Performance Prediction of AGV Systems

The influence of the number of single-load AGVs on the performance of the AGV systems is investigated first. The total operating time that is taken by the system to complete 15,000 missions for the layout in Figure 6.1 was calculated for systems containing 1 to 10 AGVs. It is assumed that the AGV is always saturated with tasks, which means there is no time gap between the tasks of each AGV. The calculation results are listed in Table 6.2. In the table, the second column is the time taken to complete all missions by the AGV system. The third column is the sum of operation time by all AGVs in the system during the process. The fourth column is loss in operational efficiency due to the increase in the number of AGVs. The efficiency loss ƞ can be calculated by using the following equation

6150 6160 6170 6180 6190 6200 6210 6220 0 500 1000 1500 2000 2500 3000 3500 T otal ope ra ti on ti me Number of simulations

_{ƞ =} 𝑂𝑇𝑖−𝑂𝑇1

𝑂𝑇1 × 100% (6.2)

where 𝑂𝑇𝑖 represents the total operation time of the 𝑖-th single-load AGV. The last

column is the number of conflicts that happen during the period of completing the required number of missions.

Table 6.2 Total operation time taken by the systems consisting of different numbers of single-load AGVs Number of single-load AGVs Time taken to complete 15,000 missions Total operation time of all single-

load AGVs Loss in operational efficiency Number of conflicts in the process 1 6099.6060 6099.6060 0.00% 0 2 3075.6296 6151.2593 0.85% 1755.9603 3 2064.2229 6192.6688 1.53% 3396.8913 4 1556.8209 6227.2837 2.09% 4922.8177 5 1251.0290 6255.1448 2.55% 6340.2453 6 1046.6469 6279.8813 2.96% 7666.1243 7 900.0698 6300.4888 3.29% 8885.5333 8 789.7964 6318.3717 3.59% 10064.1040 9 703.7405 6333.6648 3.84% 11153.4090 10 634.7416 6347.4161 4.06% 12183.7830

From Table 6.2, it is found that the more single-load AGVs are used, the less time will be taken by the system to complete the missions (see the results listed in the second column). However, the total operation time of all AGVs listed in the third column increases with the increase of the number of AGVs, due to the increased chance of traffic conflict as shown in the fourth column. This implies that the operational efficiency of the AGV system will decrease when more AGVs are employed in this application. But different tendencies could be observed from other AGV applications, which are characterised by different values of the predefined parameters (such as the time taken for pickup or drop items).

In addition, as the total operation time of all AGVs can directly reflect the operational cost of the AGV system, the increasing tendency of the total operation time of all AGVs versus the number of AGVs means that the operational cost of the AGV system will monotonically increase with the increasing number of AGVs.

Subsequently, an AGV system that contains only one multi-load AGV is considered in order to investigate the influence of the load-carrying capacity of multi- load AGV on the performance of the system. It is assumed that the multi-load AGV always travels at a constant speed and its load-carrying capacity varies from 1 to 10 items, the corresponding total operation time that the system will take to complete 15,000 missions in the system layout shown in Figure 6.1 is calculated. Also, as the orders of the stations to be visited are important for the multi-load AGV, the importance of reordering and predefining missions is investigated through assuming 4 possible scenarios. As both mission allocation and the routing problem of multi-load AGVs in an actual AGV system layout have never been studied before, these four scenarios are proposed as initial setups to the area. They are:

1. First Come First Served (FCFS) scenario – as described in [117], the order of target stations is not optimised. The route the vehicle travels is based on the order of the subtasks received;

2. Optimise the order of target stations – the order of target stations is optimised to ensure the shortest journey;

3. If all the missions were known in advance, the missions sharing the same stations can be grouped together for completion. Given the order of the target stations is still optimised, the unload station is fixed in each mission – in other words, there is only one unload station in each mission;

4. In addition, given the order of target stations is still optimised, both pickup and unload stations are fixed– there is only one pair of pickup and unload stations in each mission.

The calculation results of the time of completing 15,000 missions by a multi-load AGV in all the above 4 scenarios are listed in Table 6.3 and graphically displayed in Figure 6.14.

Table 6.3 Time (hours) to complete 15,000 missions by a multi-load AGV

Load-carrying

capacity (items) Scenario1 Scenario 2 Scenario 3 Scenario4

1 6099.6060 6099.6060 6099.6060 6099.6060 2 5295.9048 4972.8478 4314.6740 3349.9406 3 4681.1233 4291.8075 3543.6099 2433.6573 4 4202.7873 3809.4410 3072.6713 1975.3732 5 3822.9014 3443.2901 2742.1501 1700.2785 6 3514.1916 3152.1014 2493.1356 1517.0789 7 3258.9378 2913.2522 2296.5783 1385.8178 8 3045.2775 2713.3601 2137.6648 1287.9843 9 2863.0643 2542.4237 2005.0836 1211.2480 10 2706.6132 2396.0947 1893.5317 1150.6632

Figure 6.14 The tendencies of operation time versus the capacity of multi-load AGV

From Table 6.3 and Figure 6.14, it is found that

1. The operation time shows a gradually decreasing tendency in all four scenarios 0 1000 2000 3000 4000 5000 6000 7000 0 2 4 6 8 10 Ope ra ti on ti me ( hours)

Load-carrying capacity of the multi-load AGV Scenario 1 Scenario 2 Scenario 3 Scenario 4

with the increase of the load-carrying capacity of the multi-load AGV. This further proves that the operation efficiency of the AGV system can be improved by increasing the capacity of the multi-load AGVs;

2. In Figure 6.14, the line representing the operational time for scenario 2 is always below the line representing the operational time for scenario 1 under all AGV load-carrying capacity conditions except when the capacity is ‘1’. This suggests that optimisation of the order of target stations is able to increase the performance of the multi-load AGV system;

3. Further observation of Figure 6.14 has shown that based on the optimised order of target stations, the system efficiency can be further improved if the pickup and unloading stations in a mission are fixed, although investigation should be conducted to see whether this is achievable in real applications such as a good distribution centre.

Using the data listed in Table 6.3, the improvement of system efficiency in all scenarios can be calculated using the following equation

_{∆𝐸𝑓𝑓 =}(𝑇𝐹𝐶𝐹𝑆− 𝑇)

𝑇_{𝐹𝐶𝐹𝑆}

⁄ × 100% (6.3)

where ∆𝐸𝑓𝑓 indicates the improvement of system efficiency, 𝑇_{𝐹𝐶𝐹𝑆} is the operation time of the multi-load AGV in the FCFS scenario, 𝑇 is the operation time of the multi- load AGV in the other scenarios considered. The values of ∆𝐸𝑓𝑓 are graphically shown in Figure 6.15.

From Figure 6.15, it is seen that efficiencies increase rapidly when capacity increases from 1 to 3 but the increase levels off with further capacity increase. After the loading capacity of the AGV is greater than 6, the efficiency improvement tends to be constant. In other words, after a capacity of approximately ‘6’, the efficiency improvement by increasing the load-carrying capacity of the multi-load AGV is limited. This implies that there is an ‘optimal capacity’ of the multi-load AGV, 6 for this research system, which is important to the future scaling up the design of multi-load AGV systems. In addition, from Figure 6.15 it is also found that the effect of increasing the capacity of the AGV on the efficiency improvement is the greatest in Scenario 4.

This suggests that the shorter the route in a mission, the more the efficiency will be improved by the approach of increasing the capacity of the AGV.

Figure 6.15 Efficiency improvement in different multi-load AGV scenarios

To demonstrate the superiority of multi-load AGV over single-load AGV in the application, a comparison is made between the operation time obtained in the most inefficient FCFS scenario, Scenario 1, in Figure 6.14 and those operation times listed in Table 6.2. The comparison results are shown in Figure 6.16. Three curves representing the operation time obtained in the FCFS scenario using one multi-load AGV, time taken by single-load AGVs, and total operation time of all single-load AGVs are plotted, respectively.

From Figure 6.16, it is found that except at capacity ‘1’, the curve representing ‘Time taken by the multi-load AGV to complete missions’ is always above the one for ‘Time taken by single-load AGVs to complete missions’. This indicates that in contrast to using a multi-load AGV, to use multiple single-load AGVs does reduce the time required to complete missions. However, the solid line representing ‘Total operation time of all single-load AGVs’ is always found to lie above the curve representing ‘Time taken by the multi-load AGV to complete missions’ with the exception of capacity ‘1’. This suggests although using multiple single-load AGVs can reduce the system

0 10 20 30 40 50 60 70 0 2 4 6 8 10 Ef fic ienc y im provme nt (% )

Capacity of multi-load AGV

Scenario 2 Scenario 3 Scenario 4

operation time, it leads to a much higher system operational time than that obtained by a multi-load AGV. This demonstrates the superiority of multi-load AGV over single- load AGV in practical applications.

Figure 6.16 Performance comparison of multi-load and single-load AGVs

6.7 Conclusions

In order to investigate the performance of multi-load AGVs and demonstrate their advantages over single-load AGVs in applications, the CPN method is applied to simulate a multi-load AGV system in this Chapter. Moreover, the CPN models of a number of single-load multi-AGV systems are also developed for comparison. Through performing a series of simulations, the following important conclusions can be drawn:

1. As opposed to the conventional mathematical programming methods, the CPN does provide a powerful tool to simulate and address the traffic conflict issues that are often encountered in the operation of AGV systems;

2. Increasing the number of single-load AGVs in a system can reduce mission completion time. However, it increases the total operation time of all single- load AGVs. So, it can be concluded that the operation efficiency of AGV systems will decrease when more single-load AGVs are employed;

0 1000 2000 3000 4000 5000 6000 7000 0 2 4 6 8 10 O per ai ton ti m e

Number of single-load AGVs or the Capacity of a single multi-load AGV

Time taken by single-load AGVs to complete missions

Time taken by the multi-load AGV to complete missions

Total operation time of all single-load AGVs

3. Compared to employing multiple single-load AGVs, the use of a multi-load AGV does lead to a longer mission completion time. However, the total operation time when using a multi-load AGV is much lower than that taken by all single-load AGVs. Since the total operation time determines the operating cost of the system, it can be said that the application of a multi-load AGV will bring the operator more economic benefit than using multiple single-load AGVs; 4. The research has shown that after the load-carrying capacity of the multi-load

AGV exceeds a certain value, to further increase its load-carrying capacity will no longer improve the system efficiency significantly. As that value indicates the ‘optimal capacity’ of the multi-load AGV, it is of great significance to scaling up the design of the future multi-load AGVs.

The application of the simulation model developed in this Chapter can be further extended to study more complex AGV applications, such as the multiple multi-load AGVs that will be considered in Chapter 7. In addition to this, more complex operational conditions, such as AGV failures, maintenance etc., have not been considered in the research of this Chapter. They will be studied in the following Chapters.