具有工作站数量约束的多人工作站混合装配线平衡问题研究

针对装配线设计或改造过程中存在的因场地或成本原因导致的工作站数量不易变更的问题,研究了节拍已知情况下,具有工作站数量约束的多人工作站混合装配线平衡问题,建立以装配线总人数最小、工人负荷量标准差最小、各产品在各工作站装配时间与节拍之间的标准差最小为目标的数学模型,设计了一种结合差分进化的多目标混合遗传算法对该问题求解。通过案例计算以及与其他算法的对比分析表明,本文算法在收敛性和综合性能方面优于NSGAII和DEMO,在装配线人数和工人负荷标准差方面优于Roshani和Nezami提出的算法。     

Sequencing mixed-model assembly lines: Survey,classification and model critique

Manufacturers in a wide range of industries nowadays face the challenge of providing a rich product variety at a very low cost. This typically requires the implementation of cost efficient, flexible production systems. Often, so called mixed-model assembly lines are employed, where setup operations are reduced to such an extent that various models of a common base product can be manufactured in intermixed sequences. However, the observed diversity of mixed-model lines makes a thorough sequence planning essential for exploiting the benefits of assembly line production. This paper reviews and discusses the three major planning approaches presented in the literature, mixed-model sequencing, car sequencing and level scheduling, and provides a hierarchical classification scheme to systematically record the academic efforts in each field and to deduce future research issues.     

Shortest-route formulation of mixed-model assembly line balancing problem

A shortest-route formulation of the mixed-model assembly line balancing problem is presented. Common tasks across models are assumed to exist and these tasks are performed in the same stations. The formulation is based on an algorithm which solves the single-model version of the problem. The mixed-model system is transformed into a single-model system with a combined precedence diagram. The model is capable of considering any constraint that can be expressed as a function of task assignments.     

Optimal parking of idle elevators under myopic and state-dependent policies

In this paper we discuss the problem of optimally parking single and multiple idle elevators under light-traffic conditions. The problem is analyzed from the point of view of the elevator owner whose objective is to minimize the expected total cost of parking and dispatching the elevator (which includes the cost incurred for waiting passengers). We first consider the case of a single elevator and analyze a (commonly used but suboptimal) state-independent myopic policy that always positions the idle elevator at the same floor. Building on the results obtained for the myopic policy, we then show that the optimal non-myopic (state-dependent) policy calls for dispatching the idle elevator to the state-dependent median of a weight distribution. Next, we consider the more difficult case of two elevators and develop an expression for the expected dispatching distance function. We show that the objective function for the myopic policy is non-convex. The non-myopic policy is found to be dependent on the state of the two idle elevators. We compute the optimal state-dependent policy for two elevators using the results developed for the myopic policy. Next, we examine the case of multiple elevators and provide a general recursive formula to find the expected dispatching distance functions. Finally, we generalize the previous models by incorporating a fixed cost for parking the idle elevators that results in a two-sided optimal policy with different regions. Every policy that we introduce and analyze is illustrated by an example. The paper concludes with a short summary and suggestions for future research.     

Analysis and design of sequencing rules for car sequencing

This paper presents novel approaches for generating sequencing rules for the car sequencing (CS) problem in cases of two and multiple processing times per station. The CS problem decides on the succession of different car models launched down a mixed-model assembly line. It aims to avoid work overloads at the stations of the line by applying so-called sequencing rules, which restrict the maximum occurrence of labor-intensive options in a subsequence of a certain length. Thus to successfully avoid work overloads, suitable sequencing rules are essential. The paper shows that the only existing rule generation approach leads to sequencing rules which misclassify feasible sequences. We present a novel procedure which overcomes this drawback by generating multiple sequencing rules. Then, it is shown how to apply both procedures in case of multiple processing times per station. For both cases analytical and empirical results are derived to compare classification quality.     

A branch-and-bound based solution approach for the mixed-model assembly line-balancing problem for minimizing stations and task duplication costs

A common assumption in the literature on mixed-model assembly line balancing is that a task that is common to multiple models must be assigned to a single station. In this paper, we relax this restriction, and allow a common task to be assigned to different stations for different models. We seek to minimize the sum of costs of the stations and the task duplication. We develop an optimal solution procedure based on a backtracking branch-and-bound algorithm and evaluate its performance via a large set of experiments. A branch-and-bound based heuristic is then developed for solving large-scale problems. The heuristic solutions are compared with a lower bound and experiments show that the heuristic provides much better solutions than those obtained by traditional approaches.     

多周期多种设备公用工程系统优化模型的改进及应用

本文提出了多周期多种设备公用工程系统改进的混合整数双线性优化模型,它含有两种优化变量和系统运行过程的离散动态约束,期望系统总设备投资(含设备折旧)与全周期运行操作费用之和最小。针对改进优化模型求解上的困难,给出将改进优化模型分解成有限多个关于连续变量的线性规划。论述了改进优化模型与分解模型的等价性以及两种模型的主要数学性质,并在此基础上提出了求解策略。最后将改进优化模型应用于某石化企业的蒸汽动力系统最优设计与运行优化集成实例。     

Batch arrival queues with vacations and server setup

We study a single server queueing system whose arrival stream is compound Poisson and service times are generally distributed. Three types of idle period are considered: threshold, multiple vacations, and single vacation. For each model, we assume after the idle period, the server needs a random amount of setup time before serving. We obtain the steady-state distributions of system size and waiting time and expected values of the cycle for each model. We also show that the distributions of system size and waiting time of each model are decomposed into two parts, whose interpretations are provided. As for the threshold model, we propose a method to find the optimal value of threshold to minimize the total expected operating cost.     

Pattern Based Vocabulary Building for Effectively Sequencing Mixed-Model Assembly Lines

In this paper, the problem of sequencing mixed-model assembly lines in case of fixed rate launching and closed stations is considered. The problem consists of finding an intermixed sequence of different models of a basic product, which are jointly produced on an assembly line, such that customer demands are fulfilled and total work overload is minimized. For solving this problem an informed tabu search procedure with a pattern based vocabulary building strategy is developed. Computational tests demonstrate that considerable improvements are obtained by comparison to methods which do not incorporate such an approach.     

Algorithms for Toyota's goal of sequencing mixed models on an assembly line with multiple workstations

Toyota's goal of sequencing mixed models on an assembly line is to keep the constant usage rate of every part used in the assembly line. This paper deals with Toyota's goal of sequencing mixed models on an assembly line with multiple workstations. A sequencing problem with Toyota's goal is formulated. Two algorithms based on different mechanisms, respectively modified goal chasing and simulated annealing, are developed for solving the sequencing problem. A number of numerical experiments are carried out for evaluating the efficiency of the algorithms. Computational results show that one of the algorithms generates good sub-optimal solutions with very short CPU times, while the other can reach optimal solutions with longer, but acceptable, CPU times.     

Resequencing of mixed-model assembly lines: Survey and research agenda

Nowadays, mixed-model assembly lines are applied in a wide range of industries to mass-produce customized products to order, e.g., in automobile industry. An important decision problem in this context receiving a lot of attention from researchers and practitioners is the sequencing problem, which decides on the succession of workpieces launched down the line. However, if multiple departments with diverging sequencing objectives are to be passed or unforeseen disturbances like machine breakdowns or material shortages occur, a resequencing of a given production sequence often becomes equally essential. This paper reviews existing research on resequencing in a mixed-model assembly line context. Important problem settings, alternative buffer configurations, and resulting decision problems are described. Finally, future research needs are identified as some relevant real-world resequencing settings have not been dealt with in literature up to now.     

Multi-server system with single working vacation

We consider an M/M/R queue with vacations, in which the server works with different service rates rather than completely terminates service during his vacation period. Service times during vacation period, service times during service period and vacation times are all exponentially distributed. Neuts’ matrix–geometric approach is utilized to develop the computable explicit formula for the probability distributions of queue length and other system characteristics. A cost model is derived to determine the optimal values of the number of servers and the working vacation rate simultaneously, in order to minimize the total expected cost per unit time. Under the optimal operating conditions, numerical results are provided in which several system characteristics are calculated based on assumed numerical values given to the system parameters.     

混合型装配线平衡问题求解方法研究

对混合型装配线平衡问题进行了描述和数学建模,提出一种启发式求解算法,求解目标是最小化工作站数目.为进一步优化求解结果,对启发式算法求解的结果进行仿真研究,分析各工作站的工作率、等待率和阻塞率,并以此为依据调整部分作业任务的分配,允许不同品种产品的相同作业任务安排在不同的工作站中,以对求解结果进行修正,进一步均衡各工作站的作业量.该求解方法既简化了求解过程,又兼顾到了系统的瞬时特性和作业任务的不可拆分性对求解结果的影响,实例分析验证了方法的有效性.     

Car sequencing versus mixed-model sequencing: A computational study

The paper deals with the two most important mathematical models for sequencing products on a mixed-model assembly line in order to minimize work overload the mixed-model sequencing (MMS) model and the car sequencing (CS) model. Although both models follow the same underlying objective, only MMS directly addresses the work overload in its objective function. CS instead applies a surrogate objective using so-called sequencing rules which restrict labor-intensive options accompanied with the products in the sequence. The CS model minimizes the number of violations of the respective sequencing rules, which is widely assumed to lead to minimum work overload. This paper experimentally compares CS with MMS in order to quantify the gap in the solution quality between both models. The paper studies several variants of CS with different sequencing rule generation approaches and different objective functions from the literature as well as a newly introduced weighting factor. The performance of the different models is evaluated on a variety of random test instances. Although the objectives of CS and MMS are positively linearly correlated, results show that a sequence found by CS leads to at least 15% more work overload than a solution found by MMS. For none of the considered test instances and for none of the three different objective functions, CS is able to produce competitive results in terms of solution quality (work overload) compared to MMS. The results suggest that decision makers using CS should investigate whether MMS would lead to better sequencing orders for their specific instances.     

Minimizing the Number of Machine Idle Intervals with Minimum Makespan in a Flow-Shop

This paper considers a selected sequence in a permutation flow-shop. The objective is to minimize the number of machine idle intervals with minimum makespan (or total production time) for this selected sequence. There are at least two advantages of minimizing the number of machine idle intervals. The first reduces the number of times necessary to restart machines. The second achieves a longer period of idle time for each idle interval, and hence the idle time may be used more efficiently. An integer programming formulation is presented to provide the optimal solution. A heuristic algorithm is also proposed to solve large-sized problems. The heuristic finds the optimal solution for the three-machine case and is found to provide the optimal or near-optimal solution for other cases.     

A survey on problems and methods in generalized assembly line balancing

Assembly lines are traditional and still attractive means of mass and large-scale series production. Since the early times of Henry Ford several developments took place which changed assembly lines from strictly paced and straight single-model lines to more flexible systems including, among others, lines with parallel work stations or tasks, customer-oriented mixed-model and multi-model lines, U-shaped lines as well as unpaced lines with intermediate buffers.In any case, an important decision problem, called assembly line balancing problem, arises and has to be solved when (re-) configuring an assembly line. It consists of distributing the total workload for manufacturing any unit of the product to be assembled among the work stations along the line.Assembly line balancing research has traditionally focused on the simple assembly line balancing problem (SALBP) which has some restricting assumptions. Recently, a lot of research work has been done in order to describe and solve more realistic generalized problems (GALBP). In this paper, we survey the developments in GALBP research.     

A cost minimization procedure for mixed model production lines with normally distributed task times

This paper presents design procedures for mixed model production lines. The design objective is to minimize the total operating cost, composed of labor cost, in-process inventory cost, and set-up cost. This paper is an extension of our previous work in which we recognize the variability associated with task times and propose a procedure that can handle either deterministic or stochastic task times.     

Supply chain models for an assembly system with preprocessing of raw materials

In this paper, we investigate the material procurement and delivery policy in a production system where raw materials enter into the assembly line from two different flow channels. The system encompasses batch production process in which the finished product demand is approximately constant for an infinite planning horizon. Two distinct types of raw materials are passed through the assembly line before to convert them into the finished product. Of the two types of raw materials, one type requires preprocessing inside the facility before the assembly operation and other group is fed straightway in the assembly line. The conversion factors are assigned to raw materials to quantify the raw material batch size required. To analyze such a system, we formulate a nonlinear cost function to aggregate all the costs of the inventories, ordering, shipping and deliveries. An algorithm using the branch and bound concept is provided to find the best integer values of the optimal solutions. The result shows that the optimal procurement and delivery policy minimizes the expected total cost of the model. Using a test problem, the inventory requirements at each stage of production and their corresponding costs are calculated. From the analysis, it is shown that the rate and direction change of total cost is turned to positive when delivery rates per batch reaches close to the optimal value and the minimum cost is achieved at the optimal delivery rate. Also, it is shown that total incremental cost is monotonically increasing, if the finished product batch size is increased, and if, inventory cost rates are increased. We examine a set of numerical examples that reveal the insights into the procurement-delivery policy and the performance of such an assembly type inventory model.     

Scheduling in a multi-class series of queues with deterministic service times

We consider a problem of scheduling in a multi-class network of single-server queues in series, in which service times at the nodes are constant and equal. Such a model has potential application to automated manufacturing systems or packet-switched communication networks, where a message is divided into packets (or cells) of fixed lengths. The network is a series-type assembly or transfer line, with the exception that there is an additional class of jobs that requires processing only at the first node (class 0). There is a holding cost per unit time that is proportional to the total number of customers in the system. The objective is to minimize the (expected) total discounted holding cost over a finite or an infinite horizon. We show that an optimal policy gives priority to class-0 jobs at node 1 when at least one of a set ofm–1 inequalities on partial sums of the components of the state vector is satisfied. We solve the problem by two methods. The first involves formulating the problem as a (discrete-time) Markov decision process and using induction on the horizon length. The second is a sample-path approach using an interchange argument to establish optimality.The research of this author was supported by the National Science Foundation under Grant No. DDM-8719825. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.     

Mixed integer programming formulations for the Biomass Truck Scheduling problem

In this paper, we introduce the Biomass Truck Scheduling (BTS) problem that originated in a real-life herbaceous biomass supply chain (HBSC) around Pécs, Hungary. BTS can be considered as a Parallel Machine Scheduling with a Single Server problem, where identical trucks (parallel machines) deliver biomass from satellite storage locations to a central biorefinery operating a single unloader (single server). We make two particular assumptions regarding the server: the server operation has a unit time length for each trip and idle periods are not allowed for it (server no idle time constraint). We consider two objective functions associated with the revealed HBSC logistic cost structure. First, the number of trucks is minimized (resource availability cost) following which the total truck idle time is minimized. Three mixed integer programming formulations are constructed to solve BTS, and their efficiency is evaluated using a number of test cases. We found that, even if the number of trucks is locked at its minimum value, there is always a schedule with zero truck idle time—that is, there is no trade-off between these two objective functions.