Production scheduling optimisation with machine state and time-dependent energy costs

The increase of energy costs specially in manufacturing system encourages researchers to pay more attention to energy management in different ways. This paper investigates a non-preemptive single-machine manufacturing environment to reduce total energy costs of a production system. For this purpose, two new mathematical models are presented. The first contribution consists of an improvement of a mathematical formulation proposed in the literature which deals and deals with a scheduling problem at machine level to process the jobs in a predetermined order. The second model focuses on the generalisation of the previous one to deal simultaneously with the production scheduling at machine level as well as job level. So, the initial predetermined fixed sequence assumption is removed. Since this problem is NP-hard, an heuristic algorithm and a genetic algorithm based on the second model are developed to provide good solutions in reasonable computational time. Finally, the effectiveness of the proposed models and optimisation methods have been tested with different numerical experiments. In average, for small size instances which the mathematical model provides a solution in reasonable computational time, a gap of 2.2% for the heuristic and 1.82% for GA are achieved comparing to the exact method’s solution. These results demonstrate the accuracy and efficiency of both proposed algorithms.     

Parallel flowshop scheduling using Tabu search

Production scheduling problems in manufacturing systems with parallel machine flowshops are discussed. A mathematical programming model for combined part assignment and job scheduling is developed. The objective of solving the scheduling problem is to minimize a weighted sum of production cost and the cost incurred from late product delivery. The solution of the model is NP-hard. To solve the problem efficiently, a heuristic algorithm combining Tabu search and Johnson's method was proposed. Several numerical examples are presented to illustrate the developed model and the algorithm. Computational results from these example problems are very encouraging.     

A discrete artificial bee colony algorithm for single machine scheduling problems

This paper presents a discrete artificial bee colony algorithm for a single machine earliness–tardiness scheduling problem. The objective of single machine earliness–tardiness scheduling problems is to find a job sequence that minimises the total sum of earliness–tardiness penalties. Artificial bee colony (ABC) algorithm is a swarm-based meta-heuristic, which mimics the foraging behaviour of honey bee swarms. In this study, several modifications to the original ABC algorithm are proposed for adapting the algorithm to efficiently solve combinatorial optimisation problems like single machine scheduling. In proposed study, instead of using a single search operator to generate neighbour solutions, random selection from an operator pool is employed. Moreover, novel crossover operators are presented and employed with several parent sets with different characteristics to enhance both exploration and exploitation behaviour of the proposed algorithm. The performance of the presented meta-heuristic is evaluated on several benchmark problems in detail and compared with the state-of-the-art algorithms. Computational results indicate that the algorithm can produce better solutions in terms of solution quality, robustness and computational time when compared to other algorithms.     

Optimal process plan selection in networked based manufacturing using game-theoretic approach

This paper proposes a scheme for generating optimal process plans for multi jobs in a networked based manufacturing system. Networked manufacturing offers several advantages in the current competitive atmosphere such as reducing short manufacturing cycle time and maintaining the production flexibility, thereby achieving several feasible process plans. An N-person non-co-operative game with complete information is proposed and a mathematical model has been developed to generate the payoff functions. To be part of a game, we divided the game into two sub-games such as games to address sub-game (GASG) and games to solve sub-game (GSSG) which try to interact with each other and achieve the Nash equilibrium (NE). Consequently, a hybrid dynamic-DNA (HD-DNA) based evolutionary algorithm approach has been developed for more effective solutions of the game and also for finding the perfect NE points. The objective of this game is to generate the optimal process plans to minimise the makespan. Finally, three cases having different job complexities are presented to demonstrate the feasibility of the approach. The proposed algorithm is validated and results are analysed to benefit the manufacturer.     

Costing-based coordination between mt-iPSS customer and providers for job shop production using game theory

The industrial product-service system for Computer Numerical Control machine tool (mt-iPSS) has drawn much interest. Under the new paradigm of functional result-oriented mt-iPSS, mt-iPSS customer (i.e. owner of the workshop) pays for time or results of mt-iPSS providers. The present problem for mt-iPSS customer is how to timely identify the optimal machine tools, sequence and cutting parameters of operation to finish the jobs while mt-iPSS providers try to maximise their benefit in a non-cooperative game structure. In this paper, a Stackelberg game model is put forward to solve the coordination problem based on the costing of different job shop scheduling solutions under the result-oriented mt-iPSS paradigm. Then, to solve the established bi-level programming model of the Stackelberg game, a solution procedure based on hierarchical particle swarm optimisation is proposed. Finally, a case from a printing machinery enterprise is analysed to validate the proposed model. This research is expected to improve the quality and effectiveness of coordination for scheduling and process planning decision between mt-iPSS customer and multi-providers.     

A genetic algorithm-based approach to machine assignment problem

Over the last few decades, production scheduling problems have received much attention. Due to global competition, it is important to have a vigorous control on production costs while keeping a reasonable level of production capability and customer satisfaction. One of the most important factors that continuously impacts on production performance is machining flexibility, which can reduce the overall production lead-time, work-in-progress inventories, overall job lateness, etc. It is also vital to balance various quantitative aspects of this flexibility which is commonly regarded as a major strategic objective of many firms. However, this aspect has not been studied in a practical way related to the present manufacturing environment.

In this paper, an assignment and scheduling model is developed to study the impact of machining flexibility on production issues such as job lateness and machine utilisation. A genetic algorithm-based approach is developed to solve a generic machine assignment problem using standard benchmark problems and real industrial problems in China. Computational results suggest that machining flexibility can improve the overall production performance if the equilibrium state can be quantified between scheduling performance and capital investment. Then production planners can determine the investment plan in order to achieve a desired level of scheduling performance.     

An improved imperialist competitive algorithm based photolithography machines scheduling

Abstract: Photolithography machine is one of the most expensive equipment in semiconductor manufacturing system, and as such is often the bottleneck for processing wafers. This paper focuses on photolithography machines scheduling with the objective of total completion time minimisation. In contrast to classic parallel machines scheduling, it is characterised by dynamical arrival wafers, re-entrant process flows, dedicated machine constraints and auxiliary resources constraints. We propose an improved imperialist competitive algorithm (ICA) within the framework of a rolling horizon strategy for the problem. We develop a variable time interval-based rolling horizon strategy to decide the scheduling point. We address the global optimisation in every local scheduling by proposing a mixed cost function. Moreover, an adaptive assimilation operator and a sociopolitical competition operator are used to prevent premature convergence of ICA to local optima. A chaotic sequence-based local search method is presented to accelerate the rate of convergence. Computational experiments are carried out comparing the proposed algorithm with ILOG CPLEX, dispatching rules and meta-heuristic algorithms in the literature. It is observed that the algorithm proposed shows an excellent behaviour on cycle time minimisation while with a good on time delivery rate and machine utilisation rate.     

考虑工序并行的差异工件批调度研究

针对铸造车间差异工件组批多约束的问题,在工序可并行加工的前提下构建以最小化最大完工时间和最小化沙箱空置率为优化目标的并行工序批调度模型,设计一种改进和声算法求解该调度模型,提出一种单工序编解码方式和2种机器分配规则用于解决工件分批、沙箱选择、工序分配及机器选择的问题。在算法中提出一种新的和声产生方式和更新机制,同时为改善算法的局部搜索能力,加入模拟退火算法执行局部搜索过程。最后根据企业实际生产数据进行仿真实验,验证本文模型的有效性。     

面向成套订单的生产与配送协调的排序研究

在工件体积和运输车辆容量的双重约束条件下,建立了以最大化成套订单数和最小化工件总配送时间的多目标规划模型,使用多目标排序寻找"约束解"的方法结合遗传算法求解此模型.最后通过算例分析,给出多目标规划模型及其综合算法在FLOW SHOP生产作业环境中的应用.计算结果表明,应用此模型和算法能够满足最大化成套订单数的要求,同时节省总的工件配送时间,有潜在的应用价值.     

Multitasking parallel-machine scheduling with machine-dependent slack due-window assignment

We consider the problem of parallel-machine scheduling with machine-dependent slack (SLK) due-window assignment in the multitasking environment, which exists in various application domains such as Internet services, project management, and manufacturing. Motivated by practical observations, we extend the original model of multitasking to a more general model where each job’s interruption proportion depends on the job itself and its processing position. In the light of individualised service, we consider SLK due-window assignment. Our objective is to minimise the total cost that comprises the earliness, tardiness, and due-window-related costs. Finding that an optimal schedule exists when each machine is occupied by at least one job, we show that the problem is polynomially solvable. We provide a more efficient solution algorithm for a special case of the problem. Finally, we present numerical examples to illustrate the application of the theoretical results and working of the solution algorithms.     

有模具约束的并行机批量流调度问题研究

大多数调度问题均假设产品以单个或整批的方式进行生产,而实际生产过程中,会把产品分批后再进行生产。但当考虑模具约束时,对如何解决产品分批以及制定合理调度方案的问题,本文以最小化最大完工时间为优化目标,建立了考虑模具约束的并行机批量流调度模型,并提出了一种基于遗传算法和差分算法结合的混合差分遗传算法（DEGA）,实现分批与调度两个问题并行优化。最后通过对算例测试,DEGA算法得到更优的解,证明了该算法的优越性和稳定性。结合实际案例,验证了模型和算法的可行性。     

Scheduling with alternatives: a link between process planning and scheduling

The objective of this research is to develop and evaluate effective, computationally efficient procedures for scheduling jobs in a large-scale manufacturing system involving, for example, over 1000 jobs and over 100 machines. The main performance measure is maximum lateness; and a useful lower bound on maximum lateness is derived from a relaxed scheduling problem in which preemption of jobs is based on the latest finish time of each job at each machine. To construct a production schedule that minimizes maximum lateness, an iterative simulation-based scheduling algorithm operates as follows: (a) job queuing times observed at each machine in the previous simulation iteration are used to compute a refined estimate of the effective due date (slack) for each job at each machine; and (b) in the current simulation iteration, jobs are dispatched at each machine in order of increasing slack. Iterations of the scheduling algorithm terminate when the lower bound on maximum lateness is achieved or the iteration limit is reached. This scheduling algorithm is implemented in Virtual Factory, a Windows-based software package. The performance of Virtual Factory is demonstrated in a suite of randomly generated test problems as well as in a large furniture manufacturing facility. To further reduce maximum lateness, a second scheduling algorithm also incorporates a tabu search procedure that identifies process plans with alternative operations and routings for jobs. This enhancement yields improved schedules that minimize manufacturing costs while satisfying job due dates. An extensive experimental performance evaluation indicates that in a broad range of industrial settings, the second scheduling algorithm can rapidly identify optimal or nearly optimal schedules.     

混合工作日历下批量生产柔性作业车间多目标调度方法

提出了一种混合工作日历下批量生产柔性作业车间多目标调度方法。考虑设备的混合工作日历约束,构建了以生产周期最短、制造成本最低为优化目标的批量生产柔性作业车间多目标调度模型。设计了一种带精英策略的非支配排序遗传算法(NSGA II)求解该模型。算法中,采用“基于工序和设备的分段编码”方式分别对工序和设备进行编码;采用“基于工序和设备的分段交叉和变异方式”进行交叉和变异操作,采用“遗传算子改进策略”保证交叉、变异后子代个体的可行性;解码操作采用“基于平顺移动的原理”和“基于工作日历的时间推算技术”推算工序的调整开始、调整结束、加工开始和加工结束时刻。最后,通过案例分析验证了所提方法的有效性。     

广告视角下智能小区实时定价博弈分析

考虑连续时间内供电商对用户的争抢行为，将广告微分博弈引入智能电网系统中以刻画供电商之间的相互竞争，并建立多供电商多用户Stackelberg博弈模型研究智能电网实时定价问题。通过求解用户侧优化问题及供电商之间非合作微分博弈纳什均衡，最终获得供电商与用户之间Stackelberg博弈均衡，以此得到供电商广告竞争下的智能电网实时电价。数值仿真结果表明：采取广告行为供电商的最大支付随其广告成本和定价先增后减，而随用户规模扩大而递增；另外，随着单位广告成本的增加，供电商统一电价逐渐降低，带来用户效用提高，且拥有较低广告成本的供电商售电较多。     

遗传算法的双目标柔性作业车间调度研究

研究了FMS环境下先进制造车间路径柔性的优化调度问题.同时考虑现代生产准时制的要求,建立了柔性作业车间调度问题的双目标数学优化模型,并给出了求解模型的遗传算法的具体实现过程;针对模型的特殊性,提出了染色体两层编码结构,将AOV网络图应用到解码和适应度函数的计算中,通过一个调度实例进行验证,给出了相应的选择、交叉、变异操作设计方案.     

供应链中生产和运输协调调度问题初探

提出了解决供应链中生产和航空运输协调调度问题的理论框架.基于对生产调度和航空运输调度彼此制约关系的分析,协调调度问题被分解为两个子调度问题.建立了航空运输子调度问题的整数规划模型,并证明了该问题为NP完全问题.提出了基于倒排调度方法(backward scheduling method)的调度算法解单机生产调度子问题.     

Measuring the R&D efficiency of regions by a parallel DEA game model

This paper proposes a model that can measure the R&D efficiency of each region (DMU) or each production unit while taking the inter-DMU competition and inter-subprocesses competition into account. The game cross-efficiency concept is introduced into the parallel DEA model. Furthermore, each DMU (subprocess) tries to maximize its own efficiency without harming the cross efficiency of each of the other DMUs (subprocess). We carry out an algorithm to obtain the best game cross-efficiency scores. This score has been proved to converge to a Nash equilibrium point. We use the proposed model to measure the R&D efficiency of the 30 provinces of China. The results show that the algorithm converges to a unique cross efficiency and our model indeed takes the bargaining power of DMUs and subprocesses into account.     

A batch splitting method for a job shop scheduling problem in an MRP environment

The job shop scheduling problem has been a major target for many researchers. Unfortunately though, most of the previous research was based on assumptions that are different from the real manufacturing environment. Among those distorted assumptions, two assumptions about set-up time and job composition can greatly influence the performance of a schedule. First, most of the past studies ignored the impact of the before-arrival set-up time. If we know the sequence of operations in advance, we can obtain an improved schedule by preparing the setup before a job arrives. Secondly, most of the past studies assumed that a job consists of only a single part, that is a batch of size one. However, if we assume that a job consists of a batch size greater than one, as in many real manufacturing environments, then we can obtain an improved schedule because we can fill up the idle times of machines with jobs which have smaller processing times by splitting the original batches. However, the number of job orders may then increase due to the split, and the size of the scheduling problem would become too large to be solved in a practical time limit. Consequently, there may be an optimum batch size considering trade-off between better solution and tractability. The current study is the result of an attempt to find an acceptable solution when the production requirement from a MRP system for a planning period exceeds the capacity of a production system. We try to get an improved schedule by splitting the original batch into smaller batches, and consider setting up a machine before the actual arrival of jobs to that machine. Thereby we can meet the due date requirement without resorting to rescheduling of the master production schedule. For the given batch, we disaggregate it according to the algorithm we are proposing. A so-called 'modified shifting bottleneck procedure' is then applied to solve the job shop scheduling problem with a before-arrival family set-up time considering release date, transportation time and due date. The study also shows that we can adapt to unexpected dynamic events more elegantly by allowing the splitting of batches.     

Remanufacturing-oriented process planning and scheduling: mathematical modelling and evolutionary optimisation

Remanufacturing has been widely studied for its potential to achieve sustainable production in recent years. In the literature of remanufacturing research, process planning and scheduling are typically treated as two independent parts. However, these two parts are in fact interrelated and often interact with each other. Doing process planning without considering scheduling related factors can easily introduce contradictions or even infeasible solutions. In this work, we propose a mathematical model of integrated process planning and scheduling for remanufacturing (IPPSR), which simultaneously considers the process planning and scheduling problems. An effective hybrid multi-objective evolutionary algorithm (HMEA) is presented to solve the proposed IPPSR. For the HMEA, a multidimensional encoding operator is designed to get a high-quality initial population. A multidimensional crossover operator and a multidimensional mutation operator are also proposed to improve the convergence speed of the algorithm and fully exploit the solution space. Finally, a specific legalising method is used to ‘legalise’ possible infeasible solutions generated by the initialisation method and mutation operator. Extensive computational experiments carried out to compare the HMEA with some well-known algorithms confirm that the proposed HMEA is able to obtain more and better Pareto solutions for IPPSR.     

A genetic algorithm for the multi-stage and parallel-machine scheduling problem with job splitting – A case study for the solar cell industry

This paper studies a multi-stage and parallel-machine scheduling problem with job splitting which is similar to the traditional hybrid flow shop scheduling (HFS) in the solar cell industry. The HFS has one common hypothesis, one job on one machine, among the research. Under the hypothesis, one order cannot be executed by numerous machines simultaneously. Therefore, multiprocessor task scheduling has been advocated by scholars. The machine allocation of each order should be scheduled in advance and then the optimal multiprocessor task scheduling in each stage is determined. However, machine allocation and production sequence decisions are highly interactive. As a result, this study, motivated from the solar cell industry, is going to explore these issues. The multi-stage and parallel-machine scheduling problem with job splitting simultaneously determines the optimal production sequence, multiprocessor task scheduling and machine configurations through dynamically splitting a job into several sublots to be processed on multiple machines. We formulate this problem as a mixed integer linear programming model considering practical characteristics and constraints. A hybrid-coded genetic algorithm is developed to find a near-optimal solution. A preliminary computational study indicates that the developed algorithm not only provides good quality solutions but outperforms the classic branch and bound method and the current heuristic in practice.