System Assumptions

In order to simplify the simulation models by eliminating aspects that are not likely to have significant impact on the accuracy of its results, and to give adequate consideration to the limitations and capabilities of the simulation modelling tool, the following assumptions are made about the two systems:

ƒ Parts are assumed to be always available to the system so the first stage is never starved of raw parts [14, 87, 87, 118].

ƒ The WIP measurement approach that considers parts as WIP as soon as they have been authorised for processing at the first stage is followed. The alternative approach is described in Section 2.7.3.

ƒ A minimal blocking policy [83, 174] is applied by having an input and output buffer for each manufacturing stage’s machine. This means that a machine does not have to stop processing parts if the succeeding machine is busy processing another part. It can continue processing parts and store them in its output buffer until its basestock limit has been reached. Also, parts that are authorised for processing at a machine while it is busy processing another part can be kept in its input buffer and released to it as it becomes available.

ƒ Negligible setup time is assumed, so that the different part types waiting for processing at a stage are processed in FIFO order [20].

ƒ A demand information and a Kanban both represent single items and the parts are also processed a single unit at a time [6].

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ƒ The transmission of demand and Kanban information and the movement of parts are instantaneous and take negligible time.

ƒ Demands that cannot be immediately satisfied are backlogged as described in Section 2.7.3.

3.4.3 Simulation Warmup Period

Welch’s procedure is applied for determining the warmup period of the system, and based on a pessimistic approach, the two strategies (BSCS and CONWIP) that are most susceptible to the initialisation bias are chosen for the analysis. BSCS does not use Kanbans and as such has looser WIP control compared to the others. As the initialisation of inventory only occurs at the final stage of a CONWIP controlled system, it will require a relatively longer time to overcome any initialisation bias effect. Using these two in estimating the warmup period for the other strategies can only overestimate the warmup periods. While this may result in a waste of useful data, it does not give as much cause for concern as when the warmup period is underestimated and the data used is not truly representative of the system.

Since system optimisation cannot be done before the warmup period analysis, arbitrary Kanban and basestock settings that would yield close to the eventual target service level of 95% are set for the two strategies in conducting their warmup period analysis. Seven replications of 40,000 hours run length each are conducted with the basestock levels of the BSCS set to 2, 4 and 20 for the two products at Stages 1, 2 and 3 respectively. For the CONWIP strategy, 27 cards are allocated to each product type. The average WIP at the last stage is recorded for every 100 hour time frame and averaged across the seven replication runs. With smoothing window sizes of 20 and 10 for the CONWIP and the BSCS respectively, it was observed as shown in Figure 3-3 that the CONWIP model assumes consistency from around 12,000 hours while for the BSCS, the consistency begins from about 11,000 hours.

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Figure 3-3: CONWIP and BSCS Warmup period Welch graph

Based on recommendations in literature to allow for a considerable number of occurrences of infrequent events such as machine breakdowns, a 15,000 hours warmup period in which up to 100 breakdown and restart cycles would have occurred was eventually chosen [106, 107].

3.4.4 Simulation Run Length and Number of Replications

In addition to removing the initialisation bias, the subsequent simulation run length has to be sufficient for the system to run adequately in its steady state, and to achieve this, the deletion and replication method, which involves running multiple replications of warmup-deleted simulation runs, is applied.

A trial of different run lengths and numbers of replications was used to determine the right combination of both that would yield a desirable level of precision in the mean values of the performance measures, i.e. the run length and number of replications that would yield a confidence interval half-width that does not exceed 3% of the mean value, at a 95% confidence level. For the CONWIP, it can be observed in Figure 3-4 (a) that this was achieved for SL1 and SL2 with 20 replications, at which the half-widths were about 0.005 to mean values of 0.97 and 0.98 respectively. For the BSCS, 30 replications yielded half-widths of about 0.006 to mean values of 0.96 for SL1 and SL2, as shown in Figure 3-4 (b). Since 30 replications also reduced the width of the confidence intervals for the WIP in both models to less than 1 unit, this number of replications of 50,000 hours run length each was eventually chosen.

30 32 34 36 38 40 42 44 46 48 50 0 5000 10000 15000 20000 25000 30000 35000 40000 Stage 3 Average WIP

Simulation time (Hours)

RAW CONWIP DATA RAW BSCS DATA WINDOW SIZE 20 WINDOW SIZE 10

Indicative Warmup Period for Strategy Selected Warmup Period for analysis

52 (a) CONWIP

(b) BSCS

Figure 3-4: Confidence Intervals for different replication numbers

This implies ending up with a simulation data of 35,000 hours per replication, after the 15,000 hours warmup period has been deleted. In total 1,050,000 hours of simulation data would be collected over the 30 replications.