Approximations for fork/join systems with inputs from multi-server stations.

Fork/join stations are commonly used to model synchronization constraints in queuing network models of computer and manufacturing systems. This paper presents an exact analysis of a fork/join station in a closed queuing network with inputs from multi-server stations with two-phase Coxian service distributions. The underlying queue length process is analyzed exactly to determine performance measures such as through put, and distributions of the queue length at the fork/join station. By choosing suitable parameters for the two-phase Coxian distributions, the effect of variability in inputs on system performance is studied. The study reveals that for several system configurations, analysis of the simpler system with exponential inputs provides efficient approximations for performance measures. Both, the exact analysis and the simple approximations of fork/join systems constitute useful building blocks for developing efficient methods for analyzing large queuing networks with fork/join stations.queueing; fork/join; synchronization; assembly systems; closed queuing networks;

The assembly line feeding problem: classification and literature review

In recent years some trends in several product assembly systems emerged, namely mass-customization [Boysen et al., 2007], integration of new product functionalities [Göpfert et al., 2016] and increase in the number of models (e.g. BMW, a German car manufacturer, increased the average number of models offered per year to 37.85 in the period between 2010 and 2016, compared to only 22.3 in the period between 2000 and 2010). These trends have a significant impact on assembly systems since all of them lead to an increasing number of parts required for the final assembly, either by increasing the number of parts required at the border of line (BOL) in general (for new functionalities or new models) or by increasing the number of part variants (mass-customization). Within the assembly line feeding problem (ALFP), the optimal way of supplying assembly stations with parts is examined by assigning different feeding policies to parts. This is mostly based on cost minimizing considerations. The most prevalent line feeding policies are line stocking, kanban, sequencing and kitting [Limere et al., 2015, Sali and Sahin, 2016]. Line stocking and kanban both provide parts in homogeneous filled load carriers. Applying line stocking, a full load carrier (as supplied by the supplier) is provided to the BOL, whereas applying kanban means providing smaller quantities by splitting load carriers into bins. In sequencing and kitting, parts are prepared in the order of demand. In case of sequencing, a container holds variants of one particular component, whereas in case of kitting, different components are grouped and load carriers are filled heterogeneously. The focus of this research is on reviewing literature about the actual ALFP, namely on the assignment of line feeding policies to parts, as well as about related subproblems like e.g. the optimization of milkrun transports within assembly systems. This problem is highly complex due to different decision levels, processes, variable parameters and constraints. In order to help structuring previous and future work, we provide a classification with a three tuple notation as firstly introduced by Graham et al. for machine scheduling [Graham et al., 1979]. Significant decisions and subproblems, occuring in different processes within the ALFP, are classified. This problem includes only in-house logistics and can hence be delimited from external logistics or SCM. Research in this field is becoming more and more attractive to researchers, which can be seen by the rising number of publications. Research is mainly initiated in 1992 [Bozer and McGinnis, 1992] and round about 100 papers are analyzed in this review. The main contribution of this work is twofold. First, we do not only summarize previous research topics but also indicate open research fields, which hopefully motivates researchers to fill the research gaps. Secondly, this work provides, through the classification, a comprehensive framework for researchers to easily identify decisions and subproblems of the ALFP, which can be included in future work

Designing a robust production system for erratic demand environments.

Production systems must have the right type of material in the right quantities when required for production. They must minimize the work in progress while ensuring no stock-outstock-out occurs. While these twin opposing goals are achievable when demand is stable, they are difficult to realize under an erratic demand pattern. This dissertation aims to develop a production system that can meet erratic demands with minimal costs or errors. After a detailed introduction to the problem considered, we review the relevant literature. We then conduct a numerical analysis of current production systems, identify their deficiencies, and then present our solution to address these deficiencies via the ARK (Automated Replenishment System) technique. This technique is applied to a real-world problem at Methode Engineering ©. We conclude by detailing the scientific benefit of our technique and proposing ideas for future research

The consequences of time-phased order releases on two M/M/1 queues in series.

A key characteristic of MRP applications includes the coordination of assembly and purchased component requirements by time-phased order releases. In the literature on order review and release strategies, time- phased order releases are described as a worthy alternative to load limited release mechanisms. This paper initializes the development of a stochastic model that quantifies the consequences of time-phased order releases on the stochastic system behavior. This is done by introducing them in an open queueing network composed of two M/M/1 stations. The core of the analysis is focused on the modified flow variability which is specified by the second-order stationary departure process at the first station in the routing. It is a process characterized by a negligible autocorrelation. Based on the stationary-interval method and the asymptotic method, we propose an approximating renewal process for the modified departure process. The modelling efforts provide interesting conclusions and practical insights on some coordination issues in stochastic multi-echelon systems.

Modeling and Analysis of Manufacturing Systems with Multiple-Loop Structures

Kanban and Constant Work-In-Process (CONWIP) control methods are designed to impose tight controls over inventory, while providing a satisfactory production rate. This paper generalizes systems with kanban or CONWIP control as assembly/disassembly networks with multiple-loop structures. We present a stochastic mathematical model which integrates the information control flows into material flows. Graph theory is used to analyze the multiple-loop structures. An efficient analytical algorithm is developed for evaluating the expected production rate and inventory levels. The performance of the algorithm is reported in terms of accuracy, reliability and speed.Singapore-MIT Alliance (SMA

Analysis of delayed product differentiation under pull type policies

Delayed product differentiation (DPD) increases manufacturers\u27 competitiveness in the market by enabling them to more quickly respond to changes in customers\u27 demands. DPD has also been shown to require less Work-in-Process (WIP) than a non-DPD setup in some cases. Previous research was mainly focused on the level of semi-finished and/or finished good inventory under a base-stock policy. The control of WIP inventory was not considered. DPD may also improve response times under pull inventory control schemes, in which the amount of WIP is controlled directly. These systems can be modeled as closed queueing networks in which a fixed number of kanbans circulate as customers among each set of one or more processing stages.;In this study, we first developed models to analyze the performance of simple kanban and CONstant-WIP (CONWIP) controlled systems and set the number of kanbans to achieve a specified performance level. The models help us better understand the behavior of pull systems. The performance evaluation method uses nonlinear programming (NLP) models to bound the throughput for fixed number of kanbans or minimize the number of kanbans necessary to achieve a specified throughput. The model shows how random supplies and demands prevent equilibrium from occurring in a single-stage kanbans system.;We studied a model for a system of two products with unlimited supply and demand using three CONWIP loops to represent the common processes and the differentiated processes for each product. The same system after DPD has more common processes and fewer differentiated processes. The NLP model can determine numbers of kanbans for each loop to achieve specified throughput targets. Because the throughput bounds are not as tight as desired, we developed a heuristic algorithm that starts from the NLP solution and adjusts the kanbans using simulation to evaluate the performance. A comparison of the result of the heuristic algorithm for the systems with and without DPD indicates that DPD reduces the amount of WIP necessary to achieve a specified throughput. Furthermore, we show how models of systems with similar structure can be generalized

Setting Real Time WIP Levels in Production Lines

A new algorithm is developed for setting WIP level in production lines. It is a pull policy that determines when to authorize a job to be processed. Dynamic information in the system such as machine failures and repairs, and demand variations are taken into consideration to provide an efficient method to dynamically determine the WIP level. Two types of production lines are examined in this paper. The first is production lines which have few random interruptions and the second production line is exposed to frequent interruptions. Experiment results from these two types of production lines illustrate that the new algorithm generates higher service level with lower WIP compared to the CONWIP policy. In addition, the superiority of the new algorithm is more significant when the production line is exposed to frequent random interruptions.Singapore-MIT Alliance (SMA

Kanban devs modelling, simulation and verification

Kanban Control Systems (KCS) have become a widely accepted form of inventory and production control. The creation of realistic Discrete Events Simulation (DES) models of KCS require specification of both information and material flow. There are several commercially available simulation packages that are able to model these systems although the use of an application specific modelling language provides means for rapid model development. A new Kanban specific simulation language as well as a high-speed execution engine is verified in this paper through the simulation of a single stage single part type production line. A single stage single part KCS is modelled with exhaustive enumeration of the decision variables of container sizes and number of Kanbans. Several performance measures were used; 95% Confidence Interval (CI) of container Flow Time (FT), mean line throughput as well as the Coefficient of Variance (CV) of FT and Cycle Time were used to determine the robustness of the control system.<br /