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The availability of several variants of pull strategies and corresponding policies usually poses a challenge to prospective users on which one would be the most suitable for their manufacturing environment. Simulation modelling approaches, such as in [8, 40, 83, 100-102], and some analytical techniques have been applied in conducting studies to determine the suitability of available strategies under different conditions. Markov Time

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Chain Analysis [62], Multiclass queuing network approximation technique [84, 103, 104] and State Space representation approach [24, 29], are some of the most commonly used analytical methods of study.

Discrete event simulation has been recommended as a preferred method for studying the complex dynamics of stochastic manufacturing systems because of its ability to handle the unpredictability of such systems [61, 105]. It has been widely applied in existing literature and a lot of the present understandings of manufacturing systems has stemmed from it, mostly because it allows for an offline representation and experimentation of a system without tampering with it physically.

However, there are steps that must be taken to ensure a successful conduct of a simulation study, as described in the following sub-sections in regard to the steady state (or non-terminating) type of simulation that will be conducted in this research. The other type of simulation is the terminating simulation, and there are many available texts which provide detailed explanation of the two types [106, 107].

2.7.1 Simulation Warmup Period

In steady state simulation studies, it is of importance to eliminate the possible bias of the initialisation state of the system, in order not to defeat the essence of conducting such studies, which is to be able to make judgements about a system at any point in time irrespective of its initial state. Three popular approaches have been followed to reduce/eliminate the bias of this initial state – called the warmup period – on the statistics collected from the system [108]. First is to delete the initial set of data that is believed to be affected by this warmup period. The second approach runs the simulation for a very long time that would be sufficient for the effect of the warmup period to have been overshadowed. The third approach attempts to set the simulation in a steady state right from the beginning. The most effective is a combination of the first and the third approach, and, in a Kanban controlled manufacturing system, this might mean filling the buffers with the basestock items right at the beginning, so that the first set of demands that arrive to the system do not arrive to an empty buffer. This would give a close estimate of the steady state performance of the system, and would therefore reduce the length of data that has to be removed for the warmup period. However, rare system

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events, such as machine breakdowns, would nevertheless necessitate that a longer duration of data is deleted, because of the need for them to have occurred multiple times during the system’s warmup period [106, 107].

Welch’s graphical procedure is the most commonly applied technique for identifying the warmup period, and this is mostly due to its relative simplicity [109, 110]. However, Welch’s procedure, like some of the other methods of determining the warmup period, is reported to be sometimes conservative in its estimation of the deletion point [106, 108]. Nevertheless, the method is generally considered acceptable, and studies that have compared different methods often recommend its use [111-113].

2.7.2 Simulation Run Length and Number of Replications

Furthermore, in conjunction with the warmup period data removal, two possible approaches are applied to conducting the subsequent steady state statistics collection. The first, which is called the deletion and replication method, is to replicate the warmup-deleted run multiple times and use the statistics from all the runs to construct averages and confidence intervals for the statistics of interest [106]. The second approach – the batching method – involves conducting a very long single run which is then partitioned into batches across which the desired statistics’ averages and confidence intervals can be estimated. The first approach is more suitable for studies comparing alternative systems, especially when combined with random number synchronisation.

In both approaches, the confidence interval is often used as a measure of the adequacy of the simulation run length and the number of replications, as a higher number of replications often yields narrower confidence interval, meaning higher precision in the statistic being estimated [114]. However, there needs to be a trade-off between the computational resource requirements for a high number of replications and the level of precision that stands to be achieved. A sequential approach is commonly applied in determining this trade-off point by starting with a pilot number of replications, measuring the confidence interval obtained to see if it is within acceptable limit and gradually increasing the number of replications until it falls within the acceptable limit.

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The acceptable limit of confidence interval depends on the nature of the research and the intended application of the result.

2.7.3 Performance Measures

The common measures for comparing the performance of pull strategies are service level (SL), WIP, cycle time, stability of throughput rate, average wait time of backlogged demands, and the average duration and frequency of demand backlog [8, 12, 21, 33]. Historically, according to a study [115], SL and WIP have been the most desirable performance measures in the study of pull strategies [11, 40, 83], and this can be attributed to them having direct relationships with the outcomes of the other performance measures.

Service Level (SL)

Service level or Fill rate is the proportion of customer demands that were immediately satisfied on arrival to the system. It is a measure of system responsiveness which is the main aim of operating a pull control strategy, albeit with the added and equally important goal of reducing the level of WIP [115]. Its application as a performance measure has varied in literature; for instance, a study compared the number of Kanbans that would be needed by different pull strategies to meet a target service level at different levels of machine reliability, demand variability and safety stock levels [21]. An approach which is slightly different from direct service level measurement is to define a penalty cost for not immediately fulfilling demands and incorporate it into an objective function [62, 116]. Also, demands that cannot be fulfilled immediately have been treated in different ways in existing literature. Some allow such demand items to be backlogged in a demand item buffer until finished products become available [14, 14, 23, 63, 63, 115, 115, 117, 117, 118], while others simply regard them as sales that are lost to competitors [33, 80, 115, 119]. The true effect of lost sales resulting from the latter approach cannot be fully quantified because, in addition to the loss of a potential sales opportunity, it might also mean an outright loss of the custom of the unimpressed customer [120], and ideally the consequence of such loss should be quantified and dynamically deducted from the demand arrival rate during the long term simulation of the manufacturing system. However, this would result in severe intractability in the

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experimentation and analysis of systems. Therefore, the former approach of backlogging demand items is more directly captured within the scope of production and inventory control research. It penalises the backlog of demand items by, in some cases, assigning penalty costs corresponding to the duration of the delay [23, 63, 70]. This cost is then included as part of the objective function in a cost minimization optimization process.

As an alternative in cases when an unlimited demand is assumed, the throughput is used instead of the SL [8, 82, 96, 121]. Another category of studies consider the situation whereby there is advance demand information (ADI) that can be used to initiate production at a lead time ahead of the actual required time of fulfilment of the demand [120, 122-126]. The aim of such studies is to compare the value of the advance information on the ability of different strategies to keep inventory level low. For instance, a study reports that if the ADI lead time is long enough and stable, a system can operate with zero basestock [127].

Work In Progress (WIP)

WIP has been described as a key factor, among others, for the success of a manufacturing system, based on a study’s findings in a case implementation of lean controlled manufacturing system [37]. It is a hold up of resource and it has quantifiable cost implications which can be in the form of storage space, depreciation cost, pilferage cost, cost of monitoring, and the profits that could be derived if the economic resources tied down in inventory were used in other business ventures. As a result, it is common for studies to be carried out to compare different pull strategies based on the level of WIP they needed to achieve a target SL [12, 40]. They measure the WIP by assigning cost to every unit of inventory in the system, and this cost is multiplied by the average time for which the inventory was kept in the system. The total cost obtained is then used as part of a minimization type objective function, in a similar fashion as the demand backlog cost [23]. Other WIP measurement variations involve either assigning different costs to semi-finished inventory and finished goods inventory in the objective function [116], or simply assigning equal values (costs) to inventories across all the stages [8, 40]. In some cases, the total number of Kanbans or buffer space needed by a system is counted instead of measuring the WIP [21].

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The items that should constitute system WIP also differs in literature. While some studies regard raw parts as WIP as soon as they have been authorised for processing at the first stage [81, 101], others do not count them until their processing has actually commenced at that first stage [14, 29, 102, 115]. This impacts the WIP measured from study to study, especially in the CONWIP. In studies that use the former approach, the average WIP measured will be constantly equal to the CONWIP’s set total number of system Kanbans, while it would be slightly lower or equal in the latter approach.

SL versus WIP trade-off remains the most common performance measure applied in studies [11, 40, 83, 101, 102], and it involves seeking to achieve the best (or a target) SL with the least amount of WIP possible.