Analysis of Local Decision Rules in a Dual-Kanban Flow Shop

A recent article reported the results of a study on the effects of two kanban policy variables—the length of withdrawal cycle and the type of priority rule—on average customer wait time and total inventory. This study extends that work by adding two kanban policy variables and two performance criteria. It reports the results of simulation experiments that were conducted to determine how four policy variables—withdrawal cycle, priority rule, status of waiting withdrawal kanbans, and number of kanbans influence four performance criteria—average customer wait-time, total inventory, and average number of full containers in the input and output stock points of stations. It was found that the information about waiting withdrawal kanbans in sequencing decisions results in the simultaneous improvement in two conflicting objectives—customer wait time and total inventory. Also, the effects of including the information regarding the status of waiting withdrawal kanbans on system performance are larger than the effects associated with the type of priority rule. The results provide insights into determining the level of each policy variable while fully considering the possible interactions among the variables and the levels of other policy variables to improve system performance. These insights allow for setting the levels of policy variables to make the improvement process smooth.     

An Approximate Solution to Deterministic Kanban Systems

This paper presents a simple heuristic for computing the number of kanbans in a kanban system. The production systems under consideration have a multistage, uncapacitated, assembly tree structure, with every stage producing only one item at a time. The experimental results show that this method generates very good solutions. In more realistic problems where the master production schedule incorporates a smoothed demand, the solution found under the proposed method is identical to that of the linear programming approximation. This simple heuristic can be used in the real world to quickly determine the number of kanbans for daily just-in-time operations.     

An Analysis of Dual‐Kanban Just‐In‐Time Systems in a Non‐Repetitive Environment

Recent advances in approaches and production technologies for the production of goods and services have made just‐in‐time (JIT) a strong alternative for use in intermittent and small batch production systems, especially when time‐based competition is the norm and a low inventory is a must. However, the conventional JIT system is designed for mass production with a stable master production schedule. This paper suggests supplementing the information provided by production kanbans with information about customer waiting lines to be used by operators to schedule production in each work‐station of intermittent and small batch production systems. This paper uses simulation to analyze the effect of four scheduling policy variables—number of kanbans, length of the withdrawal cycle, information about customer waiting lines, and priority rules on two performance measures—customer wait‐time and inventory. The results show that using information about customer waiting lines reduces customer wait‐time by about 30% while also reducing inventory by about 2%. In addition, the effect of information about customer waiting lines overshadows the effect of priority rules on customer wait‐time and inventory.     

Analysis and Approximation of a JIT Production Line: A Comment

A recent Decision Sciences article by Jordan [9] presented a Markov-chain model of a just-in-time (JIT) production line. This model was used to estimate average inventories and production rates to find the optimal number of kanbans. Results for expected production rate were found to be consistently lower than those obtained by Huang, Rees, and Taylor [8] in a previous Decision Sciences article. Jordan attributed this unexpected outcome to some procedural problems in Huang et al.'s simulation methodology. In this paper, Markov-numerical analysis is used to compare the performance of Jordan's and Huang et al.'s methods of production control. Simulation analysis is then used to determine the effects of finite withdrawal cycle times. Results show that, for equal numbers of kanbans, Huang et al.'s two-card method of production control provides substantially greater expected production rates than Jordan's method. These results suggest that the Jordan model should not be applied to the problem of setting kanban numbers on manual JIT lines. Finally, we comment on the efficiency of Jordan's iterative method to obtain performance measures of tandem queues.     

An Evaluation of the NERJIT Priority Rule in a Kanban‐Controlled Flowshop

Significant progress in production and information technologies and innovations in management of operations during the last couple of decades have made the production of small lots and deployment of Just‐In‐Time (JIT) concepts in flowshops possible. As a result, some researchers and practitioners have been seeking to improve the performance of non‐repetitive systems using JIT concepts. In this process, the JIT concepts that were originally designed for mass production have been modified to adapt JIT to non‐repetitive systems. This article uses a priority rule that is based on real‐time demand and production information for sequencing jobs in a kanban‐controlled flowshop. The analysis of the effect of this priority rule; the number of kanbans; the length of the withdrawal cycle; First‐Come, First‐Served (FCFS); and Shortest Processing Time (SPT) on four performance measures—customer wait time, total inventory, input stock‐point inventory, and output stock‐point inventory, shows that the use of this priority rule results in a significant reduction of customer wait time and a slight decrease in inventory.     

A REVIEW OF THE KANBAN PRODUCTION CONTROL RESEARCH LITERATURE

Station interdependence, blocking caused by finite buffer capacities, and periodic material handling make modeling and analysis of kanban-controlled lines challenging. Also, one must consider flows of material as well as flows of kanbans. The many models given in the literature contribute to the confusion and debate that often characterize kanban research. The only element common to all kanban systems appears to be finite buffer capacities. I describe blocking by total queue size, blocking by part type, and the single-card and twocard systems. I review the kanban literature and organize it by type of system and decision area. First, I discuss elements of system design, including setting kanban numbers, performance measures, material-handling frequencies, and container sizes. Then I cover the production control topics of sequencing and batch-sizing. I conclude with a comparison of kanban and conventional methods of production control and with suggestions for future research.     

A Simulation Study of Sequencing Rules in a Kanban-Controlled Flow Shop*

This paper addresses the problem of sequencing in decentralized kanban-controlled flow shops. The kanban production control system considered uses two card types and a constant withdrawal period. The flow shops are decentralized in the sense that sequencing decisions are made at the local workstation level rather than by a centralized scheduling system. Further, there are no material requirements planning (MRP)-generated due dates available to drive dispatching rules such as earliest due date, slack, and critical ratio. Local sequencing rules suitable for the decentralized kanban production-control environment are proposed and tested in a simulation experiment. These rules are designed so that they can be implemented with only the information available at the workstation level. Example sequencing problems are used to show why the shortest processing time rule minimizes neither average work-in-process inventory nor average finished-goods withdrawal kanban waiting time. Further, it is shown how work station supervisors can use the withdrawal period, in addition to the number of kanbans, to manage work-in-process inventories.     

MANAGING A FLOW LINE WITH SINGLE‐KANBAN,DUAL‐KANBAN OR CONWIP

To control the production of different parts on a single flow line, managers can choose between the Single‐kanban, Dual‐kanban, and Conwip. This paper therefore compares the three different systems. The results show that Conwip consistently produces the shortest mean customer wait time and lowest total work‐in‐process. Our results also contradict the finding of a previous study, which showed that Dual‐kanban performed better than Single‐kanban. The different findings can, however, be attributed to the use of a material transfer policy, which favors the Dual‐kanban modeled in the previous study. Our study shows that transferring replenished containers immediately to downstream stations, increasing the number of cards, and reducing the withdrawal cycle reduce the mean customer wait time significantly.     

A review of quantitative approaches in just-in-time manufacturing

The objectives of this survey are four-fold: (1) to describe the principle of just-in-time production, (2) to provide an overview of the problems and research issues in scheduling, lot sizing and determining the number of kanbans, (3) to describe prior studies which use quantitative approaches to study JIT production and its variant systems including simulation, stochastic process, and mathematical programming, and (4) to identify fertile opportunities for further research in the quantitative analysis of JIT production.     

The optimal operation planning of a Kanban system with variable lead times

In the majority of the previous research on Kanban systems delivery lead time is treated as a fixed value. In many practical situations, however, the lead time is variable. In this paper, optimal operation planning of a fixed interval withdrawal Kanban with variable lead times is proposed. A cost is incurred for inventory level less than the safety inventory level, since the risk of shortage of inventory must be considered. Behaviour of the optimal number of Kanbans and the withdrawal interval of Kanbans are investigated in terms of various parameters such as standard deviation and mean lead time.     

面向并行制造的多生产单元协同调度研究

为提升多生产单元制造系统整体效率，在其系统内开展面向并行制造的协同调度研究，在考虑运输、换线等时间的基础上，构建多生产单元并行协同调度模型，采用并行分段协同遗传算法求解；在此基础上，将所研究协同调度方法应用于某复杂机电产品多生产单元制造车间，并与变批量调度与等批量调度比较。研究表明，所提的并行协同调度方法可以显著提升生产单元效率，提高生产单元设备和人员利用率。     

An Evolutionary Algorithm for Sequencing Production on a Paced Assembly Line

A new sequencing method for mixed‐model assembly lines is developed and tested. This method, called the Evolutionary Production Sequencer (EPS) is designed to maximize production on an assembly line. The performance of EPS is evaluated using three measures: minimum cycle time necessary to achieve 100% completion without rework, percent of items completed without rework for a given cycle time, and sequence “smoothness.” The first two of these measures are based on a simulated production system. Characteristics of the system, such as assembly line station length, assembly time and cycle time, are varied to better gauge the performance of EPS. More fundamental variation is studied by modeling two production systems. In one set of tests, the system consists of an assembly line in isolation (i.e., a single‐level system). In another set of tests, the production system consists of the assembly line and the fabrication system supplying components to the line (i.e., a two‐level system). Sequence smoothness is measured by the mean absolute deviation (MAD) between actual component usage and the ideal usage at each point in the production sequence. The performance of EPS is compared to those of well‐known assembly line sequencing techniques developed by Miltenburg (1989), Okamura and Yamashina (1979), and Yano and Rachamadugu (1991). EPS performed very well under all test conditions when the criterion of success was either minimum cycle time necessary to achieve 100% production without rework or percent of items completed without rework for a given cycle time. When MAD was the criterion of success, EPS was found inferior to the Miltenburg heuristic but better than the other two production‐oriented techniques.     

Determination of the optimal number of kanbans and kanban allocation in a FMS: A simulationbased study

A simulation-based study is presented to compare the performance of a set of kanban allocation rules in a flexible manufacturing system (FMS) operating in a pull mode. This paper also presents a simulation-based direct search approach to determine the optimal number of kanbans and their simultaneous allocation to different part types. This paper presents a realistic cost function that includes a penalty for failing to meet the demand on time, and a penalty for rescheduling delivery of materials from vendors. The model captures limited flexibility in the form of operational flexibility in a FMS. Future extensions to this study are discussed.     

自动生产线的同步维修模型及实例研究

自动生产线故障停机时间长、停机费用高,其原因在于:设备种类多且相关联,存在各设备协同维修的难题。首先,寻求生产线故障时间和检查时间之间的平衡点,建立检查周期与总停机时间之间关系的目标函数。其次,借鉴同步维修的"对故障隐患集中式批处理,减少分散维修的停机时间"思想,以及时间延迟维修理论,建立生产线的同步维修模型,该模型利用生产线每天停机次数、每次停机时间及检查时发现的缺陷数,计算出合理的生产线检查周期,并以此为依据制定维修计划,实现"提高维修批量,减少生产线停机时间"的目标。最后,实例研究。收集某生产线近十年的故障记录数据,在分析生产流程、设备布局、各设备停机影响的基础上,提出对策指导生产线维修管理。     

IMPLICIT OPTIMAL AND HEURISTIC LABOR STAFFING IN A MULTIOBJECTIVE,MULTILOCATION ENVIRONMENT*

This paper presents a tractable set of integer programming models for the days-off scheduling of a mix of full- and part-time employees working α to β days/week (cycle) in a multiple-objective, multiple-location environment. Previous models were formulated to specifically schedule part-time employees working either two or three days per week. These models were intractable because they required complete employee schedule information. The new models are deemed implicit optimal since they are required to supply only essential information. While the number of variables in previous models is an exponential increasing function of β-α, the size of three of the new models is independent of α and β. The first three models developed here (as in [18]) deal with the trade-offs between idle time, the number of employees required to work at multiple “locations,” and the size of the total labor pool. The inherent flexibility of the implicit modeling approach is illustrated by the presentation of various modifications of the basic models. These modifications permit the use of preference weights on the number of employee work days/week (cycle) or the minimization of payroll costs where differential pay rates exist. These latter models may also be formulated such that idle time is ignored, constrained or minimized. The execution time for the implicit models (on a CDC CYBER 730 computer with commercially available software) averaged well under five seconds on 1200 trial problems for the type of application considered in [18]. A solution was obtained in less than 46 seconds of CPU time for a trial problem which would have required over 1.4 million integer variables with previous models. The availability of optimal solutions was invaluable in the development of two heuristics designed to deal with the trade-offs of [16]. In an experimental analysis a previous heuristic produced results which averaged from 74 to 508 percent above optimum across six experimental conditions. The comparable new heuristic produced results which averaged from 3 to 8 percent above optimum for the same experimental conditions. The paper concludes by developing a framework to integrate the results of this research with the tour scheduling problem and by identifying several other areas for related research.     

Improved approximation algorithms for non-preemptive multiprocessor scheduling with testing

Multiprocessor scheduling, also called scheduling on parallel identical machines to minimize the makespan, is a classic optimization problem which has been extensively studied. Scheduling with testing is an online variant, where the processing time of a job is revealed by an extra test operation, otherwise the job has to be executed for a given upper bound on the processing time. Albers and Eckl recently studied the multiprocessor scheduling with testing; among others, for the non-preemptive setting they presented an approximation algorithm with competitive ratio approaching 3.1016 when the number of machines tends to infinity and an improved approximation algorithm with competitive ratio approaching 3 when all test operations take one unit of time each. We propose to first sort the jobs into non-increasing order of the minimum value between the upper bound and the testing time, then partition the jobs into three groups and process them group by group according to the sorted job order. We show that our algorithm achieves better competitive ratios, which approach 2.9513 when the number of machines tends to infinity in the general case; when all test operations each takes one time unit, our algorithm achieves even better competitive ratios approaching 2.8081.

     

Simulation Tests of FCFS and SPT Sequencing in Kanban Systems

One of the basic tenets of scheduling theory is that the SPT sequencing rule maximizes average production rates and minimizes average in-process inventories. This paper shows that on single-card kanban-controlled lines FCFS often has greater average production rates than SPT. Further, the performance of SPT declines relative to FCFS for larger queue capacities and less frequent material handling. Results for the single-card system are also compared to those of Berkley and Kiran [1]. In that article it was shown that for two-card systems with periodic material handling, SPT has larger average inventories than FCFS. This paper shows that these surprising results can be attributed to Berkley and Kiran's material-handling mechanism.     

Time window capacity analysis for synchronous production

Synchronous production is a philosophy that suggests that the right part should arrive at the right machine at the right time to minimize the inventory and operating costs. To achieve this goal a synchronous material flow is required. How ever, this is not an easy task in the discrete manufacturing environment because it requires management commitment and algorithmic development. This paper proposes a time window capacity analysis (TWCA) approach to implement the synchronous production. By dividing the production time into small time windows, simple rules, heuristics and algorithms are developed to assign operations among available resources such that the inventory and operating costs are kept low. The synchronization is achieved by resolving the demands of each operation in the order of time windows. The approach is simple and has been implemented and tested in an actual manufacturing company. The results show that TWCA is practical and promising. TWCA has the potential to be used in either single, multiple, or parallel machines, one stage or multi-stage, job shops or flow shops, and closed or open systems.     

COUNTRY PORTFOLIOS IN OPEN ECONOMY MACRO‐MODELS

This paper develops a simple approximation method for computing equilibrium portfolios in dynamic general equilibrium open economy macro‐models. The method is widely applicable, simple to implement, and gives analytical solutions for equilibrium portfolio positions in any combination or types of asset. It can be used in models with any number of assets, whether markets are complete or incomplete, and can be applied to stochastic dynamic general equilibrium models of any dimension, so long as the model is amenable to a solution using standard approximation methods. We first illustrate the approach using a simple two‐asset endowment economy model, and then show how the results extend to the case of any number of assets and general economic structure.     

A Note on ‘An Approximate Solution to Deterministic Kanban Systems’: A Commentary and Further Insights

In a recent paper, Vemuganti, Batta, and Zhu (1996) stated that the linear programming model suggested by Moeeni and Chang (1990) could result in infeasibility. They also suggested an alternative mathematical formulation for determining the number of kanbans. The intention of this article is twofold. First, we maintain that the finding of Vemuganti et al., while valid, is based on a misplaced emphasis on the purpose of the Moeeni and Chang article. Second, we demonstrate that the Vemuganti et al. formulation is a special case of a more general model proposed by Bitran and Chang (1987).