Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm

The traditional production scheduling problem considers performance indicators such as processing time, cost, and quality as optimization objectives in manufacturing systems; however, it does not take energy consumption or environmental impacts completely into account. Therefore, this paper proposes an energy-efficient model for flexible flow shop scheduling (FFS). First, a mathematical model for a FFS problem, which is based on an energy-efficient mechanism, is described to solve multi-objective optimization. Since FFS is well known as a NP-hard problem, an improved, genetic-simulated annealing algorithm is adopted to make a significant trade-off between the makespan and the total energy consumption to implement a feasible scheduling. Finally, a case study of a production scheduling problem for a metalworking workshop in a plant is simulated. The experimental results show that the relationship between the makespan and the energy consumption may be apparently conflicting. In addition, an energy-saving decision is performed in a feasible scheduling. Using the decision method, there could be significant potential for minimizing energy consumption.     

System capacity for a two-commodity multistate flow network with unreliable nodes and capacity weight

The system capacity of a single-commodity flow network is the maximum flow from the source to the destination. This paper discusses the system capacity problem for a two-commodity multistate flow network composed of multistate components (edges and nodes). In particular, each component has both capacity and cost attributes. Both types of commodity, which are transmitted through the same network simultaneously, consume the capacities of edges and nodes differently. That is, the capacity weight varies with types of commodity, edges and nodes. We first define the system capacity as a 2-tuple vector and then propose a performance index, the probability that the upper bound of the system capacity is a given pattern subject to the budget constraint. Such a performance index can be easily computed in terms of upper boundary vectors. An efficient algorithm based on minimal cuts is thus presented to generate all upper boundary vectors. The manager can apply this performance index to measure the quality level of supply-demand systems such as computer, logistics, power transmission, telecommunication and urban traffic systems.     

A holonic approach to flexible flow shop scheduling under stochastic processing times

Flexible flow shop scheduling problems are NP-hard and tend to become more complex when stochastic uncertainties are taken into consideration. This paper presents a novel decomposition-based holonic approach (DBHA) for minimising the makespan of a flexible flow shop (FFS) with stochastic processing times. The proposed DBHA employs autonomous and cooperative holons to construct solutions. When jobs are released to an FFS, the machines of the FFS are firstly grouped by a neighbouring K-means clustering algorithm into an appropriate number of cluster holons, based on their stochastic nature. A scheduling policy, determined by the back propagation networks (BPNs), is then assigned to each cluster holon for schedule generation. For cluster holons of a low stochastic nature, the Genetic Algorithm Control (GAC) is adopted to generate local schedules in a centralised manner; on the other hand, for cluster holons of a high stochastic nature, the Shortest Processing Time Based Contract Net Protocol (SPT-CNP) is applied to conduct negotiations for scheduling in a decentralised manner. The combination of these two scheduling policies enables the DBHA to achieve globally good solutions, with considerable adaptability in dynamic environments. Computation results indicate that the DBHA outperforms either GAC or SPT-CNP alone for FFS scheduling with stochastic processing times.     

Flexible flow shop scheduling with stochastic processing times: A decomposition-based approach

Flexible flow shop scheduling problems are NP-hard and tend to become more complex when stochastic uncertainties are taken into consideration. Although some methods have been developed to address such problems, they remain inherently difficult to solve by any single approach. This paper presents a novel decomposition-based approach (DBA), which combines both the shortest processing time (SPT) and the genetic algorithm (GA), to minimizing the makespan of a flexible flow shop (FFS) with stochastic processing times. In the proposed DBA, a neighbouring K-means clustering algorithm is developed to firstly group the machines of an FFS into an appropriate number of machine clusters, based on their stochastic nature. Two optimal back propagation networks (BPN), corresponding to the scenarios of simultaneous and non-simultaneous job arrivals, are then selectively adopted to assign either SPT or GA to each machine cluster for sub-schedule generation. Finally, an overall schedule is generated by integrating the sub-schedules of machine clusters. Computation results show that the DBA outperforms SPT and GA alone for FFS scheduling with stochastic processing times.     

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.     

Scheduling jobs and maintenances in flexible job shop with a hybrid genetic algorithm

Most flexible job shop scheduling models assume that the machines are available all of the time. However, in most realistic situations, machines may be unavailable due to maintenances, pre-schedules and so on. In this paper, we study the flexible job shop scheduling problem with availability constraints. The availability constraints are non-fixed in that the completion time of the maintenance tasks is not fixed and has to be determined during the scheduling procedure. We then propose a hybrid genetic algorithm to solve the flexible job shop scheduling problem with non-fixed availability constraints (fJSP-nfa). The genetic algorithm uses an innovative representation method and applies genetic operations in phenotype space in order to enhance the inheritability. We also define two kinds of neighbourhood for the problem based on the concept of critical path. A local search procedure is then integrated under the framework of the genetic algorithm. Representative flexible job shop scheduling benchmark problems and fJSP-nfa problems are solved in order to test the effectiveness and efficiency of the suggested methodology. Received: June 2005 /Accepted: December 2005     

解决具有混合约束柔性流水车间调度问题的粒子群优化算法

针对既存在阻塞限制工件又存在无等待约束工件的柔性流水车间调度问题, 提出了一种离散粒子群优化的求解方法。该方法采用基于排列的编码形式, 设计了推进—迭代算法进行解码并计算问题目标值, 利用离散粒子群优化算法进行全局优化, 利用迭代贪婪(iterated greedy, IG)算法提高种群个体的局部搜索能力。此外, 根据问题特点, 提出最早释放优先(first release first, FRF)和最早完工优先(first complete first, FCF)两种机器分配策略。仿真结果表明, 所提出的方法求解混合约束下柔性流水车间调度问题是可行的、有效的。     

Scheduling of multi-component products in a two-stage flexible flow shop

In this research, the problem of scheduling and sequencing of two-stage assembly-type flexible flow shop with dedicated assembly lines, which produce different products according to requested demand during the planning horizon with the aim of minimizing maximum completion time of products is investigated. The first stage consists of several parallel machines in site I with different speeds in processing components and one machine in site II, and the second stage consists of two dedicated assembly lines. Each product requires several kinds of components with different sizes. Each component has its own structure which leading to difference processing times to assemble. Products composed of only single-process components are assigned to the first assembly line and products composed of at least a two-process component are assigned to the second assembly line. Components are placed on the related dedicated assembly line in the second phase after being completed on the assigned machines in the first phase and final products will be produced by assembling the components. The main contribution of our work is development of a new mathematical model in flexible flow shop scheduling problem and presentation of a new methodology for solving the proposed model. Flexible flow shop problems being an NP-hard problem, therefore we proposed a hybrid meta-heuristic method as a combination of simulated annealing (SA) and imperialist competitive algorithms (ICA). We implement our obtained algorithm and the ones obtained by the LINGO9 software package. Various parameters and operators of the proposed Meta-heuristic algorithm are discussed and calibrated by means of Taguchi statistical technique.     

Stochastic models for performance analysis of multistate flexible manufacturing cells

Performance analysis of flexible manufacturing cells (FMCs) can help companies find the pros and cons of production processes. However, the emphasis has been on issues like cell formation, layout design and scheduling optimization. Little seems to have been done to assess the reliability of an FMC. In this paper, we develop the stochastic models for the performance analysis mainly on the reliability of two different FMCs configured from a set of teaching intelligent flexible manufacturing system (TIFMS). The closed form solutions of probabilities of system states are obtained. Then, utilization rate of equipment in the cell and productivities of the two FMCs as the performance indexes are calculated and optimized. Compared to simulation methods, the closed form solutions make calculations of the performance indexes faster and more accurate. When random variables in the stochastic models are assumed to follow non-exponential distributions, the effects of them on the performance indexes are discussed. The objective of this paper is to fill up the gap that the closed form solutions are difficult to obtain as the number of machine tool increases. Another objective is to optimize the performance indexes to help engineers better evaluate the performance of FMC. Numerical analysis cases are used to illustrate the proposed stochastic models.     

A decentralized model for flow shop production with flexible transportation system

The recent advances in technology sectors often clash with traditional organizational paradigms which can limit or make difficult an efficient implementation in the real world. In this paper we show how it is possible to exploit the advantages of innovative technologies in manufacturing when these are supported by new and efficient methods for production management. More in details, we face a flow shop scheduling problem in a shoe manufacturing system in which overtaking of jobs is allowed thanks to an innovative transportation system. Overtaking means that a job can be put in waiting state and another job can surpass it, allowing the change of the scheduling sequence. Preemption is not allowed. The objective function of the problem is the minimization of the maximum lateness. We propose a decentralized model, based on multi-agent system theory, to represent the production cells of the plant and to include the potentiality offered by overtaking of jobs at decisional level. The adoption of a decentralized approach increases the system flexibility since each machine is able to solve its local scheduling problem. Adding or removing machines to the plant will not imply a change in the scheduling algorithms. The outcomes of this work are reached firstly through a formulation of the problem with three flow shop scheduling models, secondly through a comparison of the models with respect to different performance indicators. The results highlight as the decentralized approach is able to reach comparable performances with the centralized one for a relevant number of instances. Moreover sensitivity analysis shows as in the decentralized model the computational time required to solve bigger instances increases less quickly than in the case of centralized ones. Finally, simulations of the decentralized approach clarify as the correlation of the local solution procedure is effected by the number of machines of the flow shop and the coordination mechanism is effected by the number of the jobs to be scheduled.     

Reliability assessment of a multistate freight network for perishable merchandise with multiple suppliers and buyers

This study develops a multistate freight network for single and perishable merchandise to assess the freight performance, where a node denotes a supplier, a distribution centre, or a buyer, while a logistics company providing a freight traffic service is denoted by an edge. For each logistics company, carrying capacity should be multistate since partial capacity may be reserved by some customers. The merchandise may perish or be perished during conveyance because of disadvantageous weather or collision in carrying such that the number of intact cargoes may be insufficient for the buyers. Hence, according to the perspective of supply chain management, the reliability, a probability of the network to successfully deliver the cargoes from the suppliers to the buyers subject to a budget, is proposed to be a performance index, where the suppliers and buyers are not the previous customers. An algorithm in terms of minimal paths to assess the reliability is developed. A fruit logistics case is adopted to explore the managerial implications of the reliability using sensitivity analysis.     

基于混合差分进化算法的无等待流水车间总流水时间优化*

以调度的总流水时间为优化目标, 提出一种混合差分进化算法。 首先, 建立无等待流水车间调度的问题模型,并用快速方法评估总流水时间指标。 其次,采用LPV规则,实现离散问题的连续编码; 用差分进化算法对总流水时间指标执行优化;引入插入邻域和基于pairwise的局部搜索算法, 分别对差分进化算法产生的新个体和差分进化算法的最优解执行邻域搜索, 达到优化目标全局和局部的最优。 最后,通过计算标准算例, 并与其他算法比较, 验证该混合差分进化算法的有效性。     

A comparison of scheduling algorithms for flexible flow shop problems with unrelated parallel machines,setup times,and dual criteria

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0–1 mixed integer program is formulated. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operating time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing (SA), tabu search (TS) and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion-based approach is superior to the others, whereas the proposed SA algorithms are better than TS and genetic algorithms among the iterative metaheuristic algorithms.     

New local diversification techniques for flexible job shop scheduling problem with a multi-agent approach

The Flexible Job Shop problem is among the hardest scheduling problems. It is a generalization of the classical Job Shop problem in that each operation can be processed by a set of resources and has a processing time depending on the resource used. The objective is to assign and to sequence the operations on the resources so that they are processed in the smallest time. In our previous work, we have proposed two Multi-Agent approaches based on the Tabu Search (TS) meta-heuristic. Depending on the location of the optimisation core in the system, we have distinguished between the global optimisation approach where the TS has a global view on the system and the local optimisation approach (FJS MATSLO) where the optimisation is distributed among a collection of agents, each of them has its own local view. In this paper, firstly, we propose new diversification techniques for the second approach in order to get better results and secondly, we propose a new promising approach combining the two latter ones. Experimental results are also presented in this paper in order to evaluate these new techniques.     

改进离散粒子群算法求解柔性流水车间调度问题

针对以最小化完工时间为目标的柔性流水车间调度问题(FFSP),提出了一种改进离散粒子群(DPSO)算法.所提算法重新定义粒子速度和位置的相关算子,并引入编码矩阵和解码矩阵来表示工件、机器以及调度之间的关系.为了提高柔性流水车间调度问题求解的改进离散粒子群算法的初始群体质量,通过分析初始机器选择与调度总完工时间的关系,首次提出一种基于NEH算法的最短用时分解策略算法.仿真实验结果表明,该算法在求解柔性流水车间调度问题上有很好的性能,是一种有效的调度算法.     

A hybrid ant-tabu algorithm for solving a multistate flow network reliability maximization problem

Network reliability optimization for multistate flow networks (MFN) is an important issue for many system supervisors. Network reliability maximization for an MFN by determining the optimal component assignment, where a set of multistate components are ready to be assigned to the network, is a common problem. Previous research solved this problem by developing and applying genetic algorithm. Ant colony optimization (ACO) finds a good solution quickly by utilizing the experience of the proceeding ant but sometimes falls into local optimum. Tabu search (TS) adopts a tabu list to avoid searching in the same direction, and thus it explores other possible solutions. This strategy enlarges the search space. Therefore, we propose a hybrid ant-tabu (HAT) algorithm integrating the advantages of ACO and TS to solve this problem, where network reliability is evaluated in terms of minimal paths (MPs) and Recursive Sum of Disjoint Products. Experimental (RSDP) results show that the proposed HAT has better computational efficiency than several soft computing algorithms for networks with more than six MPs or 10 arcs.     

求解批量流水线调度问题的和声算法

针对以最大完工时间和总流经时间为目标的批量流水线调度问题,提出了改进的和声调度算法。该算法采用基于最大位置值(LPV)规则的编码方式,使具有连续性质的和声算法应用于求解调度问题;提出新的初始化方法,应用了多种群进化的思想更新和声库,并结合和声算法和模拟退火算法各自的特点,给出了两种混合调度算法。仿真实验表明所提算法的可行性和有效性。     

Reliability analysis for an apparel manufacturing system applying fuzzy multistate network

This paper addresses the reliability analysis for a real-world apparel manufacturing system by using fuzzy mathematics. The studied apparel manufacturing system is a precise handicraft profession which involves a great amount of labor-intensive processes. To consider human performance, the apparel manufacturing system is constructed as a fuzzy multistate network, termed apparel manufacturing network (AMN). The workload state of a workstation in the AMN is defined by three fuzzy membership functions: “under-normal-workload”, “normal-workload”, and “over-normal-workload”. Hence, the workload of a workstation is fuzzy multistate and the workstation-reliability is measured by three fuzzy membership functions. Subsequently, the system reliability is evaluated in terms of all workstation-reliabilities, and is derived by fuzzy intersection. The reliability analysis can help the production manager to understand the demand satisfaction of the AMN.     

A stochastic model for the analysis of a two-machine flexible manufacturing cell

This paper presents a stochastic model to determine the performance of a flexible manufacturing cell (FMC) under variable operational conditions, including random machining times, random loading and unloading times, and random pallet transfer times. The FMC under study consists of two machines, pallet handling system, and a loading/unloading robot. After delivering the blanks by the pallet to the cell, the robot loads the first machine followed by the second. Unloading of a part starts with the machine that finishes its part first, followed by the next machine. When the machining of all parts on the pallet is completed, the handling system moves the pallet with finished parts out and brings in a new pallet with blanks. A model with these characteristics turns out to be a Markov chain with a transition matrix of size 5n+3, where n is the number of parts on the pallet. In this paper, we present exact numerical solutions and economic analysis to evaluate FMC systems, to determine optimal pallet capacity and robot speed that minimize total FMC cost per unit of production.     

Improved cuckoo search algorithm for hybrid flow shop scheduling problems to minimize makespan

The multistage hybrid flow shop (HFS) scheduling problems are considered in this paper. Hybrid flowshop scheduling problems were proved to be NP-hard. A recently developed cuckoo search (CS) metaheuristic algorithm is presented in this paper to minimize the makespan for the HFS scheduling problems. A constructive heuristic called NEH heuristic is incorporated with the initial solutions to obtain the optimal or near optimal solutions rapidly in the improved cuckoo search (ICS) algorithm. The proposed algorithm is validated with the data from a leading furniture manufacturing company. Computational results show that the ICS algorithm outperforms many other metaheuristics.