Transient behavior in a flexible assembly system (original) (raw)
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Moving policies in cyclic assembly line scheduling
Theoretical Computer Science, 2006
We consider an assembly line problem that occurs in various kinds of production automation. Our original motivation lies in the automated manufacturing of PC boards. The assembly line has to process a (potentially infinite) number of identical workpieces in a cyclic fashion. In contrast to common variants of assembly line scheduling, the forward steps are variable and may be smaller than the distance of two stations. Therefore, each station may process parts of several workpieces at the same time, and parts of a workpiece may be processed by several stations at the same time. The throughput rate is determined by the number of (cyclic) forward steps, the offsets of the individual forward steps, and the distribution of jobs over the stationary stages between the forward steps. The number of forward steps as well as the offsets are part of the output. However, no matter whether they are part of the input or the output, the optimal assignment of the jobs to the stationary stages is NP-hard.
Simulation Practice and Theory, 1996
Queueing models are widely used for performance analysis of Flexible Manufacturing Systems (FMS). Most studies are done under steady state assumptions. The inherent flexibility of FMS in terms of input, volume, and mix makes such an assumption hard to justify. In this paper, we investigate the convergence rate to steady state in simple queueing models that constitute the basic building blocks of more complex FMS models. The study reveals that steady-state conditions are not achieved during the execution of batches of moderate size. We therefore conclude that although equilibrium models are appropriate for studying long-term planning problems, for the operational control of FMSs, it is highly desirable to study the transient behaviour of the system. On a broader scope, our investigation also shows that steady-state assumptions used in the analysis of any inherently transient system should be carefully validated. Keywords: FMS; Queue dynamics; Steady state of dynamic queuing problem * Corresponding author. 0928-4869/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SSDIO928-4869(95)00020-8
Stability analysis of an optimal balance for an assembly line with fixed cycle time
European Journal of Operational Research, 2006
We address the simple assembly line balancing problem: minimize the number of stations m for processing n partially ordered operations V = {1, 2, . . ., n} within the cycle time c. The processing time t i of operation i 2 V and cycle time c are given. However, during the life cycle of the assembly line the values t i are definitely fixed only for the subset of automated operations V n e V . Another subset e V V includes manual operations, for which it is impossible to fix the exact processing times during the whole life cycle of the assembly line. If j 2 e V , then operation time t j can be different for different cycles of production process. For the optimal line balance b of a paced assembly line with vector t = (t 1 , t 2 , . . ., t n ) of the operation times, we investigate stability of its optimality with respect to possible variations of the processing times t j of the manual operations j 2 e V . In particular, we derive necessary and sufficient conditions when optimality of the line balance b is stable with respect to sufficiently small variations of the operation times t j , j 2 e V . We show how to calculate the maximal value of independent variations of the processing times of all the manual operations, which definitely keep the feasibility and optimality of the line balance b.
Performance analysis of assembly systems with unreliable machines and finite buffers
European Journal of Operational Research, 2005
An unreliable assembly system is studied in which different types of components are processed by two separate work centers before merging to an assembly station with random breakdown. Blocking at the work centers and starvation at the assembly station may occur because of finite buffer sizes and uncertainties in job arriving times and processing/ assembly times. We derive the system stability condition, and obtain formulas for the system state probabilities, blocking probabilities, starvation probability, stockout probability, system availability in the steady state. We also obtain the distributions of blocking times and first failure times, respectively. Through numerical examples, we elaborate on the monotonous properties of the performance measures, and draw the insights into the impacts of the system parameters on its various performance indices, which provide important guidance for design of assembly systems.
Stability radius of the optimal assembly line balance with fixed cycle time
We address the simple assembly line balancing problem: Minimize the number of stations m for processing n partially ordered operations V={1, 2, ..., n} within the given cycle time c. The processing time ti is given for each operation iV but cannot be changed only for the operations from the subset of automated and semi-automated operations Ṽ \ V . If Ṽ \ V i , then operation time ti is strictly positive real number, which is fixed during the life cycle of the assembly line. Subset Ṽ of set V includes manual operations, for which it is hard or even impossible to fix processing time for the whole life cycle of the assembly line. We assume that if Ṽ j
Cyclic Scheduling of Flexible Mixed Model Assembly Lines
IFAC Proceedings Volumes, 2013
In this paper, the problem of balancing and cyclic scheduling of flexible mixed model assembly lines with parallel stations is studied. To exploit the connection between balancing and cyclic scheduling problems for an efficient line management, they are considered simultaneously. A novel constraint programming model including problem specific symmetry breaking constraints is proposed to solve this problem. Experiments on extensive number of test instances with various sizes are also presented.
Lead time control in multi-class multi-stage assembly systems with finite capacity
Computers & Industrial Engineering, 2013
In this paper, we model multi-class multi-stage assembly systems with finite capacity as queueing networks. It is assumed that different classes (types) of products are produced by the production system and products' orders for different classes are received according to independent Poisson processes. Each service station of the queueing network specifies a manufacturing or assembly operation, in that processing times for different types of products are independent and exponentially distributed random variables with service rates, which are controllable, and the queueing discipline is First Come First Served (FCFS). Different types of products may be different in their routing sequences of manufacturing and assembly operations. For modeling multi-class multi-stage assembly systems, we first consider every class separately and convert the queueing network of each class into an appropriate stochastic network. Then, by using the concept of continuous-time Markov processes, a system of differential equations is created to obtain the distribution function of manufacturing lead time for any type of product, which is actually the time between receiving the order and the delivery of finished product. Furthermore, we develop a multi-objective model with three conflicting objectives to optimally control the service rates, and use goal attainment method to solve a discrete-time approximation of the original multi-objective continuous-time problem.
European Journal of Operational Research, 1986
Recently flexible manufacturing systems (FMSs) have been modelled as closed networks of queues. In this paper we develop an exponentialization approach to the modeling of FMS networks with general processing times. The idea of the approach is to transform the network into an (approximately) equivalent exponential network, where each station has exponential processing times with state-dependent rates. The approach is formulated as a fixed-point problem. Numerical examples have indicated excellent accuracies of the approach. This approach can also be readily adapted to accommodate limited local buffers and dynamic parts routing.
Evaluative Models of Discrete Part Production Lines
Analysis and Design of …, 2009
The focus here is on discrete part production lines with asynchronous movement where each part produced is distinct. Production lines processing fluids and other continuous materials are not considered. From here on, when reference is made to production lines, discrete part production lines will be understood. In a production or flow line, all jobs are required to pass through each station in the same sequence once. These lines are usually associated with scale rather than scope, and a major advantage of production lines is the associated simple materials handling requirements.