Discrete time model for two-machine one-buffer transfer lines with restart policy

The paper deals with analytical modeling of transfer lines consisting of two machines decoupled by one finite buffer. In particular, the case in which a control policy (referred as “restart policy”) aiming to reduce the blocking frequency of the first machine is addressed. Such a policy consists of forcing the first machine to remain idle (it cannot process parts) each time the buffer gets full until it empties again. This specific behavior can be found in a number of industrial production systems, especially when some machines are affected by outage costs when stops occur. The two-machine one-buffer line is here modeled as a discrete time Markov process and the two machines are characterized by the same operation time. The analytical solution of the model is obtained and mathematical expressions of the most important performance measures are provided. Some significant remarks about the effect of the proposed restart policy on the behavior of the system are also pointed out.     

A Genetic Algorithm for the Allocation of Buffer Storage Capacities in a Production Line with Unreliable Machines

In this paper, we consider a flow-line manufacturing system organized as a series of workstations separated by finite buffers. The failure and repair times of machines are supposed to be exponentially distributed. The production rate of each machine is deterministic, and different machines may have different production rates. The buffer allocation problem consists in determining the buffer capacities with respect to a given optimality criterion, which depends on the average production rate of the line, the buffer acquisition and installation cost, and the inventory cost. For this problem we propose a genetic algorithm where the tentative solutions are evaluated with an approximate method based on the Markov-model aggregation approach.     

Throughput optimization in robotic cells with input and output machine buffers: A comparative study of two key models

We consider the problem of scheduling operations in a robotic cell processing a single part type. Each machine in the cell has a one-unit input buffer and a one-unit output buffer. The machines and buffers are served by one single gripper robot. The domain considered is free-pickup cells with additive inter-machine travel time. The processing constraints specify the cell to be a flow shop. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes throughput. Bufferless robotic cells have been studied extensively in the literature. However, the few studies of robotic cells with output buffers at each machine have shown that the throughput can be improved by such a configuration. We show that there is no throughput advantage in providing machine input buffers in addition to output buffers. The equivalence in throughput between the two models has significant practical implications, since the cost of providing additional buffers at each machine is substantial.     

Intermediate buffer analysis for a production system

In this paper, a production system consisting of two serial machines and an intermediate buffer is studied. A shortage cost is incurred when the upstream machine is down and the buffer is exhausted. The practical example for this type of system can be an automated work center or an automobile general assembly.Researches on a similar two-machine system have been done in some articles where maintenance and an intermediate buffer are considered, but the spare parts are not involved. Nevertheless, spare parts are essential for maintenance implementation, and there is interaction between the buffer inventory and the spare parts due to maintenance activity. This paper is aimed to investigate three types of cost related to the intermediate buffer inventory, and obtain their expectations as functions of several decision parameters on maintenance, buffer, and spare parts during a renewal cycle, by using mathematical analysis. The proposed method can be an important basis for further study of system cost calculation and decision making optimization.     

On modelling the maximum workload allocation for parallel unrelated machines with setups

Consider a manufacturing process in which a group of machines (or people) perform a single operation on a number of different parts. The processing time depends on both the part and the machine. In addition, each machine requires significant setup time between processing different part types. The problem consists of obtaining a feasible allocation of parts to machines such that the makespan (i.e. greatest machine workload) is minimized. We present two equivalent 0–1 models. The first model arises by considering the assignment of individual parts to machines. It is amenable to Lagrangian decomposition techniques. The second model is more hierarchical in nature; it considers the two options of assigning an entire part type to a single machine, or of splitting the type across machines. The second model is more amenable than the first to branch-and-bound techniques. We report about our computational experience for finding lower bounds of the optimal solution by appending violated cuts and, ultimately, obtaining the optimal solution of real-life problems.     

Development of a model for a two-station serial transfer line subject to machine and buffer failure

In modern automated production lines, it is common to connect pairs of machines with mechanical storage devices in order to provide buffering between processing stations. Since these devices are mechanical, they are prone to failure. Previous research concerning the analytical modeling of a class of production lines, the serial transfer line, assumes that these buffers are completely reliable. The concept of an unreliable buffer is introduced and an analytic model of a two machine line with an unreliable buffer is developed. It is proposed that this model will form the foundation for an analytic model of the more complex K > 2 machine serial transfer line with unreliable buffers.     

Tandem queueing system with infinite and finite intermediate buffers and generalized phase-type service time distribution

A tandem queueing system with infinite and finite intermediate buffers, heterogeneous customers and generalized phase-type service time distribution at the second stage is investigated. The first stage of the tandem has a finite number of servers without buffer. The second stage consists of an infinite and a finite buffers and a finite number of servers. The arrival flow of customers is described by a Marked Markovian arrival process. Type 1 customers arrive to the first stage while type 2 customers arrive to the second stage directly. The service time at the first stage has an exponential distribution. The service times of type 1 and type 2 customers at the second stage have a phase-type distribution with different parameters. During a waiting period in the intermediate buffer, type 1 customers can be impatient and leave the system. The ergodicity condition and the steady-state distribution of the system states are analyzed. Some key performance measures are calculated. The Laplace–Stieltjes transform of the sojourn time distribution of type 2 customers is derived. Numerical examples are presented.     

Decomposition of unreliable assembly/disassembly networks with limited buffer capacity and random processing times

An assembly/disassembly (A/D) network is a manufacturing system in which machines perform assembly and/or disassembly operations. We consider tree-structured systems of unreliable machines that produce discrete parts. Processing times, times to failure and times to repair in the inhomogeneous system are assumed to be stochastic and machine-dependent. Machines are separated by buffers of limited capacity. We develop Markov process models for discrete time and continuous time systems and derive approximate decomposition equations to determine performance measures such as production rate and average buffer levels in an iterative algorithm. An improved parameter updating procedure leads to a dramatic improvement with respect to convergence reliability. Numerical results demonstrate that the methods are quite accurate.     

Scheduling Parts in a Combined Production-transportation Work Cell

This paper is concerned with a combined production-transportation scheduling problem. The problem comprises a simple, two-machine, automated manufacturing cell, which either stands alone or is a subunit of a complete flexible manufacturing system. The cell consists of two machines in series with a dedicated part-handling device such as a crane or robotic arm for transferring parts from the first machine to the second. The loading of a new piece on the first machine and the ejection of a finished piece from the second machine are performed by dedicated automated mechanisms. The introduction of parts into the system is done n at a time, whereby the parts are reshuffled into a sequence that minimizes completion time. All processing and transfer times are considered deterministic—a reasonable assumption for a cell comprising a robotic transfer device and two CNC machining units. What complicates the problem is the assumption of a non-negligible time for the transfer device to return (empty) from the second machine to the first. The operation is a generalization of a two-machine flowshop problem, and is formulated as a specially structured, asymmetric travelling salesman problem. An approximate polynomial time 0(n log n) algorithm is proffered. The procedure incorporates a lower bound using the Gilmore–Gomory algorithm for the no-wait, two-machine flowshop problem.     

On the Decay Rates of Buffers in Continuous Flow Lines

Consider a tandem system of machines separated by infinitely large buffers. The machines process a continuous flow of products, possibly at different speeds. The life and repair times of the machines are assumed to be exponential. We claim that the overflow probability of each buffer has an exponential decay, and provide an algorithm to determine the exact decay rates in terms of the speeds and the failure and repair rates of the machines. These decay rates provide useful qualitative insight into the behavior of the flow line. In the derivation of the algorithm we use the theory of Large Deviations.     

Contribution of simulation to the optimization of maintenance strategies for a randomly failing production system

This paper compares two strategies for operating a production system composed of two machines working in parallel and a downstream inventory supplying an assembly line. The two machines, which are prone to random failures, undergo preventive and corrective maintenance operations. These operations with a random duration make the machines unavailable. Moreover, during regular subcontracting operations, one of these machines becomes unavailable to supply the downstream inventory. In the first strategy it is assumed that the periodicity of preventive maintenance operations and the production rate of each machine are independent. The second strategy suggests an interaction between the periods of unavailability and the production rates of the two machines in order to minimize production losses during these periods. A simulation model for each strategy is developed so as to be able to compare them and to simultaneously determine the timing of preventive maintenance on each machine considering the total average cost per time unit as the performance criterion. The second strategy is then considered, and a multi-criteria analysis is adopted to reach the best cost-availability compromise.     

A decomposition method for approximate evaluation of continuous flow multi-stage lines with general Markovian machines

In this paper, a decomposition method for evaluating the performance of continuous flow lines with machines characterized by general Markovian fluid models and finite capacity buffers is proposed. This study uses the exact solution of general two-stage Markovian fluid models as a building block. Decomposition equations are provided to propagate the effect of partial and complete blocking and starvation phenomena throughout the system. A decomposition algorithm that solves the new decomposition equations is proposed. Numerical results prove the good accuracy of the developed method. In particular, a comparison with existing techniques shows that our method is generally more accurate, especially in the estimation of the average buffer levels. Moreover, additional information can be collected by the application of our approach which enables a deeper analysis of the system behavior. Finally, the generality of the approach allows for modeling and studying many different system configurations within a unique framework, also including several previously uninvestigated layouts.     

Cyclic scheduling of a 2-machine robotic cell with tooling constraints

In this study, we deal with the robotic cell scheduling problem with two machines and identical parts. In an ideal FMS, CNC machines are capable of performing all the required operations as long as the required tools are stored in their tool magazines. However, this assumption may be unrealistic at times since the tool magazines have limited capacity and in many practical instances the required number of tools exceeds this capacity. In this respect, our study assumes that some operations can only be processed on the first machine while some others can only be processed on the second machine due to tooling constraints. Remaining operations can be processed on either machine. The problem is to find the allocation of the remaining operations to the machines and the optimal robot move cycle that jointly minimize the cycle time. We prove that the optimal solution is either a 1-unit or a 2-unit robot move cycle and we present the regions of optimality. Finally, a sensitivity analysis on the results is conducted.     

含有批处理机的三机流水作业加工总长问题在某些情形下的强NP困难性

本文研究含有批处理机的三台机器流水作业加工总长问题在某些情形下的计算复杂性。在批处理机上同时加工的工件组成一个工件批，一个工件批的所有工件同时开始、同时结束。当批处理机的容量有限时，我们证明了下列情形为强NP困难的：第一台机器是批处理机、其余两台机器是单机；第二台机器是单机、其余两台机器是批处理机；第三台机器是批处理机、其余两台机器是单机。     

Single-job lot streaming in m − 1 two-stage hybrid flowshops

This paper studies the single-job lot streaming problem in a two-stage hybrid flowshop that has m identical machines at the first stage and one machine at the second stage, to minimise the makespan. A setup time is considered before processing each sublot on a machine. For the problem with the number of sublots given, we prove that it is optimal to use a rotation method for allocating and sequencing the sublots on the machines. With such allocation and sequencing, the sublot sizes are then optimised using linear programming. We then consider the problem with equal sublot sizes and develop an efficient solution to determining the optimal number of sublots. Finally optimal and heuristic solution methods for the general problem are proposed and the worst-case performance of the equal-sublot solution is analysed. Computational results are also reported demonstrating the close-to-optimal performances of the heuristic methods in different problem settings.     

Machine utilizations achieved using balanced FMS production ratios in a simulated setting

Stecke [21] has developed mathematical programming approaches for determining, from a set of part type requirements, the production ratios (part types to be produced next, and their proportions) which maximize overall machine utilizations by balancing machine workloads in a flexible manufacturing system (FMS). These mathematical programming (MP) approaches are aggregate in the sense that they do not take into account such things as contention for transportation resources, travel time for work-in-process, contention for machines, finite buffer space, and dispatching rules. In the current study, the sensitivity of machine utilizations to these aggregations is investigated through simulation modeling. For the situation examined, it is found that achieved machine utilizations are a strong function of some of the factors ignored in the MP methodology, ranging from 9.1% to 22.9% less than those theoretically attainable under the mathematical programming assumptions. The 9.1% degradation results from modeling with nonzero work-in-process travel times (i.e. 2 minutes per transfer) and using only central work-in-process buffers. Resource levels (e.g. the number of automated guided vehicles; the amount of work-in-process; the number of slack buffers) needed to limit the degradation to 9.1% correspond to FMS operating conditions which are feasible in practice.     

Approximate analysis of unreliable transfer lines with splits in the flow of material

This paper presents a Markov process model and an approximate decomposition technique for a discrete material transfer line with limited buffer capacity. A fraction of the parts processed at some stations in the line may be scrapped or reworked at dedicated machines to meet product quality requirements. Reworked parts are not sent back into the main line. This leads to splits in the flow of material. Processing times are deterministic and identical for all machines and are taken as the time unit. Machine specific times to failure and to repair are geometrically distributed. The model is analyzed through a decomposition into twomachine systems. We develop new decomposition equations for machines performing split operations. Production rates and inventory levels are computed and compared to simulation results. The results indicate that the method produces useful results for a variety of systems.     

Approximate performance analysis of CONWIP disciplines in unreliable non homogeneous transfer lines

For a given choice of the maximum allowable total storage parameter, the performance of constant work-in-process (CONWIP) disciplines in unreliable transfer lines subjected to a constant rate of demand for parts, is characterized via a tractable approximate mathematical model. For a (n−1) machines CONWIP loop, the model consists of n multi-state machine single buffer building blocks, separately solvable once a total of (n−1)² unknown constants shared by the building blocks are initialized. The multi-state machine is common to all building blocks, and its n discrete states approximate the joint operating state of the machines within the CONWIP loop; each of the first (n−1) blocks maps into a single internal buffer dynamics, while the nth building block characterizes total work-in-process (wip) dynamics. The blocks correspond to linear n component state equations with boundary conditions. The unknown (shared) constants in the block dynamics are initialized and calculated by means of successive iterations. The performance estimates of interest—mean total wip, and probability of parts availability at the end buffer in the loop—are obtained from the model and validated against the results of Monte Carlo simulations.     

模糊有限状态机的一些性质

讨论模糊有限状态机的一些代数性质,得到模糊有限状态机在同态作用下子系统(强子系统)的前像仍是子系统(强子系统),证明若两个模糊有限状态机之间存在满足一定条件的同态映射时,前一个模糊有限状态机是强连通的(循环的),则后一个模糊有限状态机也是强连通的(循环的),且若这个同态是强满同态,则其中一个模糊有限状态机是完全的当且仅当另一个模糊有限状态机是完全的。对模糊有限状态机的积与原来的模糊有限状态机的完全性、强连通性、循环性、交换性等关系也进行讨论,得到一些结果。     

基于系统双重风险共担的多项目鼓缓冲设置研究

为了提高关键链多项目缓冲管理的效率,首次提出了一种基于多项目双重风险共担的鼓缓冲设置方法。新方法从系统角度分析了多项目不同层级的风险共担作用,以同时落在在子项目关键链和多项目系统关键链上的系统关键活动工期占比为切入点对缓冲进行分层管理,抽取部分项目缓冲集中到系统层面,同时综合考虑风险独立因子以及鼓活动有效产出影响指数对鼓缓冲进行了定量设置。仿真结果表明,本文方法在多项目按时完工率、项目缓冲平均消耗率、系统关键链上鼓活动平均延误百分比、多项目系统总工期和成本这几个绩效方面的表现更优,提高了多项目系统的风险应对能力。