BUS606: Operations and Supply Chain Management

6.1 Quantitative analysis of mixed model assembly lines

Many factors affect the dynamic behaviour of work flow in manual assembly systems. The average utilisation and the number of tasks per job obviously affect average flowtime and work-in-process inventory levels. It is also intuitive, based on elementary queuing theory, that the variance of job inter-arrival times and the variance of processing times on individual machines affect flowtimes. Basic terminology about queuing systems for both infinite and finite sources has been adequately covered by Stevenson. This includes the characteristics of waiting lines, arrival and service patterns, queue discipline, and measures of waiting line performance. The case scenario is an infinite source situation, single-channel, multi-phase system. The inter-arrival times are considered to be constant, and vehicles are assembled on a first-come, first-served basis.

According to Little's law, for a stable system the average number of vehicles in the assembly line $Ls$ is equal to the average vehicle arrival rate $λ$, multiplied by the average time spent by a vehicle in the assembly line $Ws$. That is:

$L_{s}=\lambda W_{s}$

System utilisation $ρ$ is computed as:

$\rho=\frac{\lambda}{M \mu}$

where $λ$ = vehicle arrival rate at station 1; M = number of servers; $µ$ = service rate/ server. The average time a vehicle is in the assembly line $Ws$ is given as:

$W_{s}=W_{q}+\frac{1}{\mu}$

where $Wq$ = the average time a vehicle waits in the queue.

The performance metrics for the manual assembly line, including the average number of vehicles waiting in the line, the average time a vehicle waits in the line, and system utilisation, were used for the bottleneck analysis in Section 3.5, and are based on equations 1, 2, and 3. $LsLsLsLsLs$ was obtained by physically counting the vehicles on the assembly line, and $Ws$ from the desired takt time, which was a function of the demand.

The quantitative analysis of mixed model assembly lines used in the paper was derived from Groover. The number of workers $w$ is computed as:

$W=\frac{W L}{A T}$

where $WL$ = workload to be accomplished by the workers in the scheduled time period (min/hr); $AT$ = available time per worker (min/hr per worker), where

$W L=\sum_{j=1}^{p} R_{p j} T_{w c j}$

where $Rpj$ = production rate of model j (vehicles/hr) and $Twcj$ = work content of model $j$ (min/vehicle). $p$ = number of vehicle models to be produced during the period, and $j$ is used to identify the model.

$Rpj$ is computed as a function of annual demand, and $Da$ for the vehicle models shown in Table 1, using equation 6.

$R_{p j}=\frac{D_{a}}{50 s_{w} H_{s h}}$

where $sw$ is the number of shifts per day and $Hsh$ is the number of working hours per shift. Equations 4, 5, and 6 were used to determine the number of workers required, as shown in the last column of Table 3.

For instance, for station 1, using eight hours per shift, one shift per day, 50 weeks per year, and annual demand values from Table 1, the hourly assembly rate is 0.36 for VW, 0.42 for TGM, 2.79 for TGS, 0.6 for CLA, and 0.81 for HB Bus. This gives an average production rate of one vehicle/hr for the assembly line.

To compute the available time per worker (WL), the work content of each model is obtained from the first row of Table 3, and the average production rate of the line is one vehicle/hr, to give WL = 166 min/hr.

Assume AT = 60 minutes as the available time per hour, and factor in an efficiency of 80 per cent; this results in 48 minutes being available per hour. Computing the number of workers w will give 3.45, which we rounded up to 4 workers.

In mixed model assembly line balancing, the objective function can be expressed as:

$\text { Minimize }(w A T-W L)$

This constraint was crucial in optimally assigning the workers to stations to minimise worker idling or maximise worker labour utilisation. The decisions about optimal bottleneck management in Section 6.3 are based on this constraint.

6.2 Bottleneck analysis

The model was simulated for a 30-day period, with five vehicle models entering the assembly line while different parameters were varied. A low value of every 15 minutes for the rate of vehicle entry to the first station was chosen so that it would not bottleneck the process. Bottleneck analysis was then conducted by analysing the effect of vehicle sequence, batch sizes, individual vehicle models, subassemblies, and downtime on the desired performance metrics.

6.2.1 Analysis of effect of vehicle sequencing

Bottleneck analysis was begun by simulating 25 combinations of assembly sequences for the five vehicle models to find a better sequence than VW-HB-TGM-TGS-CLA, which was being used, based on the shortest total processing time rule. Figure 2 shows the results for the comparison of station waiting times for five assembly sequences (sequences for A, B, C, D, and E are shown in Table 5).

Table 5: Output and waiting times for five vehicle sequences

The sequence TGS-HB-TGM-CLA-VW outperformed other sequences in the number of vehicles produced, the total waiting time, and the average queues of vehicles at stations, as shown in Table 5. The results also demonstrated slight disparities in station utilisation. Analysis of the status diagram of the simulation results indicated a high frequency of blockages at stations 10 and 6, while stations 2 and 4 were the most idle ones.

6.2.2 Analysis of effect of batch sizes

The effect of assembling a single-unit batch sizes, compared with batch sizes of up to a maximum of 20 vehicles, was then analysed using the sequence TGS-HB-TGM-CLA-VW. It found that the single unit batch size was superior for the number of vehicles produced, for higher station utilisation, and for lower average queue lengths. Figure 3 shows the effect of increasing the batch size on production output.

6.2.3 Analysis of individual vehicle models

The individual vehicle models were then simulated to identify precisely the effects of individual models and the actual locations of bottleneck stations; these results are shown in Table 6. Analysis of simulation results revealed that the CLA truck and HB bus were the most problematic, owing to the complexity of the assembly activities executed. The results from the simulation model demonstrate that the first station was a bottleneck when assembling the CLA truck, as it had the longest waiting time for vehicles in the queue when using the FIFO queue discipline.The main reason for this bottleneck was that the operators have to assemble the cross members and fit them at the same time. The average waiting time of the assembly line at station 14 was also adversely increased by the HB bus, because mounting operations of the bumper, head light, battery box, trailer loom, mirror, and rear mudguards, as well as brake tests, are undertaken by six workers.

6.2.4 Analysis of the effect of a subassembly

When demand increased, there was a need to reduce the takt time from one hour to 50 minutes. A subassembly was introduced at station 14 when assembling the HB bus, and at station 1 when assembling the CLA truck, to reduce the takt time. The results from the simulation model shown in Table 7 were used to analyse the effect of subassemblies on both single mode and mixed mode. The results show that introducing a subassembly for the HB bus results in an increase in average utilisation of the assembly line compared with the single mode, although the single mode will produce two more vehicles during the simulated 30-day period.

Conversely, for the CLA truck using the same scenario, the average line use decreases while the total number of vehicles produced increases. Adding subassemblies for both CLA and HB under the same production run yields one more vehicle for the 30-day period at a slightly lower line utilisation of 61.8 per cent.

6.2.5 Analysis of the effect of downtime

Simulation of the model was also conducted with a special focus on station 9, assuming four per cent downtime on the painting station and exponential distribution of the runtime. The results show a production loss of about 10 vehicles for every 30 working days.

The stop-time simulation settings were also varied to determine the actual number of vehicles that could be produced to meet particular due dates for orders from customers, if the vehicles were assembled in mixed mode. For example, 68 vehicles could be produced in 10 days, 108 vehicles in 15 days, 148 vehicles in 20 days, and 227 vehicles in 30 days.

6.3 Decision-making for optimal bottleneck management

Analysing the vehicle sequencing revealed that, if there is demand for all five vehicle models, the best sequence would be TGS-HB-TGM-CLA-VW. It is advisable to ensure that the model with the longest total assembly time is followed by the one with the shortest, the one with the second longest is followed by the one with the second shortest, and the one with average assembly time is in the middle. This helps to reduce the throughput time and effectively utilises the workers. Bottlenecks can also be effectively managed by assembling the vehicles in single-unit batch sizes.

In manual assembly, the time the assemblers spend fetching parts often constitutes a considerable portion of each work cycle, thus impacting substantially on assembly cost. Consequently, the use of kitting, which can reduce the time for fetching parts, is an important aspect to consider to reduce vehicle queues. 

 The recommendation would be to reduce the number of operators at a work station if the labour utilisation at a station is too low. Conversely, if the labour utilisation at a particular station is too high and constrains the whole line, the number of operators working on this work station should be increased. If the labour utilisation is just below the required target, the recommendation would be to move functions from another work station to this work station. If the labour utilisation is just above the required target, functions should be moved from this work station to another station that has the capacity to work on the functions. 

Using this logic, it was imperative to introduce the cross member sub-assembly next to station 1 when assembling the CLA truck; this resulted in a reduction in assembly time from 64 minutes to 50 minutes. A battery box sub-assembly at station 3 was also introduced for the CLA truck. An additional worker will be required at station 14 when processing an HB bus, since the functions cannot be moved to another station.

It was also highly recommended to use a variable takt time that would be a function of the monthly demand. When demand increases, takt time should decrease up to 40 minutes. This calls for more resources at stations 2 and 3 for the CLA, station 5 for CLA and VW, station 7 for CLA, station 12 for VW and CLA, and station 14 for TGM, CLA, and VW. It is also critical to institute a reliability-centred maintenance programme that ensures an optimal preventive maintenance scheme, especially for station 9.