Authors: Jongi Lawrence; Omar Ahmednajib
Abstract
The paper is the optimization of Autonomous Guided Vehicles System (AGVS) for material handling in an automotive industry, it proposed a hybrid approach to optimization, which is both deterministic and stochastic. By using kinematic principles to measure AGV time in system for each section could help in establishing number of AGVs per section in 14.5 hours shift per day, feeding the AnyLogic simulation tool with these time in system produced output datasets per each section. To bring sustainability into the perspective the paper adopted the minimalist and maximalist methodology, so as to find the least possible solution, as any increase in AGV procurement has environmental, social and economic impacts, this approach is a bid to decouple negative impacts of the investment. The methodology was hierarchical on multi-levels, because of this the authors employed two methods to optimize the parameters; Purposive Sampling and Multi Criteria Decision Analysis on all sections, to find the optimum solution. The paper also looked into the confidence interval and correlation of parameters and KPIs, a positive relation exists between number of AGVs and AGV Idle time and a negative relation exist between number of AGVs and AGV utilization, which is pragmatic. However, a positive relation exists between AGV utilization and AGV Idle time, this is mainly because of the material handling flow not perfectly balanced, hence any improvement in utilization will ultimately increase AGV idle time, mainly contributed by less utilized sections. One and four AGVs are two options which attracts benefits independently, however, some structural and infrastructural changes into material handling flow also improve the AGVS performance.
Keywords: Optimization, Deterministic, Stochastic, Sustainability, Simulation, Utilization,
1.0 Introduction
In the Scania material flow in the Axel Assembly has the following sections: AXB1, AXB2, AXP1, AXP2, AXP3, AXP4, AXP5, ABAH2, ABAH3, and ABAH4 with reference to figure 1.b. Material follows from warehouse in form of pallets to AXB2. Pallets which goes straight to assembly section (ABAH4) go to a buffer section (ABAH3), these materials need not be kitting, which will be requested from assembly sections. Other pallets are requested by operators to other sections from section AXB2, except ABAH4 and ABAH2, in these sections kitting takes place, of which after kitting takes places, pallets are taken to the assembly section ABAH2 and ABAH4. All empty pallets are taken to AXB1 section and all finished axels are taken from the production by lift. Scania wants to invest in automated guided vehicle (AGV) system with an average speed of 1m/s in a straight line and 0.3m/s in a curve from manufacturers specifications. The AGV system runs for seven hours before it reaches 30% battery capacity, and it takes one hour to fully charge an AGV from 30% to 100%, and the Scania available production time is 14.5 hours per day. The implementation of the AGV system is aimed at reducing incidents, damage to property, and lost time injury. However, to achieve optimal results in the material handling system, we had to conduct a situational analysis, this included having a plant visit at Scania and inspect the data they provided us. The analysis includes understanding the various sections of the material handling system by simply analyzing the volume of material flow gave us an indication sections that with high intensity.
To conduct the situational analysis, we also considered the target problem and the data required to model the problem. This data includes the average and maximum number of orders per hour, the maximum number of orders per day, the total production time per day, the pickup/delivery time of pallets, any other constraints and the total number of pallets handle in each section. Although Scania gave us some data, but it is critical to note that the data is based on assumptions because Scania does not have AGVs installed in any of its sites, hence treating this data as such will give us room for flexibility. In conclusion, the situational analysis of Scania's material handling system is critical to clearly understand the problem. 1.1 Problem Definition Before clearly defining the problem, we drew an Ishikawa Fishbone Diagram to do an analysis of the situation at hand.
From the figure 1. Scania material handling issues can be affected by: AGV idle time, incidents, disturbances, poor plant layout, ergonomics, complex production-line, in-flexible production line and production not levelled. Scania wants to know the number of AGVs with their utilization that can handle this flow of materials, locating the positions of bottlenecks and the utilization of 5 chargers.
2.0 Literature Review
The authors looked into AGV technologies, particularly the optimization techniques and challenges of AGVS in material handling and AGV sustainability looking into the triple bottom line, and see the implication of AGV investments on all systems.
2.1 AGV Technology
In addition to the production scheduling on machines, the transportation scheduling process on automated guided vehicles (AGVs) is considered as another optimization process, (Wangming Li, 2022), Wangming et al proposed to use certain number of AGVs by establishing a task pool then use a genetic tabu search algorithm to optimize the number of AGVs. Automated Guided Vehicle System (AGVS) provides the flexibility and automation demanded by Flexible Manufacturing System (FMS), development process of a new Memetic Algorithm (MA) for optimizing partitioning problem of tandem AGVS, using Tabu Search, (Pourrahimian, 2018). To solve the conflict and dead lock problem in an AGVS, there are generally three approaches: first, to avoid conflicts by special design of AGV guide paths; second, to control the system traffic by dividing the traffic area into several non-overlapping control zones; and third, to use routing and scheduling strategies to prevent deadlocks, (Pourrahimian, 2018). The third strategy is more applicable to the Scania case, since it has several sections, understanding the material flow of each section, and assigning an AGV according and clearly see its utilization.
Manufacturing systems that produce multiple components and function in highly volatile environments are increasingly challenged to meet consistently high levels of operational efficiency and flexibility such a challenge can be addressed partly by designing appropriate facility layouts, (Farhad Shafigh, 2015). Sometimes failure to balance and inefficiencies in material handling, complex plant layout and inflexibility is sometimes an issue, AGVS demand Production Flexibility on the plant layout with respect to disturbances pattern. When AGVs offloads there is always some delays because of competing resources, the solution divides the offloading optimization problem into two parts: firstly, the load balancing algorithm and greedy algorithm are utilized to find the optimal allocation of tasks for a single AGV under limited conditions, then, multiple AGVs are asynchronously trained by applying the Reinforcement Learning-based A3C algorithm to optimize the offloading scheme, (Peng Liu, 2022). Balancing the material flow on the plant is critical, for efficiency and higher performance. In group Multi Criteria Decision Making (MCDM), a group of decision makers provide their opinions based on their own observations and intuitions over a set of attributes the individual opinions are finally converted to a collective opinion using some suitable procedure, (Sujit Das, 2013). As many parameters and KPIs exist as outputs of a model, they will always compete for importance as some will be antagonizing each other, it is critical to find a way to analyze them and make decision under uncertainty.
2.2 AGV Sustainability Perspective
Even though AGV is claimed to have sustainable benefits, every intervention always has some feedback loop, this section seeks to have an introspect on all subsystems with their reinforcements and spillovers
2.2.1 Economic
The concept of minimalist and maximalist approach is meant to stream line sustainability in this investment portfolio, because, a unit AGV is costing USD200 000. Although AGVs are expensive, their capacity to reduce accidence, reduces number of plant incidence, this will ultimately reduce lost work time and ultimately reduce lost sales due to disturbances, penalties due to incident statistics will also be reduced, cost associated with managing incidences will greatly be reduced. Experiment done at Scania clearly shows that the wireless technology is considerably affected by electromagnetic waves, which will increase as digitalization and electrification of society and industry intensify, (Herdís Hanna Yngvadóttir, 2023), this destructive interference will add to aliasing and causing to delay in signal processing by the AGV, ultimately increasing time in system of the AGV hence reducing productivity. The capability of an AGV to work 24 hours without any complaining or rest ensures continuity and smooth flow of production, however, power consumption needs to be inspected with respect to battery life and battery cycle time.
2.2.2 Social
Social sustainability is related to the autonomous nature of AGV systems along with their capability to cooperate with humans and their functioning environment to promote reductions in the number of work accidents, to minimize human errors and to effectively explore feasible scheduling and routing solutions, standardization of performance and service levels, the elimination of uncertainty in response times and the reduction in operational costs and human errors, (Dimitrios Bechtsis, 2016). It is critical to mention that Scanias’ brown field was relying on forklifts which was manned by personnel, who will probably loose their jobs unless, they are trained in managing the AGVs which is also a cost which needs to be incurred. The development in Artificial Intelligence is demanding consideration of the human factor system through human-centric design because autonomy of production should not compromise the creativity, ethics, participation and value of human beings in an enterprise. While telecommunication technologies are still seen as clean technologies, they can have some harmful impacts on the environment. The whole humanity is now exposed to various levels of so-called Effects of Electromagnetic Fields (EMF) and surely, the level of these fields will continue to grow with the advancement of science and development of technology. The waves classified as microwave, in which the mobile systems operate, are the electromagnetic radiation with wavelength ranging from 10 cm to 1 m and are called nonionizing radiation and its effects are the object of study worldwide, and scientist are skeptic to give a conclusion to that effect, (Siqueira, 2009).
2.2.3 Environmental
Environmental benefits emerging from the utilization of AGVs, especially for the case of logistics operations and distribution, (Dimitrios Bechtsis, 2016). The few studies that have compared the environmental impacts of wireless technologies to applications have concluded that wireless technologies impose a lower environmental burden. However, the effect of these rare materials which are used in wireless technologies, for example Indium Gallium Phosphide and Cobalt, on land degradation during extraction and the footprint it leaves during processing can never be over-emphasized. It is evidence that the increase of AGV into the system will also increase the amount of internet usage, of which the GHG emission cause by internet are at 5% which will definitely increase by increasing number of AGVs, that’s why the authors had the minimalist approach. As most of materials used in making the AGVs comes from mining activities upstream: it has the following the impacts - Air quality is adversely affected by mining operations, Wind erosion and nearby vehicular traffic cause such materials to become airborne. Lead, arsenic, cadmium, and other toxic elements are often present in such particles. These pollutants can damage the health of people living near the mining site, (Atlas, 2023). The creation of landscape blots like open pits and piles of waste rocks due to mining operations can lead to the physical destruction of the land at the mining site. Such disruptions can contribute to the deterioration of the area's flora and fauna, the destruction or drastic modification of the pre-mined landscape can have a catastrophic impact on the biodiversity of that area, (Atlas, 2023), this comes with the loss of eco-system services which spans from, provisioning service, supporting services, regulating services, and cultural services, (FAO, 2023).
It is against this sustainability perspective that the number of AGV investment should not be taken lightly but should really justify investment criteria on all sub-systems, because of spillovers and reinforcing feedbacks in the environment, economic landscape and the social sub-system.
3.0 Methodology
The methodology employed was a hybrid of both deterministic and stochastic approach. The deterministic is to import the pdf plant layout drawing into AutoCAD and measure dimensions on all the paths of the AGV which are not on the plant layout, counting the number of turns an AGV can make on its path in the workflow, this approach uses kinematics to calculate the AGV time in system and the number of AGV per section. Separating our approach into two aspects, that is, the minimalist and the maximalist approach so as to analyze our situation with minimum investment and maximum investment and have some trade-offs. Generation of stochastic statistics is to be done by AnyLogic, with parametric and KPIs performance accordingly to the number of AGVs per section. At this point it is critical to understand that number of AGVs is an independent variable whilst AGV idle time, AGV utility and AGV chargers are all dependent variables.
Sensitivity analysis will be done against with route restriction versus without route restriction on all sections. Statistical analysis of the system performance is a multi-level because of data hierarchies, from sections performances with respect to the number of AGVs for with and without route restrictions, separating minimalist and maximalist results, considering all parameters and KPIs and coming up with an optimum solution that is overall. The authors will do purposive sampling in some stages of statistical analysis, to separate the minimalist approach and the maximalist approach based on objective function. Another method the authors will employ for multi variable optimization is called Multi Criteria Decision Analysis since it is evidence from the problem definition that more than one parameter and KPIs will come up. By conducting a sensitivity analysis of parameter variations and comparing the results with and without route restrictions, we can determine the optimal number of AGVs and idle time for each section of the material handling system. With this analysis, Scania can improve its material handling system, enhance efficiency, and reduce costs.
3.1 Initial Conditions
Initial conditions at time 0 include:
There are no pallets in the sections;
There are no pallets in the outbound position;
There are no pallets in the inbound position;
The AGV moves from home to take the payload and then takes it to requester;
3.2 Assumption
Since we are starting with the deterministic method, it is critical to clearly expose all the assumptions, these includes:
The number of obstacles in the AGV path is unknown;
For maximalist approach the AGV will take the longest route;
For minimalist approach the AGV will take the shortest route;
According to the AGV manufacturer speed of AGV in linear motion is 1m/sec;
According to the AGV manufacturer speed of AGV on curves is 0.3 m/sec;
Curvature distance is 1.5meters; • There are no production disturbances;
The flow of material is normally distributed;
The AGV has 100% battery life;
The time taken in scanning and picking by the plant operator is infinitesimal to be considered in the simulation;
The speed of the AGV is not affected by payload;
3.3 Delimitations
The system boundary for our case includes:
The AGV has priority in the aisles;
The focus is on the plant layout proposed by Scania;
There is a total of 151 cells;
The outbound section has seven cells;
The inbound section has eight cells;
Materials into the inbound is generated accordingly;
The empty pallets are moved from the outbound section accordingly;
The assembled materials or finished products are removed from the system accordingly, hence, the authors are not concerned out the movement of materials to the system and outside the system;
Locating the AGV home with its charging port in the central position, to save AGV time in system and save energy use from home to requisition picking area makes sense;
The production time per day is 14.5 hours;
A pallet contains all components required by an order;
The flow of material as per day are normally distributed with minimum value of 336.51 pallets/day, average value of 420 pallets per day and maximum value of 600 pallets per day.
3.4 Conceptual Model Design
The workflow of the AGV is as follows:
Movement of AGVs from home to remove the empty pallet from the picking area;
Take the pallet and place the empty pallet at the outbound position;
Move from empty pallet section and move to the inbound position;
Take a pallet with materials from the inbound position;
Move the pallet to the requesting picking station.
The conceptual model was amended to give the following;
System initiates material arrival to the inbound bay;
AGV move from home to inbound bay;
AGV takes payload to requester;
AGV returns moves until a request to remove empty pallet is initiated;
AGV takes empty pallet to outbound section;
AGV takes kitted pallet from Section 1 and 3 to Section 4;
AGV takes pallet straight from supplier from Section 2 to Section 4;
System disposes finished products from the system The amended conceptual model is as follows in figure 3
4.0 Deterministic Approach
We are going to assume that loading will not adversely affect the performance of the AGV. With reference to Appendix – AGV movement distribution minimalist approach and AGV movement distribution maximalist approach excel sheets for all sections. Below are based on minimalist and maximalist scenarios of the possible route taken by the AGV in the plant. The distance is calculated by using the detailed drawing dimensions from the plant layout, (the authors imported the plant layout pdf into AutoCAD 2023 to determine the distances for the AGVs’ respective path) adding each piece of distance until it reaches its destination. It is possible to count the number of bends from the chosen path, and the authors have assumed that the curvature of each bend is 1.5m. The manufacturer specifications specify that the AGVs’ speed on linear paths is 1m/s and on bends it is 0.3m/s. With this type of data, the authors were able to calculate the time taken when the AGV was moving on all straight paths and time taken through bends, and Scania has provided the information that 80 seconds is time taken to actual interchange a pallet from the time the AGV arrives to the fixture with/without pallet, to the time till the AGV leaves the fixture with/without the pallet. Summing up the time on linear path, on bends and the time taken for the AGV to retrieve and position pallets throughout all workflow will give the authors the total time of the AGV in a system. Verification included cleaning the data from Scania to be compatible with the simulation software and also making sure that the individual cells, paths and nodes are consistent with the design and specifications from the manufacturers and the authors. The output from the Appendix excel sheets are used in the calculation of number of AGVs in the equation 1 below is shown in table 1. The authors formulated equation 1 below:
From the analysis in table 1 it is clear that although section ABAH3 has the highest percentage of material handling it is also the least in AGV time in system, this is predominantly caused by the strategy the authors used to make the AGVs home in this section since it has the largest distribution and also is strategically in the middle. Axle assembly station ABAH4 is proving to have the largest Time in System whilst having the second largest material handling station from ABAH3. Other sections seem to be leveled in terms of time in system, however, in terms of pallets handled it seems to display a bullwhip.
Table 1:Data Analysis of time in system and total pallets per day in all the sections
It is critical to understand that in as much as we need to balance the material handling flow, time in system of AGVs for each station needs also to be balanced, hence, a trade-off is demanded in this scenario as we redistribute our pallets. Other options can be explored such as eliminating stations which are displaying counter-productive such as AXP1 and ABAH2 by combining. It is clear from the above calculations that, the minimum time in system for the AGV in system (maximalist scenario) is 438 seconds and the mean is 641 seconds and the maximum time in system is equal to 935 seconds. It also critical to note that the authors calculated the average pallets from the data given by Scania it turns out to be 43 pallets per day. However, this will have a bearing on the performance of the system and robustness which the authors will investigate using sensitivity analysis.
4.1 Deterministic Method Outputs
The outputs from the deterministic method can prelimarily give an output of solutions that can be investigated or even implemented, although further analysis is needed to confirm outputs.
4.1.1 How many AGVs?
Using equation to calculate the number of AGV in each section the authors make a summation according to Table 1 of the AGVs in each section the total number of AGVs will be 4, however if the authors makes an average of the AGVs distribution the number of AGVs needed will be equal to 0.49 for minimalist case scenario which is equal to 1. Analyzing the two answers, it is critical to understand that going for 4 AGVs will result in redundancy, however, if the firm does not want to have loss of sales, that is the best option, but if budget constraints are an issue then a trade-off will be an option for less than 4 AGVs, may be two or 3. Since this is a high capital investment project, possible reduction of these AGVs needs to be considered to verify, hence, the authors will employ digital simulations to verify and validate these deterministic statistics.
4.1.2 Waiting time along path?
The average time in system is equal to 640.86 seconds, which is too high, however, there is need for trade-offs so as to optimize between Capital Expenditure, the risk of lost sale and the related cost implications, and the revenue of future order fulfillment. There is also need to verify and validate this number through software simulation, needless to say with deterministic method it is complex to calculate the waiting time in system for the AGV.
4.1.3Where are the Bottlenecks?
The bottlenecks are most likely to be experienced in the path between ABAH3 and AXP3 because this is the region with the highest AGV time in system and maximum number of pallets per day. However, simulation software will go a long way in optimizing the number of in and out bound pallet bays, because, without optimizing this, we will experience a severe bottleneck at these stations and interrupt the flow of production. Be it as it may, since we have 7 outbound and 8 inbound it should be enough, since we have 8 stations, which is highly unlikely that they will initiate two orders within the takt time causing bottlenecks at the inbound and outbound station, however, further sensitivity analysis will be done by simulation software to verify and validate this.
4.1.4 What is the AGV Occupancy?
AGV occupancy is complex to calculate at this stage, only by simulation can be ascertain the AGV occupancy. However, using the available data the authors can put the AGV utilization at 0.47 and 0.49 for maximalist scenario and minimalist scenario respectively using the deterministic approach, with 1 to 4 AGVs.
4.1.5 What is the utility of 5 chargers?
Charger utilization is affected by AGV utilization, because the lower the AGV utilization the lower the charger utilization, hence the authors formulate a formulae in equation two below Fife Battery charger utility (with AGV at 100% utilization) = (Charging time)/(available time).
It is clear that for the number of AGVs the 5 chargers will have a utilization of 8.4%. The Ultimate Charger Utilization = 0.084X0.49 (0.04116/ 4.116%) from this analogy we can put the number of chargers with 100% utility to be 1. Therefore, with 4 AGVs Scania needs to invest in only one charger.
5.0 Building of the simulation model using AnyLogic Software
The authors build initially individual cells on every section, and assigned probability calculated from the throughput per day on each cells from the data given by Scania, however this method seemed so complicated since when the authors tried running AnyLogic just left the authors hanging without running for hours, hence a call to simplify the model. Please see figure 4 below, how the model looked with complications. By looking into the deterministic analysis it is prudent to join section AXP1 and AXP2 because of the size of material handling (a total of 52 storage cells – which is 11% of the material handled which is 36 pallets per day). It is at this point that the authors saw it fit to join some sections so as to utilize 4 AGV, hence since we are taking from normal distribution of different sections, it is critical to note that their time in system is different hence giving a normal distribution regardless.
Since ABAH2 and ABAH4 are assembly sections, bringing them close to each other, combining AXP1 and AXP2 into one Section 1 and combining AXP3, AXP4 and AXP5 into one Section 3, combining ABAH2 and ABAH4 into one Section 4, and renaming ABAH3 to Section 2. By doing this it simplifies the model. Combining these sections does not only simply the simulation but is a bid to level and increase utility in some of the sections, and it is evidence that, this will reduce plant occupation space, which in-turn reduce GHG emissions caused by plant expansions in installations of green field factories.
Combining ABAH3, ABH2 and ABAH4 makes practical sense since, this the most section that has the most time in system of the AGV and the highest material movement (59%/ 193.16 pallets per day). This saves AGV battery life and energy consumption and also reduce time in system. Likewise combining AXP3, AXP4 and AXP5 which has a total of 30% of material handling (107.81 pallets per day). Since our prior calculations gave the authors a maximum of 4 AGVs it is prudent, making us left with three section, hence dedicating one AGV for each section and leaving one AGV to reduce bottlenecks.
6.0 Sensitivity Analysis
Sensitivity analysis is part of verification process were the authors sort to clearly understand the model behavior with varying parameters and KPIs, this is possible by identifying independent paraments and dependent KPIs and variables within the system. In this process, we changed positions of sections and in some instances eliminated some to observe system behavior. Changing variable scalar values and changing route restrictions are some of the strategies this paper explored.
6.1 Section Variations
Interarrival for section 1(AXP1 and AXP2) is equal to 527.557seconds on average as shown in Table 18 and for Section 2 is equal to 596.836seconds since we moved all the assembly sections to ABAH3 and removed the buffer and for section 3 (AXP3, AXP4 and AXP5) is equal to 529.289 seconds taking the average. Using information from Appendix on AGV movements we are able to know information of the AGV workflow summarized below in Table 2, we put the information into AnyLogic software, please note that the other 320seconds for AGV interchanging the load and loading in other workflows is inclusive in the averages, the only 80seconds separated is used in AnyLogic delay during unloading Pay Load.
Table 2: Interarrival Times for different Sections
However, after running the simulation it seems the strategy of removing the buffer has some implications of running out of storage, so we created a buffer in the position of ABAH4 (Section 4) and the assembly of all section to be in the position of ABAH3, since all materials converges to section 2 it saves abundant of resources by locating it near all sections, as show in figure 5 below:
The takt provided by Scania is equal to (23.2; 35; 50 pallets/hour) which is equal to (0.00644; 0.009722; 0.0139 pallets/seconds) which is not practical with utility of AGV speed, because there will be a bottleneck on the inbound section as shown in Figure 6 below. It does not match with the speed of the AGVs in the plant, because just the changeover retrieving and storing a pallet takes 80 seconds, which means 1 AGV takes 320 seconds for just retrieving and storing pallets for the complete cycle without movement time of which the minimum time in the system of the AGV is equal to 357.364. Hence, the authors will match the takt time with that of the average AGVs, by assigning the interarrival times of the pallets at the inbound section to the average time in system of AGV in each section calculated from the deterministic method.
In this section the authors broke the workflow of the AGV into chunks as shown from the appendix, now the authors took averages from each chunks by section and then feed the information into AnyLogic, as the AGV moves through its workflow.
After further simulations it is prudent to separate the section 1 and leave the buffer ABAH3 (Section 2) which handles 36% of materials and combine ABAH2 and ABAH4 (Section 3) to give us 23%, since the simulation was experiencing a bottleneck at section 2. However, when we change the takt time to 80seconds at the section 4 (assembly), still the section 2 remain a bottle neck as shown in figure 7.
When the authors changed the distribution of kitted materials to go to section 4 (as initially instructed by Scania), now the section 4 is now the bottleneck, which means assembly should align with takt time to remove the bottleneck, as shown below in figure 8.
Now the authors will add the removal of empty pallets from section to outbound section, to see what happens, results were as shown below in figure 9.
As shown in the diagram below, figure 10, the utilization of the AGV starts at 75% but reduces (to 32% even lower) when they become idle as they wait for orders.
Hence, the authors will align order arrival time with AGVs mean time in system for each section, and the times calculated from the deterministic approach on all sections will used in AnyLogic software, however the takt time at the assembly the authors left it at 80 seconds this managed to balance the system without any bottlenecks. At the moment all paths are bidirectional with restriction of 2 vehicles, we will run several simulations with variations of route restrictions and without route restriction. The takt time remained at 80 seconds, but the movement of AGVs is according to the determinist statistics result from Appendix excel sheets for both minimax and minimalist.
6.2.0 Sensitivity Analysis
Parameter Variations It is critical to mention that each simulation has a rampup stage utility of 100% which gives a false higher utility, this is mainly because all AGVs will be utilized as orders comes concurrently with the calling of AGVs, initially from home, however it decreases to a more stable state on all the variations on parameters as orders increases, and variations become more stochastic. In the following analysis, shows 10 runs on all sections, with route restrictions and without route restriction, information from Table 3, 4, 5 and 6 will be the result.
6.2.1 Variations for sections without route restrictions
Table 3: Without Route Restriction number of AGVs vs Utilization
In table 3 shows the cleaned output data from AnyLogic with bold entities filled as average (27.5% of the population size) for consistence in number of runs which is ten, this shows the performance of each section if it has one, two, three and four AGVs. The bar graph below show the distribution likewise of the data in table 3.
From figure 11 it shows that section 1 and section has less utilization this is mainly because of less number of pallets being handled in this section. Although section 2 has large amount of material handling, it is close to AGV home, and it’s a buffer, options to eliminate it are open because of this. Figure 12 is confusing because its displaying a uniform distribution, further analysis is required to clearly understand the variations. Table 4: Without Route Restriction AGV Idle Tim
In table 4 shows the AGV idle time per section when number of AGV is varied with ten runs and the bold numbers were again filled with averages, which is 37.5% of the population size.
6.2.2 The Variations for Sections With Route Restriction
Table 5: Sections Variations with route restriction AGV vs Utilization
Table 5 shows variation results with route restriction the bold entities (21.9% of the population) filled as averages as missing from simulation output for ten runs. Figure 13 shows the output bar graph from the dataset of AGV versus utilization for all sections, it is interesting to note that section 1 and 2 are displaying lower utilization, contrary to section 3 and 4.
Table 6 shows variation results with route restriction the bold entities (21.2% of the population) filled as averages as missing from simulation output for ten runs. Figure 14 shows the output bar graph from the dataset of AGV versus AGV idle time for all sections.
6.2.3 Comparison of Routes Variations
It is really difficult to place a conclusion on the different scenarios; however, it is clear that on different section, different outcomes are witnessed with reference to table 7.
6.2.4 Without Route Restriction mean distribution
Figure 15 is an attempt to see the nature of distribution on all sections and likewise holistically on all section, that is, without route restriction.
Utility in section 1 and section 2 is comparatively lower than section 3 and 4, and the idle time is comparatively the same which needs further analysis to understand closer. The idle time is uniform mainly because, the time the AGV waits for an order to be called is displaying a uniform distribution of mean 46 seconds. The overall utilization for the whole plant is 0.425 without route restriction.
6.2.5 Without route restriction minimalist and maximalist distribution
The output in figure 16 is due to purposive sampling of the population mean with respect of all section for particular number of AGVs without route restriction.
For minimalist approach needs 1 AGV for all section with utilization range from 0.124 to 0.626 with mean 0.397 with idle time of range 32 seconds to 44 seconds with mean of 40 seconds and for maximalist approach needs 3 AGVs for all section with utilization range from 0.123 to 0.679 with mean of 0.431 and the idle time of range from 49 to 57 seconds with a mean of 53 seconds.
6.2.6 With Route Restriction mean distribution
Figure 17 is an attempt to expose the nature of distribution on all sections with route restriction.
Figure 17 shows utilization in section 1, 2 and 4 is comparatively lower than section 3, and the idle time is comparatively the same mainly because the process time is constant, with mean of 54 seconds and the overall utilization mean for all section 0.333. With route restriction minimalist and maximalist distribution The output in figure 18 is due to purposive sampling of the population mean with respect of all section for particular number of AGVs with route restriction.
For minimalist approach needs 1 AGV for all section with utilization range from 0.149 to 0.631 with mean of 0.330 with idle time of range 37 seconds to 55 seconds with mean 48 seconds and for maximalist approach needs 2 AGVs for all section with utilization range from 0.338 to 0.693 with mean of 0.373 and the idle time of range from 51 to 60 seconds with mean of 56 seconds.
7.0 Outcome Analysis
The outcome shows that without route restriction is superior for minimalist approach with 1 AGV with mean utilization of 0.397 and mean idle time of 40 seconds. On the maximalist approach favors with route restriction with 2AGV with mean utilization of 0.373 with mean idle time of 56 seconds.
7.1 Purposive Sampling Outputs
With reference to table 26 Section 1 decreased in utilization by 10.1% and idle time in this section has increased by 3.9% because of route restriction. In section 2 utilization increased by 10.2% and idle time increased by 16% because of route restriction. In section 1, 2 and 3 is where Scania proposes route restrictions, however, we witness more performance variations section 3 and section 4. Utilization of section 3 decreases by 8.4% and AGV idle time increased by 16.7% whilst section 4 utilization decreased by 49.6% and AGV idle time increased by 9% because of route restrictions. These metric variations are clearly favoring without route restrictions and even though in Section 4 we do not have any route restrictions, this section is the assembly, meaning all materials leads to this section we are witnessing a snowball effect in this section from all the variations on all sections.
In purposive sampling although there is some level of biasness because some trade-off was employed in selecting the best number of AGVs versus utilization and AGV idle time. It is prudent to note that we need to have a trade-off, because AGV procurement is very expensive, understanding the cost of lost sale versus the cost of infrastructural investment is also a criterion that can be employed in case of disturbances which might be experienced in the future. Hence for system resilience Scania might opt for maximalist approach which is 2AGV and for factor of safety might add 1 AGV for system robustness, that is if the enterprise is growth oriented. If the enterprise is focused on resource efficiency 1 AGV will service the plant with some level of risk in terms because utilization on both Section 3 and 4 has a mean of 0.679 since these are sections with huge material handling, which is contrary to utilization of Section 1 and 2 which has a mean of 0.196.
It is critical to note that Section 1 and 2 and Section 3 and 4 are handling different material volume; difference in utilization is witnessed and any increase in number of AGV in the system presence a conundrum because it decreases utilization and an increase in AGV idle time. Hence, any deciding on the number of AGVs there has to be a trade-off, especially when trying to protect the system against future disturbance to create robustness, because utilization in Section 1 and 2 will decrease even more and an increase in AGV idle time will be witnessed. Such trade-offs bring in complexity into the mix, which made us made a Multi Criteria Decision Making method to evaluate the simulation.
7.2 Multi Criteria Decision Making (MCDM)
Decision-making, as a mental complex process, is a problem-solving program that aims to determine a desirable result considering different aspects. There is no way to move from a nondominated solution to another solution without sacrificing at least one of the criteria that this point can help decision-makers to select a solution-set from the set of non-dominated ones, (Hamed Taherdoost, 2023). In a mathematical form, an MCDM problem is defined as follows:
A={Ai | i=1, 2,…, m}
where A is a distinct and finite set of alternatives, and m represents the number of them.
C={Cj| j=1, 2,…, n}
where C is a set of certain criteria that are used to evaluate A, and n is the number of them. That is to say, criteria can have different units without any inter-relationships, and with different conflicting objectives (minimizing objectives in some of them and maximizing in others).
W={wj | j=1, 2,…, n}
where W is a set of normalized weights assigning to each criterion based on their importance, (Hamed Taherdoost, 2023). The mathematical form of sets discussed above is a simple way to define an MCDM problem, and the gained information commonly is organized as a matrix form that is shown in figure 19 and 20.
From the result from figure 19 making a trade-off 1 AGV, if it can stand to be superior in Section 1 and Section, hence it is the optimum solution for without route restriction especially as a minimalist. However, for the maximalist 4 AGVs is attractive since it has occupied second position twice and position one.
With reference on figure 20 minimalist is attracting 2 AGVs because it appeared twice on the first position and the maximalist is attracting 4 AGVs because it occupied first position once, second position once, and the third position once and the fourth position once, and since it occupied first position in Section 4 it means it is the optimum position for maximalist approach. However, overally for minimalist 1 AGV is showing superiority as a minimalist even for all sections on both scenarios (minimalist and maximalist) and with and without rout restriction. In the same analysis the second competent number of AGVs is 2 for section 1 and 2 which means might face challenges in section 3 and 4 with high material handling volume, hence since 4 AGVs is showing superiority for section 4. Therefore, for maximalist 4 AGVs will provide optimum solution.
Difference of Outcomes from Two methods of Optimization
The purposive sampling method and the MCDM is concurring on the minimalist number of AGV, which is one. However, using the maximalist, the purposive sampling method is showing 2 AGVs, whilst the MCDM is showing 2 AGVs to be superior however, behaves poorly in Section 3 and 4, but 4 AGVs to be superior. Hence, a decision on these outcomes will be 1 AGV and 4 AGV, by having an analysis to inference to practicality.
8.0 Validation Process
Validation process is an attempt to see whether the model the authors made speaks to the real life situation, involves calibration, in our case since we are modelling a future state model, validation might be challenging. The method the authors adopted is to check some KPIs and parameters relations, using correlation statistical tools, in real life situation some parameters and KPIs are positively or negatively correlated. If the model correlations speaks otherwise, further analysis of the anomaly is demanded with reference to the model.
Covariance and Correlation of parameters and KPIs
It is critical to investigate if there exist a relationship between number of AGVs and utilization, also number of AGVs with idle time, and it will be interesting to investigate whether a relationship exist between utilization and idle time.
Number of AGVs and AGV Utilization
Using equation 2 and equation 3 to do the statistical analysis will give results shown in table 8
Without route restriction AGV utilization versus number of AGVs is negatively correlated, although not that perfect (-0.225), which means our model is correct because an increase in AGV numbers should decrease the AGV utilization, the dataset and the mean at each multi-level is also displaying this correlation.
AGV idle time versus number of AGVs with route restriction has a positive correlation of 0.370917, which makes sense, because as the number of AGVs increases, AGV idle time should also increase if everything is hold constant.
We are witnessing an anomaly in our dataset shown by our correlation between AGV Idle time and AGV Utilization which is positive, meaning moving in the same direction, because we have Section 1 and 2 which have less utilization but high idle time almost similar to other sections. Hence, even if AGV utilization increases the AGV idle time will also increases, because this section averages performances and is part of the system. It is imperative to note that since we are having a future model with no historical data, we have no idea when the system has stabilized, which means we might be dealing with a localized optimization which might not be linear in nature.
Expect Opinion
The expect opinion from the Scania we did was on 3rd of March 2023, he said he will come back to us, and it interested him that we had a different approach comparatively to their output, and he will do a more introspect into our approach.
Regression Analysis
Taking a closer look at the behavior of data between AGV utilization and AGV idle time purposively for without route restriction, particularly for Section 1 and Section 4, because they displayed too much variances of different material handling volume. From the regression graph, it is showing a negative correlation, which is some how linear for 1 AGV and for 4 and 3 AGVs with an outlier, with reference to figure 21b.
This output becomes more practical than when generalizing the correlation for the whole plant. For section 4 figure 21a it is observed that for 1 AGV, a negative relation exist, although with some noise and outliers, maybe because of filled in missing data from AnyLogic output.
Figure 21a is showing contradicting outputs, for 1 AGV and positive correlation for 4 AGVs. It is imperative to observe that, with small amount of data points it is inconclusive to determine the nature of the relationship between the AGV utilization and AGV idle time, however, in general terms, the more the idle time the less the utilization, but it might not necessarily be so, however if we are to experience positive correlation it should be with less tipping points or poor positive correlation, which is concurring with table 8 which is between 0.017 to 0.020.
Confidence Interval
For 95% confidence interval for parameters and KPIs we will use equation 4, the output in table 9 :
With 95% confidence does AGV Utilization fall within this range 0,380741639<µUtilization< 0,469372368 and AGV Idle Time fall within the range of 42,99276 <µIdle Time< 50,77966.
9.0 Recommendations
Redistributing pallets on all the sections so that they are well balanced since we experience section 1 and 2 (AXP1, AXP2 and ABAH3) are under-utilized because of less material handling;
Eliminating stations which are displaying counter-productive such as AXP1 and ABAH2 by combining or simply balancing the material flow, refer to figure 21;
ABAH2 is syphoning too much time in system yet it has little material handling, it is prudent to combine this section with ABAH4 to reduce this imbalance, even if the two assembly might be different, at least Scania should invest in getting this section close to AGV home or flexibility, reference to figure 21;
Actual performance of AGVs on curves, linear motion and in retrieving pallets should be researched so that this time and speeds be accurate, to produce a close to practical model;
Since the model was developed on the assumption that one pallet contains all the material orders for the assembly section (as advised by Scania), it is also important to know which part is needed at what frequency to service the assembly section for a complete product. Also, whether these parts can all fit in one pallet or not, this perspective will produce an accurate model;
Scania should not restrict routes of flow of AGVs as this will have a bullwhip effect on Section 4, because small effects on all sections will be exponential at the last section, which is Section 4, with reference to figure 21;
The authors propose to eliminate the buffer ABAH3, so that materials are taken straight from the inbound to the assembly, removing the buffer also means less clatter on the shop floor meaning less movement and ultimately less incidents because of healthy ergonomics;
Scania should invest in plant flexibility, because digitalization demand agility on plant layout;
Combining section AXP1 and AXP2 to Section 1, Combining section AXP3, AXP4 and AXP5 to section 3, combining section ABAH4 and ABAH2 to section 4. Section 4 is the only section that might require capital investment to combine, because it involves movement of storage cells. However, other sections is simply combining with the objective to level material handling and to dedicate AGVs to particular zones and sections so that there is no competing for resources, which will cause bottlenecks on all the paths. Since one of our solution is 4 AGVs, it means dedicating each AGV to specific sections and specific performance for each section when it has one AGV has been simulated, this will reduce confusion on the material handling flow, please refer to figure 21, for the proposed layout
The AGV home should also be charging port, so as to utilize the AGV idle time for charging time, and the AGV home should be in the middle, refer to figure 21;
It is important to simply the model, however, conversely being critical on not losing data through biasness;
The model can be used at any plant as long as the plant layout with specific distances can be measured and the AGV linear and curvature speed is well known;
Further data mining to ascertain the behavior of the relation between utilization and AGV idle time is needed for further research, to reduce localized optimization;
It is important for Scania to critically understand the implication of AGV investment in their plant.
10.0 Challenges
AnyLogic failed to simulate from a storage cells level of 151 cell;
Order rate is at 50 pallets/hour, converting this to seconds would mean 0,387 pallets/seconds, this means every 2.586 seconds a pallet arrives at the inbound, hence we had to modify the order arrival rate to deterministic output data;
The software is not integrable with software such as AutoCAD, this is necessarily so as to place plant layouts to scale with all the graphical in the program;
Less access to the plant leads to many assumptions which causes many errors in the model;
No historical data for validation process exists with respect to the specific problem;
Dataset output came with some missing data, hence the authors had to fill with averages this will lead to some degree of errors;
Late response to non-response from the Scania personnel lead to many assumptions, this causes many variabilities in the output data;
There is too little data to give a proper account on correlation between parameters and KPIs.
11.0 Conclusion
A conundrum exists, that is, an increase in AGVs in the system does not really increase performance but reduces utilization and idle time will also increase idle time. An anomaly exists between AGV utilization and AGV idle time, the two are positively correlated, the main reason is because of an imbalance between section that is too much pronounced. For superior performance, if Scania wants to work with limited budget it buys 1 AGV and if wants to expand and have a robust system, it should buy 4 AGVs, for all the scenarios 1 charger will work with 90% utilization. Since it takes 1 hour to charge 1 AGV and takes 7 hours of battery cycle time to 30% battery capacity. It means for 1 AGV, having three batteries is sufficient for a 14.5 hour per day production time, likewise, the same for 4 AGVs, for robustness Scania can have two extra batteries. The outcome shows that without route restriction is superior for minimalist approach with 1 AGV with mean utilization of 0.397 and mean idle time of 40 seconds. On the maximalist approach favors with route restriction with 2AGV with mean utilization of 0.373 with mean idle time of 56 seconds. For efficient material handling and to improve utilization and to reduce AGV utilization Scania should change its plant layout, and the plant layout should be flexible to adopt to changes in situations of disturbances with an attempt to level the material handling. Without proper material flow balancing, bottlenecks are likely to be experienced at Section ABAH3, Inbound Bay and ABAH4, from the results without route restriction is displaying superior performance, however, this should also be closely be monitored as this might change with situations.
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