A Branch-and-Bound Based Heuristic Algorithm for Minimizing Makespan in Machining-Assembly Flowshop Scheduling

This paper proposes a heuristic algorithm, called list-based squeezing branch and bound algorithm, for solving a machine-fixed, machining-assembly flowshop scheduling problem to minimize makespan. The machine-fixed, machining-assembly flowshop consists of some parallel two-machine flow lines at a machining stage and one robot at an assembly stage. Since an optimal schedule for this problem is not always a permutation schedule, the proposed algorithm first finds a promising permutation schedule, and then searches better non-permutation schedules near the promising permutation schedule in an enumerative manner by elaborating a branching procedure in a branch and bound algorithm. The results of numerical experiments show that the proposed algorithm can efficiently provide an optimal or a near-optimal schedule with high accuracy such as mean relative error being less than 0.2% and the maximum relative error being at most 3%.

Sequencing Mixed-model Production Systems by Modified Multi-objective Genetic Algorithms

As two independent problems,scheduling for parts fabrication line and sequencing for mixed-model assembly line have been addressed respectively by many researchers.However,these two problems should be considered simultaneously to improve the efficiency of the whole fabrication/assembly systems.By far,little research effort is devoted to sequencing problems for mixed-model fabrication/assembly systems.This paper is concerned about the sequencing problems in pull production systems which are composed of one mixed-model assembly line with limited intermediate buffers and two flexible parts fabrication flow lines with identical parallel machines and limited intermediate buffers.Two objectives are considered simultaneously：minimizing the total variation in parts consumption in the assembly line and minimizing the total makespan cost in the fabrication/assembly system.The integrated optimization framework,mathematical models and the method to construct the complete schedules for the fabrication lines according to the production sequences for the first stage in fabrication lines are presented.Since the above problems are non-deterministic polynomial-hard（NP-hard）,a modified multi-objective genetic algorithm is proposed for solving the models,in which a method to generate the production sequences for the fabrication lines from the production sequences for the assembly line and a method to generate the initial population are put forward,new selection,crossover and mutation operators are designed,and Pareto ranking method and sharing function method are employed to evaluate the individuals＇ fitness.The feasibility and efficiency of the multi-objective genetic algorithm is shown by computational comparison with a multi-objective simulated annealing algorithm.The sequencing problems for mixed-model production systems can be solved effectively by the proposed modified multi-objective genetic algorithm.

Improved Estimation of Distribution Algorithm for Solving Unrelated Parallel Machine Scheduling Problem

Scheduling problem is a well-known combinatorial optimization problem.An effective improved estimation of distribution algorithm(IEDA) was proposed for minimizing the makespan of the unrelated parallel machine scheduling problem(UPMSP).Mathematical description was given for the UPMSP.The IEDA which was combined with variable neighborhood search(IEDA_VNS) was proposed to solve the UPMSP in order to improve local search ability.A new encoding method was designed for representing the feasible solutions of the UPMSP.More knowledge of the UPMSP were taken consideration in IEDA_ VNS for probability matrix which was based the processing time matrix.The simulation results show that the proposed IEDA_VNS can solve the problem effectively.

Concise review of relaxations and approximation algorithms for nonidentical parallel-machine scheduling to minimize total weighted completion times

A class of nonidentical parallel machine scheduling problems are considered in which the goal is to minimize the total weighted completion time. Models and relaxations are collected. Most of these problems are NP-hard, in the strong sense, or open problems, therefore approximation algorithms are studied. The review reveals that there exist some potential areas worthy of further research.

A novel hybrid estimation of distribution algorithm for solving hybrid flowshop scheduling problem with unrelated parallel machine

The hybrid flow shop scheduling problem with unrelated parallel machine is a typical NP-hard combinatorial optimization problem, and it exists widely in chemical, manufacturing and pharmaceutical industry. In this work, a novel mathematic model for the hybrid flow shop scheduling problem with unrelated parallel machine(HFSPUPM) was proposed. Additionally, an effective hybrid estimation of distribution algorithm was proposed to solve the HFSPUPM, taking advantage of the features in the mathematic model. In the optimization algorithm, a new individual representation method was adopted. The(EDA) structure was used for global search while the teaching learning based optimization(TLBO) strategy was used for local search. Based on the structure of the HFSPUPM, this work presents a series of discrete operations. Simulation results show the effectiveness of the proposed hybrid algorithm compared with other algorithms.

Models and Algorithms of Production Scheduling in Tandem Cold Rolling

在冷滚动的线安排问题的生产的复杂性被分析，也就是，它作为二部分被提出合并卷的优化和计划的滚动的批。钢卷合并的优化作为包装被一个新建议算法计算的问题(MCPP ) 的一只多重集装箱被构造，分离微分进化(DDE ) ，在这篇论文。一个特定的双旅行售货员问题(DTSP ) 为卷批根据进化机制计划，和一个混合启发式的方法被建模，本地搜索被介绍解决这个模型。有从安排方法的生产在这建议了纸是有效的上海 Baosteel 公司有限公司表演的真实生产数据的试验性的结果。

Simulated Annealing Algorithm to Minimize Makespanin Single Machine Scheduling Problem withUniform Parallel Machines

This paper presents a simulated annealing algorithm to minimize makespan of single machine scheduling problem with uniform parallel machines. The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, which are to be scheduled on m parallel machines with different speeds. Since, this scheduling problem is a combinatorial problem;usage of a heuristic is inevitable to obtain the solution in polynomial time. In this paper, simulated annealing algorithm is presented. In the first phase, a seed generation algorithm is given. Then, it is followed by three variations of the simulated annealing algorithms and their comparison using ANOVA in terms of their solutions on makespan.

Genetic Algorithm for Scheduling Reentrant Jobs on Parallel Machines with a Remote Server

This paper considers a reentrant scheduling problem on parallel primary machines with a remote server machine, which is required to carry out the setup operation. In this problem, each job has three operations. The first and last operations are performed by the same primary machine, implying the reentrance, and the second operation is processed on the single server machine. The order of jobs is predetermined in our context. The challenge is to assign jobs to the primary machines to minimize the makespan. We develop a genetic algorithm(GA) to solve this problem. Based on a simple strategy of assigning jobs in batches on the parallel primary machines, the standardized random key vector representation is employed to split the jobs into batches. Comparisons among the proposed algorithm, the branch and bound(BB) algorithm and the heuristic algorithm, coordinated scheduling(CS), which is only one heuristic algorithm to solve this problem in the literature, are made on the benchmark data. The computational experiments show that the proposed genetic algorithm outperforms the heuristic CS and the maximum relative improvement rate in the makespan is 1.66%.

Dual-Objective Mixed Integer Linear Program and Memetic Algorithm for an Industrial Group Scheduling Problem

Group scheduling problems have attracted much attention owing to their many practical applications.This work proposes a new bi-objective serial-batch group scheduling problem considering the constraints of sequence-dependent setup time,release time,and due time.It is originated from an important industrial process,i.e.,wire rod and bar rolling process in steel production systems.Two objective functions,i.e.,the number of late jobs and total setup time,are minimized.A mixed integer linear program is established to describe the problem.To obtain its Pareto solutions,we present a memetic algorithm that integrates a population-based nondominated sorting genetic algorithm II and two single-solution-based improvement methods,i.e.,an insertion-based local search and an iterated greedy algorithm.The computational results on extensive industrial data with the scale of a one-week schedule show that the proposed algorithm has great performance in solving the concerned problem and outperforms its peers.Its high accuracy and efficiency imply its great potential to be applied to solve industrial-size group scheduling problems.

An effective estimation of distribution algorithm for parallel litho machine scheduling with reticle constraints

In order to improve the scheduling efficiency of photolithography,bottleneck process of wafer fabrications in the semiconductor industry,an effective estimation of distribution algorithm is proposed for scheduling problems of parallel litho machines with reticle constraints,where multiple reticles are available for each reticle type.First,the scheduling problem domain of parallel litho machines is described with reticle constraints and mathematical programming formulations are put forward with the objective of minimizing total weighted completion time.Second,estimation of distribution algorithm is developed with a decoding scheme specially designed to deal with the reticle constraints.Third,an insert-based local search with the first move strategy is introduced to enhance the local exploitation ability of the algorithm.Finally,simulation experiments and analysis demonstrate the effectiveness of the proposed algorithm.

A Job Scheduling Model and Heuristic Algorithm for Minimizing the Range of Lateness and Makespan on Parallel Machines

In this paper ,based on JIT management technique, a multi objective job scheduling model is presented. After a new algorithm is presented for minimizing the range of lateness on a single machine , a heuristic algorithm (named M-R algorithm)is given to be applied to the parallel machines’ systems . Finally , an illustrative example is given.

Rolling optimization algorithm based on collision window for single machine scheduling problem

Focusing on the single machine scheduling problem which minimizes the total completion time in the presence of dynamic job arrivals, a rolling optimization scheduling algorithm is proposed based on the analysis of the character and structure of scheduling. An optimal scheduling strategy in collision window is presented. Performance evaluation of this algorithm is given. Simulation indicates that the proposed algorithm is better than other common heuristic algorithms on both the total performance and stability.

A Note on DP Algorithm for Batching Scheduling to Minimize Maximum Lateness

In parallel-batching machine scheduling, all jobs in a batch start and complete at the same time, and the processing time of the batch is the maximum processing time of any job in it. For the unbounded parallel-batching machine scheduling problem of minimizing the maximum lateness, denoted 1|p-batch|L_(max), a dynamic programming algorithm with time complexity O(n^2) is well known in the literature.Later, this algorithm is improved to be an O(n log n) algorithm. In this note, we present another O(n log n) algorithm with simplifications on data structure and implementation details.

Optimal online algorithms for scheduling on two identical machines under a grade of service

This work is aimed at investigating the online scheduling problem on two parallel and identical machines with a new feature that service requests from various customers are entitled to many different grade of service (GoS) levels, so each job and machine are labelled with the GoS levels, and each job can be processed by a particular machine only when its GoS level is no less than that of the machine. The goal is to minimize the makespan. For non-preemptive version, we propose an optimal online al-gorithm with competitive ratio 5/3. For preemptive version, we propose an optimal online algorithm with competitive ratio 3/2.

Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing

Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry,the coordinated scheduling problem of parallel machine production and transportation is investigated.The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance.A non-cooperative game model is established,considering the competition and self-interest behavior of jobs from different customers for machine resources.The job from different customers is mapped to the players in the game model,the corresponding optional processing machine and location are mapped to the strategy set,and the makespan of the job is mapped to the payoff.Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model.A Nash equilibrium solution algorithm based on the genetic algorithm(NEGA)is designed,and the effective solution of approximate Nash equilibrium for the game model is realized.The fitness function,single-point crossover operator,and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium.Rules are also designed to avoid the generation of invalid offspring chromosomes.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.Compared with other algorithms such as heuristic algorithms(FCFS,SPT,and LPT),the simulated annealing algorithm(SA),and the particle swarm optimization algorithm(PSO),experimental results show that the proposed NE-GA algorithm has obvious performance advantages.

Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early

This study examines the multicriteria scheduling problem on a single machine to minimize three criteria: the maximum cost function, denoted by maximum late work (Vmax), maximum tardy job, denoted by (Tmax), and maximum earliness (Emax). We propose several algorithms based on types of objectives function to be optimized when dealing with simultaneous minimization problems with and without weight and hierarchical minimization problems. The proposed Algorithm (3) is to find the set of efficient solutions for 1//F (Vmax, Tmax, Emax) and 1//(Vmax + Tmax + Emax). The Local Search Heuristic Methods (Descent Method (DM), Simulated Annealing (SA), Genetic Algorithm (GA), and the Tree Type Heuristics Method (TTHM) are applied to solve all suggested problems. Finally, the experimental results of Algorithm (3) are compared with the results of the Branch and Bound (BAB) method for optimal and Pareto optimal solutions for smaller instance sizes and compared to the Local Search Heuristic Methods for large instance sizes. These results ensure the efficiency of Algorithm (3) in a reasonable time.

An Optimal Online Algorithm for Scheduling on Two Parallel Machines with GoS Eligibility Constraints

We consider the online scheduling problem on two parallel machines with the Grade of Service(GoS)eligibility constraints.The jobs arrive over time,and the objective is to minimize the makespan.We develop a(1+α)-competitive optimal algorithm,whereα≈0.555 is a solution ofα^(3)−2α^(2)−α+1=0.

AN IMPROVED BRANCH-AND-BOUND ALGORITHM TO MINIMIZE THE WEIGHTED FLOWTIME ON IDENTICAL PARALLEL MACHINES WITH FAMILY SETUP TIMES

这篇文章调查与家庭安装时间安排的相同平行机器。是结束的加权的和预定的客观功能，这个问题被知道强烈 NP 难。我们建议一个建设性的启发式的算法和三互补更低的界限。二这些界限由安装时间的消除或由散布他们中的每到相应家庭的工作继续，当第三基于 lagrangian 松驰时。界限并且启发式被合并到一个 branch-and-bound 算法。获得的试验性的结果在以前的工作介绍的方法超过那些，以解决的问题的尺寸。

考虑运输时间的混合流水车间绿色生产调度

针对运输时间对混合流水车间绿色生产调度的影响这一问题,以最大完工时间、生产能耗及生产成本为优化目标,提出一种改进的多目标麻雀搜索算法(Improved Multi-Objective Sparrow Search Algorithm,IMOSSA)进行求解,参考非支配排序将种群适应度值进行划分、引入正余弦策略提高解集质量、加入多项式变异算子和Levy飞行,提高解集的收敛速度和全局搜索能力,避免陷入局部最优。而后设计16种测试算例,将IMOSSA与其他多目标优化算法进行对比,验证了IMOSSA求解的优越性。最后,以某实际生产车间为例,将其生产调度划分为4种模式,证明算法求解的实用性。