem, and provide some approximation algorithms with finite and tight worst case performance bounds for some special cases of the problem.     

An effective asexual genetic algorithm for solving the job shop scheduling problem

By using the notion of elite pool, this paper presents an effective asexual genetic algorithm for solving the job shop scheduling problem. Based on mutation operations, the algorithm selectively picks the solution with the highest quality from the pool and after its modification, it can replace the solution with the lowest quality with such a modified solution. The elite pool is initially filled with a number of non-delay schedules, and then, in each iteration, the best solution of the elite pool is removed and mutated in a biased fashion through running a limited tabu search procedure. A decision strategy which balances exploitation versus exploration determines (i) whether any intermediate solution along the run of tabu search should join the elite pool, and (ii) whether upon joining a new solution to the pool, the worst solution should leave the pool. The genetic algorithm procedure is repeated until either a time limit is reached or the elite pool becomes empty. The results of extensive computational experiments on the benchmark instances indicate that the success of the procedure significantly depends on the employed mechanism of updating the elite pool. In these experiments, the optimal value of the well-known 10 × 10 instance, ft10, is obtained in 0.06 s. Moreover, for larger problems, solutions with the precision of less than one percent from the best known solutions are achieved within several seconds.     

随机柔性Flow shop加权完成时间调度问题的启发式策略性能分析

因实际生产中调度问题的规模很大,分析其近似算法的绝对性能比很难,有时甚至不可能,所以研究近似算法的渐近性能比就很有必要．本文针对随机柔性Flow shop加权完成时间调度问题,使用单机松弛和概率分析方法,证明了基于加权最短期望处理时间需求的启发式策略是渐近最优的．     

基于改进蝙蝠算法的柔性流水车间排产优化问题研究

为解决柔性流水车间调度问题( flexible flow shop scheduling problem,FFSP),提出了一种基于精英个体集的自适应蝙蝠算法(self-adaptive elite bat algorithm,SEBA)。针对蝙蝠算法存在求解离散问题具有局限性、易陷入局部极值、优化结果精度低等问题,该算法采用ROV(ranked order value)编码方式,使算法适用于求解离散型的FFSP问题;提出基于汉明距离的精英个体集,由多个适应度高但相似度低的精英个体轮流引导种群进化,增强种群进化活力,避免寻优过程陷入局部极值;提出自适应位置更新机制,提高算法优化精度。最后采用不同规模的标准实例对改进算法进行测试,与已有算法进行对比,实验结果验证了改进蝙蝠算法求解FFSP问题的有效性。     

A modified genetic algorithm for the flow shop sequencing problem to minimize mean flow time

A modified genetic algorithm (MGA) is developed for solving the flow shop sequencing problem with the objective of minimizing mean flow time. To improve the general genetic algorithm (GA) procedure, two additional operations are introduced into the algorithm. One replaces the worst solutions in each generation with the best solutions found in previous generations. The other improves the most promising solution, through local search, whenever the best solution has not been updated for a certain number of generations. Computational experiments on randomly generated problems are carried out to compare the MGA with the general GA and special-purpose heuristics. The results show that the MGA is superior to general GA in solution quality with similar computation times. The MGA solutions are also better than those given by special-purpose heuristics though MGA takes longer computation time.