# The Selection of the Best Control Rule for a Multiple-Load AGV System Using Simulation and Fuzzy MADM in a Flexible Manufacturing System

Authors: Parham Azimi; Hasan Haleh; Mehran Alidoost
Journal: Modelling and Simulation in Engineering
 (2010)

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## Abstract

Pick up-dispatching problem together with delivery-dispatching problem of a multiple-load automated guided vehicle (AGV) system have been studied. By mixing different pick up-dispatching rules, several control strategies (alternatives) have been generated and the best control strategy has been determined considering some important criteria such as System Throughput (ST), Mean Flow Time of Parts (MFTP), Mean Tardiness of Parts (MFTP), AGV Idle Time (AGVIT), AGV Travel Full (AGVTF), AGV Travel Empty (AGVTE), AGV Load Time (AGVLT), AGV Unload Time (AGVUT), Mean Queue Length (MQL) and Mean Queue Waiting (MQW). For ranking the control strategies, a new framework based on MADM methods including fuzzy MADM and TOPSIS method were developed. Then several simulation experiments which had been based on a flow path layout to find the results were conducted. Finally, by using TOPSIS method, the control strategies were ranked. Furthermore, a similar approach was used for determining the optimal fleet size. The main contribution of this paper is developing a new approach combining the top managers' views in selecting the best control strategy for AGV systems while trying to optimize the fleet size at the mean time by combining MADM, MCDM and simulation methods.


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## Body

## 1. Introduction

In modern manufacturing systems, automated guided vehicles (AGVs) have become an integral part of material handling system (MHS). An AGV is a driverless, battery-powered vehicle (usually controlled by on-board computers), and a transport system used for horizontal movements. They were introduced in 1955 [1] for the first time and since then, several applications of AGVs have been developed day by day. In these systems, a number of AGVs—which are always called as fleet size—are dedicated to some workstations and storehouses in order to transport the materials. They can be used in inside and outside environments like manufacturing, distribution, transshipment, warehouses, and external transportation areas. One of the most important advantages of AGV systems is their high flexibility since the guide path can be easily modified to respond to any changes in the flexible manufacturing system (FMS) where routine changes are inevitable. Therefore, material handling systems have been playing an important role in an FMS as pointed out by Tompkins and White [2] such that about 13%–30% of total production costs can be attributed to material handling operations and it is why many researchers have been looking for the new approaches to optimize the MHS since 1980s. In a flexible manufacturing system, there are several cells which produce different parts, so having an efficient MHS for transportation among workstations or even among cells is a key factor for cost reduction target as one of the most important targets in nowadays market conditions. In an AGV system, several key factors can be distinguished such as vehicles, the transportation network, and the physical interface between the production/storage system and the control system. The transportation network connects all stationary installations (e.g., machines) in the centre. At stations, we have pickup and delivery points (P/D points) which are the interfaces between the production system and the transportation system of the centre. AGVs travel from one P/D point to the other on fixed or free paths. Guide paths are usually determined by wires or markings on the floor. When AGVs are operated without guide paths, they are called free-ranging AGVs [3]. In designing an AGV system, many tactical (e.g., system design like P/D points, the fleet size, flow path layout, etc.) and operational (e.g., routing or dispatching strategies) problems have been addressed. For example, the older ones were addressed by Co and Tanchoco [4], King and Wilson [5], Ganesharajah and Sriskandarajah [6], Johnson and Brandeau [7], Manda and Palekar [8], and Hoff and Sarker [9]. Co and Tanchoco discussed the operational issues of dispatching, routing, and scheduling of AGVs. King and Wilson investigated system design, routing, and scheduling of AGVs by verifying the vehicle requirements, flow paths, and types of AGVs and then showed the relationship between the tactical and operational issues on the system performances. Ganesharajah and Sriskandarajah studied the operational issues of scheduling, dispatching, and routing of AGVs in various flow path layouts. Johnson and Brandeau discussed stochastic models for the design and control of automated MHS. Manda and Palekar studied the design and control issues for MHS again. Hoff and Sarker reviewed the design of guide paths and dispatching rules. More recently, Qiu et al. [10] reviewed the literature on design and operational issues in the FMS and some tactical issues concerning fleet size and flow path design. Even some researchers like [11] used modern technologies as Mechatronics in designing of AGVs. They used several electronic devices like chip sets, boards, RFIDs, sensors, and so on to prevent any deadlocks and collisions in order to increase the system throughputs. Their method has the maximum quality which has been gained so far, but they did not consider the cost related to developing such a full mechanized system. In designing of an AGV system, at least the following tactical and operational issues have been considered in the literature:(i)
flow path layout,(ii)
traffic management for avoiding any deadlocks or collisions,(iii)
the number and the location of P/D points,(iv)
vehicle requirements,(v)
vehicle dispatching,(vi)
vehicle routing,(vii)
vehicle scheduling,(viii)
positioning of the idle vehicles,(ix)
battery management of AGVs,(x)
failure management of AGVS.AGVs are capable to transport one or more loads at the same time and the size of the unit load has to be decided by the management. A unit load refers to the number of items arranged in such a way that they can be transported as a single object. Furthermore, it has to be determined if one-load-carrying (single-load-carrying) or multiple-load-carrying AGVs will be used in the system. The majority of studies are focused on single-load AGVs despite in modern factories, the multiple-load ones are being used more. Recent studies showed that using multiple-load AGVs had many advantages such as smaller fleet size, less traffic congestions, and increasing the system throughput [12, 13]. Moreover, in an FMS environment, parts have different types and so loading and unloading time in such a system which results in more costs may be large. Therefore, for managing of such a system, multiple-load AGV systems were introduced to industries to overcome the mentioned issues [2] specially, when the loading/unloading time is greater than the transportation time. However, it should be mentioned that controlling of a multiple-load AGV system is much more complex than the single-load one, because in a multiple-load AGV system, a vehicle may consider several loads at the same time including the loads that are on the vehicle and the loads which are waiting to be picked up. In modern MHSs, some important criteria such as System Throughput (ST), Mean Flow Time of Parts (MFTP), Mean Tardiness of Parts (MFTP), AGV Idle Time (AGVIT), AGV Travel Full (AGVTF), AGV Travel Empty (AGVTE), AGV Load Time (AGVLT), AGV Unload Time (AGVUT), Mean Queue Length (MQL), and Mean Queue Waiting (MQW) were used as the system performances. Egbelu and Tanchoco [14] classified AGV dispatching rules into two categories: machine-initiated rules and vehicle-initiated rules. They compared the performance of these rules in a manufacturing system and found that in a busy shop, vehicle-initiated rules had more significant effects on the system performance. Bartholdi and Platzman [15] proposed a decentralized dispatching rule called First-Encountered-First-Served (FEFS) for AGV systems operating in a simple closed loop. According to [16] several heuristics have been developed for both approaches (machine-initiated rules and vehicle-initiated) which are categorized in Table 1.Table 1
Summary of AGV dispatching rules.
Vehicle initiatedWorkstation initiatedFirst-Come-First-Served (FCFS)Farthest Vehicle (FV)First-Encountered-First-Served (FEFS)First Available Vehicle (FAFS)Largest Queue Size (LQS)Least Cumulative Idle Time (LIT)Longest Inter-Arrival Time (LIT)Least Utilized Vehicle (LUV)Longest Travel Time (LTT)Longest Idle Vehicle (LIV)Longest Waiting Time (LWT)Most Cumulative Idle Vehicle (MIT)Maximum demand (MD)Nearest (Idle) Vehicle (NV or NIV)Maximum Outgoing Queue Size (MOQS)Random Vehicle (RV)Minimum Remaining Outgoing Queue (MROQS)Minimum Work-in-Queue (MWQ)Modified First-Come-First-Served (MFCFS)Random Workstation (RW)Shortest time to Travel First (STTF)Unit Load Shop Arrival Time (ULSAT)Vehicle Looks For Work (VLFW)Yim and Linn [17] pointed out that AGV dispatching rules in an FMS were generally based on a push or pull concept. In their paper, a Petri-net-based simulation was used to investigate the effect of different dispatching rules on the performance of a FMS. Occeńa and Yokota [18] modeled an AGV system with single-load vehicles in a JIT environment using multiple-load vehicles. Chen [19] developed a mathematical programming model for AGVs planning and control in a manufacturing system. Shiue and Guh [20] proposed a learning-based and multipass adaptive scheduling for a dynamic manufacturing cell environment. Ho and Liu [21] proposed a control process for multiple-load AGVs. They investigated two problems: task-determination problem and delivery-dispatching problem and proposed different rules for them. They also investigated performance of pickup-dispatching rules for multiple-load AGVs and concluded that the best dispatching rule is to select a machine with greatest output queue length. Again in 2009, they [22] studied the case but in a vast range of load-selection rules together with pickup-dispatching rules. To sum up, their studies were twofold, such as understanding the influences of different rules on the system performance like system throughput and the effects of each rule on the other one. In this paper, we define some control strategies in Sections 1.1 and 1.2 according to the literature. In Sections 1.3 and 1.4 Fuzzy MADAM and TOPSIS methods have been explained theoretically before using them in the approach. Afterward in Section 2, the simulation model and its defaults such as the flow path used, the fleet size, the warm-up period, and the numbers of runs were described. Section 3 presents the computational results and Section 4 explains the conclusion.


### 1.1. Selecting Rules

First of all, the controlling mechanism of a multiple-load AGV system has been defined to create a general view on the control problem and then several rules for dispatching, delivery, and load selection problems have been introduced. One of the main objectives of a control policy is to satisfy demands for transportation as fast as possible and with minimum possible conflicts between AGVs. Therefore, the following activities should be carried out by a controlling system.(i)
Dispatching of loads to AGVs: this problem defines the strategy for assigning the AGVs to machines (workstations) or assigning any special load to the available AGV. When an AGV is idle (i.e., it has no task to do), some requests for transportation arise in the manufacturing system. Now the problem is to assign the AGV to the best request. If the request is for delivery, the problem is calleddelivery-dispatching and if it is a pickup one then it is called pickup-dispatching problem. However, when an AGV arrives at a P/D point for picking up some parts, another problem arises which is selecting the best load for that AGV. This problem is called load-selection problem.(ii)
Route selection: by the time an AGV assigns to a specific machine, now a new problem arises which is selecting the best pathway from the original point to the destination. The best selected way refers to selecting a pathway to reduce transportation time as well as preventing the possible conflictions. In the literature review, There are two main categories for route selection problem which areoff-line and on-line methods. Off-line methods are studied when the system information is static, that is, there is no stochastic event in the system. In contrast on-line controlling systems are more practical because they assume that several stochastic events like machine or AGV break downs could happen. The on-line controlling systems are centralizedor decentralized. It is centralized when the controlling system has been installed on the AGV boards and it is decentralized when the controlling system has been installed on several locations in the manufacturing cell.(iii)
Dispatching the idle AGVs to the parking station(s).However, one may see more details about these problems in [21].


### 1.2. Dispatching Rules

In this section, several dispatching rules applied in the simulation experiments have been verified. When an AGV is full or empty, the next task could be determined easily because the next task will be delivery (when it is full) or pickup (when it is empty). But in some situations, the AGV is half-full so the next decision should be selected among a pickup task or delivery task. In this situation, three main strategies could be developed. One isDelivery-Task-First (DTF) rule, which just selects delivery task. Another one is Pickup-Task- First (PTF) rule and the final one is Load-Ratio (LR). According to [21], the best rule is DTF, so in the simulation experiments, this rule has been used, that is, a multiple-load AGV will always perform delivery task even when both delivery tasks and pickup tasks are available. For pickup-dispatching rules, four major rules have been used such as Longest-Time-In-System (LTIS) rule (an AGV will visit the pickup point containing the load that has been in the system for the longest time), Greatest-Queue-Length (GQL) rule (an AGV will visit the pickup point that has the greatest number of loads waiting at its output queue), Earliest Due Time (EDT) rule (an AGV will visit the pickup point containing the load with the earliest due time), and Smallest-Remaining-Processing-Time (SRPT) rule (an AGV will visit the pickup point containing the load with the smallest remaining processing time). For delivery-dispatching problem, five main rules have been used such as Shortest-Distance (SD) rule (an AGV will visit the delivery point to which it is the closest), Earliest Due Time (EDT) rule (the load that has the earliest due time will have the highest priority to be deliveried by an AGV), First-In-Queue-First-Out (FIQFO) rule (the load that has the greatest waiting time will have the highest priority to be deliveried by an AGV), Last-In-Queue-First-Out (LIQFO) rule (the load that has the latest waiting time will have the highest priority to be deliveried by an AGV), and Shortest-Queue-Length (SQL) rule (an AGV will visit the delivery point that has the latest number of loads waiting at its output queue). Finally for load-selection problem, First-In-Queue-First-Out (FIQFO) rule (the load that has the greatest waiting time at the pickup point will have the highest priority to be picked up by an AGV) has been used in the simulation experiment.


### 1.3. Evaluating Control Strategies by Fuzzy MADM Method

In this study, the method which was introduced by Chang [23] as extent analysis has been used in order to calculate the weight of assessment criteria. The steps of extent analysis approach are as follows: let X={x1,x2,…,xn} be an object set and G={g1,g2,…,gm} a goal set. According to the method, each object is taken and extent analysis for each goal is performed, respectively. Therefore, m extent analysis values for each object can be obtained, with the following signs:
(1)Mgi1,Mgi2,…,Mgim,
where all the Mgij(j=1,2,…,m) are triangular fuzzy numbers.Step 1.
The value of fuzzy synthetic extent with respect to the ith object is defined as(2)Si=∑j=1mMgij⊗(∑i=1n∑j=1mMgij)-1=(l′i,m′i,u′i)⊗(1∑i=1nu′i,1∑i=1nm′i,1∑i=1nl′i)=(l′i∑i=1nu′i,m′∑i=1nm′i,u′i∑i=1nl′i)=(li,mi,ui),
where
(3)∑j=1mMgij=(li1,mi1,ui1)⊕(li2,mi2,ui2)⊕⋯⊕(lim,mim,uim)=(∑j=1mlij,∑j=1mmij,∑j=1muij)=(l′i,m′i,u′i),∑i=1n∑j=1mMgij=(∑i=1nli,∑i=1nmi,∑i=1nui),⌊∑i=1n∑j=1mMgij⌋-1=(1∑i=1nui,1∑i=1nmi,1∑i=1nli).Step 2.
The degree of possibility is defined as(4)V(M2≥M1)=sup[minμm1(x),μm2(y)]
or
(5)V(M2≥M1)=hgt(M1∩M2)=μM2(d)={1,ifm2≥m1,0,ifl1≥u2l1-u2(m2-u2)-(m1-l1)otherwise,
where d is the ordinate of the highest intersection point d between μM1 and μM2 (see Figure 1). To compare M1 and M2, both values of V(M1≥M2) and V(M1≥M2) are needed.Figure 1
ComparingM1 and M2.Step 3.
The possibility degree for a convex fuzzy number to be greater than k convex fuzzy numbersMi,i=1,2,…,k can be defined by
(6)V(M≥M1,M2,…,Mk)=V[(M≥M1)and(M≥M2)and…and(M≥Mk)],=minV(M≥Mi),i=1,2,…,k,(7)d′(Ai)=minV(Si≥Sk),W′=(d(A1),d(A2),…,d(An))T.Step 4.
Via normalization, the normalized weight vectors can be calculated as follows:(8)W′=(d′(A1),d′(A2),…,d′(An))T.


### 1.4. TOPSIS Method

TOPSIS is a multiple criteria decision-making (MCDM) method to identify solutions from a finite set of alternatives. The basic principle shows that the chosen alternative should have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution [24]. The TOPSIS algorithm can be expressed as follows.Step 1.
Calculate the normalized decision matrix. The normalized value ofnij is calculated as, where i and j denote alternative i and ideal j, respectively,
(9)nij=xij∑i=1mxij2,i=1,…,m,j=1,…,n.Step 2.
Calculate the weighted normalized decision matrix. The weighted normalized valuevij is calculated as follows:
(10)vij=wjnij,i=1,…,m,j=1,…,n,(11)∑j=1nwj=1.Step 3.
Determine the positive ideal and negative ideal solutions as follows:(12)A+={v1+,…,vn+}={(maxjvij∣i∈I),(minjvij∣i∈J)},A-={v1-,…,vn-}={(minjvij∣i∈I),(maxjvij∣i∈J)}.Step 4.
Calculate the separation measures, using the n-dimensional Euclidean distances as follows:(13)di+=(∑j=1n(vij-vj+)2)1/2,i=1,…,m,(14)di-=(∑j=1n(vij-vj-)2)1/2,i=1,…,m.Step 5.
Calculate the relative closeness to the ideal solution. The relative closeness of the alternative Ai with respect to A+ is defined as(15)ci=di-(di++di-),i=1,…,m.Step 6.
Rank the preference order. For ranking alternatives using this index, we can rank alternatives in decreasing order. As mentioned before, the basic principle of the TOPSIS method is that the chosen alternative should have the ‘‘shortest distance” from the positive ideal solution and the ‘‘farthest distance” from the negative idea.


## 1.1. Selecting Rules

First of all, the controlling mechanism of a multiple-load AGV system has been defined to create a general view on the control problem and then several rules for dispatching, delivery, and load selection problems have been introduced. One of the main objectives of a control policy is to satisfy demands for transportation as fast as possible and with minimum possible conflicts between AGVs. Therefore, the following activities should be carried out by a controlling system.(i)
Dispatching of loads to AGVs: this problem defines the strategy for assigning the AGVs to machines (workstations) or assigning any special load to the available AGV. When an AGV is idle (i.e., it has no task to do), some requests for transportation arise in the manufacturing system. Now the problem is to assign the AGV to the best request. If the request is for delivery, the problem is calleddelivery-dispatching and if it is a pickup one then it is called pickup-dispatching problem. However, when an AGV arrives at a P/D point for picking up some parts, another problem arises which is selecting the best load for that AGV. This problem is called load-selection problem.(ii)
Route selection: by the time an AGV assigns to a specific machine, now a new problem arises which is selecting the best pathway from the original point to the destination. The best selected way refers to selecting a pathway to reduce transportation time as well as preventing the possible conflictions. In the literature review, There are two main categories for route selection problem which areoff-line and on-line methods. Off-line methods are studied when the system information is static, that is, there is no stochastic event in the system. In contrast on-line controlling systems are more practical because they assume that several stochastic events like machine or AGV break downs could happen. The on-line controlling systems are centralizedor decentralized. It is centralized when the controlling system has been installed on the AGV boards and it is decentralized when the controlling system has been installed on several locations in the manufacturing cell.(iii)
Dispatching the idle AGVs to the parking station(s).However, one may see more details about these problems in [21].


## 1.2. Dispatching Rules

In this section, several dispatching rules applied in the simulation experiments have been verified. When an AGV is full or empty, the next task could be determined easily because the next task will be delivery (when it is full) or pickup (when it is empty). But in some situations, the AGV is half-full so the next decision should be selected among a pickup task or delivery task. In this situation, three main strategies could be developed. One isDelivery-Task-First (DTF) rule, which just selects delivery task. Another one is Pickup-Task- First (PTF) rule and the final one is Load-Ratio (LR). According to [21], the best rule is DTF, so in the simulation experiments, this rule has been used, that is, a multiple-load AGV will always perform delivery task even when both delivery tasks and pickup tasks are available. For pickup-dispatching rules, four major rules have been used such as Longest-Time-In-System (LTIS) rule (an AGV will visit the pickup point containing the load that has been in the system for the longest time), Greatest-Queue-Length (GQL) rule (an AGV will visit the pickup point that has the greatest number of loads waiting at its output queue), Earliest Due Time (EDT) rule (an AGV will visit the pickup point containing the load with the earliest due time), and Smallest-Remaining-Processing-Time (SRPT) rule (an AGV will visit the pickup point containing the load with the smallest remaining processing time). For delivery-dispatching problem, five main rules have been used such as Shortest-Distance (SD) rule (an AGV will visit the delivery point to which it is the closest), Earliest Due Time (EDT) rule (the load that has the earliest due time will have the highest priority to be deliveried by an AGV), First-In-Queue-First-Out (FIQFO) rule (the load that has the greatest waiting time will have the highest priority to be deliveried by an AGV), Last-In-Queue-First-Out (LIQFO) rule (the load that has the latest waiting time will have the highest priority to be deliveried by an AGV), and Shortest-Queue-Length (SQL) rule (an AGV will visit the delivery point that has the latest number of loads waiting at its output queue). Finally for load-selection problem, First-In-Queue-First-Out (FIQFO) rule (the load that has the greatest waiting time at the pickup point will have the highest priority to be picked up by an AGV) has been used in the simulation experiment.


## 1.3. Evaluating Control Strategies by Fuzzy MADM Method

In this study, the method which was introduced by Chang [23] as extent analysis has been used in order to calculate the weight of assessment criteria. The steps of extent analysis approach are as follows: let X={x1,x2,…,xn} be an object set and G={g1,g2,…,gm} a goal set. According to the method, each object is taken and extent analysis for each goal is performed, respectively. Therefore, m extent analysis values for each object can be obtained, with the following signs:
(1)Mgi1,Mgi2,…,Mgim,
where all the Mgij(j=1,2,…,m) are triangular fuzzy numbers.Step 1.
The value of fuzzy synthetic extent with respect to the ith object is defined as(2)Si=∑j=1mMgij⊗(∑i=1n∑j=1mMgij)-1=(l′i,m′i,u′i)⊗(1∑i=1nu′i,1∑i=1nm′i,1∑i=1nl′i)=(l′i∑i=1nu′i,m′∑i=1nm′i,u′i∑i=1nl′i)=(li,mi,ui),
where
(3)∑j=1mMgij=(li1,mi1,ui1)⊕(li2,mi2,ui2)⊕⋯⊕(lim,mim,uim)=(∑j=1mlij,∑j=1mmij,∑j=1muij)=(l′i,m′i,u′i),∑i=1n∑j=1mMgij=(∑i=1nli,∑i=1nmi,∑i=1nui),⌊∑i=1n∑j=1mMgij⌋-1=(1∑i=1nui,1∑i=1nmi,1∑i=1nli).Step 2.
The degree of possibility is defined as(4)V(M2≥M1)=sup[minμm1(x),μm2(y)]
or
(5)V(M2≥M1)=hgt(M1∩M2)=μM2(d)={1,ifm2≥m1,0,ifl1≥u2l1-u2(m2-u2)-(m1-l1)otherwise,
where d is the ordinate of the highest intersection point d between μM1 and μM2 (see Figure 1). To compare M1 and M2, both values of V(M1≥M2) and V(M1≥M2) are needed.Figure 1
ComparingM1 and M2.Step 3.
The possibility degree for a convex fuzzy number to be greater than k convex fuzzy numbersMi,i=1,2,…,k can be defined by
(6)V(M≥M1,M2,…,Mk)=V[(M≥M1)and(M≥M2)and…and(M≥Mk)],=minV(M≥Mi),i=1,2,…,k,(7)d′(Ai)=minV(Si≥Sk),W′=(d(A1),d(A2),…,d(An))T.Step 4.
Via normalization, the normalized weight vectors can be calculated as follows:(8)W′=(d′(A1),d′(A2),…,d′(An))T.


## 1.4. TOPSIS Method

TOPSIS is a multiple criteria decision-making (MCDM) method to identify solutions from a finite set of alternatives. The basic principle shows that the chosen alternative should have the shortest distance from the positive ideal solution and the farthest distance from the negative ideal solution [24]. The TOPSIS algorithm can be expressed as follows.Step 1.
Calculate the normalized decision matrix. The normalized value ofnij is calculated as, where i and j denote alternative i and ideal j, respectively,
(9)nij=xij∑i=1mxij2,i=1,…,m,j=1,…,n.Step 2.
Calculate the weighted normalized decision matrix. The weighted normalized valuevij is calculated as follows:
(10)vij=wjnij,i=1,…,m,j=1,…,n,(11)∑j=1nwj=1.Step 3.
Determine the positive ideal and negative ideal solutions as follows:(12)A+={v1+,…,vn+}={(maxjvij∣i∈I),(minjvij∣i∈J)},A-={v1-,…,vn-}={(minjvij∣i∈I),(maxjvij∣i∈J)}.Step 4.
Calculate the separation measures, using the n-dimensional Euclidean distances as follows:(13)di+=(∑j=1n(vij-vj+)2)1/2,i=1,…,m,(14)di-=(∑j=1n(vij-vj-)2)1/2,i=1,…,m.Step 5.
Calculate the relative closeness to the ideal solution. The relative closeness of the alternative Ai with respect to A+ is defined as(15)ci=di-(di++di-),i=1,…,m.Step 6.
Rank the preference order. For ranking alternatives using this index, we can rank alternatives in decreasing order. As mentioned before, the basic principle of the TOPSIS method is that the chosen alternative should have the ‘‘shortest distance” from the positive ideal solution and the ‘‘farthest distance” from the negative idea.


## 2. The Simulation Model

In the simulation model, some specific assumptions were considered. All vehicles are multiple-load AGVs and the fleet size in the system is 3 units. The flow path layout and all model information are the same as the one which was adopted by [21] for the best comparison. The flow path layout is shown in Figures 2, 3, and 4 where all paths are unidirectional with capacity of one unit to prevent any conflicts. In order to unload the loads before picking up more loads from a machine by an AGV, the delivery point and the pickup point of every machine have been arranged. Every machine has a buffer area place, at which idle AGVs can stay and wait for pickup requests. All AGVs have the same loading capacity and same speed (1.8 m/s). Parts are placed in the pallets and in each pallet, there is only one type of product and for each part, the production sequence and the Mix-Ratio are known in Table 3. The load-carry capacity of these AGVs is four loads. There are 12 machines in the manufacturing system as mentioned in Figure 2. Workstations 1 and 12 are the entry and sink stations, respectively. The workstations 2–11 are processing machines. The number of part types made in the system is six. Table 4 shows the distribution functions of each machine processing time. It is assumed that parts will go through the same operations on the same workstations. It is also assumed that the setup times are included in the related processing times. Furthermore, in the simulations, a part is assigned with a due time when it arrives at the system randomly. The due time is generated by adding the arrival time with a random number. It takes 30 seconds for an AGV to perform a loading operation or an unloading operation.Figure 2
The flow path layout.Figure 3
Three-dimensional view.Figure 4
Two-dimensional view.The controlling strategies are generated by mixing the rules mentioned in Sections1.1 and 1.2 in 5 different levels. According to the levels which were shown in Table 2, there are 20 different strategies which will be used in the simulation model as controlling strategies. We used a coding system for referring any kind of strategies using the capital letters shown in the columns of Table 2. For example, a strategy (or problem) T1P1D1L1 refers to a strategy where the task rule is DTF, the pickup-dispatching rule is LTIS, the delivery-dispatching rule is SQL, and the load-selection rule is FIQFO. Meanwhile, in the simulation model, we used NV as a workstation-initiated approach for assigning the AGVs for the next task.Table 2
The levels of controlling strategies.
LevelsTasksPickup-DispatchingDelivery-DispatchingLoad-Selection1DTFLTISSQLFIQFO2DTFGQLEDTFIQFO3DTFEDTSDFIQFO4DTFSRPTLIQFOFIQFO5DTFFIFOFIQFOTable 3
The mix-ratio and process sequence of each part.
Part TypeMix-RatioSequence10.161-3-5-7-9-11-1220.171-2-4-6-8-10-1230.181-4-5-7-9-10-1240.151-3-4-5-9-11-1250.141-2-3-6-8-9-1260.201-5-6-7-10-11-12Table 4
The processing-time distribution and the production sequence of each product type.
Work stationProcessing time distribution (min)Work stationProcessing time distribution (min)2N (1,0.1)7N (2,0.2)3N (1.5,0.15)8N (1.5,0.15)4N (2,0.2)9N (1.5,0.15)5N (1,0.1)10N (2,0.2)6N (2,0.2)11N (1,0.1)In order to evaluate the control strategies, the following criteria were used in the model and the number of each criterion was used as a reference in the simulation experiments:(1)
system throughput (ST),(2)
mean flow time of parts (MFTP),(3)
the mean tardiness of parts (MTP),(4)
percentage of vehicles idle time (AGVI),(5)
percentage of time moving vehicles with full capacity (AGVTF),(6)
percent time on moving vehicles with empty capacity (AGVTE),(7)
percentage of load time (AGVL),(8)
percentage of unload time (AGVUL),(9)
the average queue length in pickup and delivery points (MQL),(10)
the average waiting time in pickup and delivery points (MQW).All simulation experiments were run by Enterprise Dynamics V8.0 software. The number of replications for each calculation was set at 30 by independent subruns. The simulation period for each replication was 170,000 seconds. For determining the warm-up period, the throughput criterion was used in 30 runs. The results were shown in Figure5. As the figure shows, when the total production reaches 750 units (480,000 seconds), the system reaches a stable state. Therefore, for simulation replications, at first a warm-up period of 480,000 seconds ran then 30 replications were executed afterward for each calculation.Figure 5
The warm-up diagram.


## 3. Computational Results

For calculating the weights of each criterion (according to Section1.3), the experts’ views which had been based on a field study were taken. At first, we had some interviews with 10 special experts. All experts were the production managers and the financial mangers of 5 local auto part manufacturers which are using multiple-load AGVs in their production sites. At the beginning of each interview, the overall approach including the terms, strategies, and targets was explained to the experts. Then, they compared each criterion in comparison with the others by a linguistic measurement system and finally, the measurements were transferred to some fuzzy triangular numbers which were shown in Table 5. Then the weight for each criterion which had been based on the method explained in Section 1.3 was calculated and the results were shown in Table 6. As the results show, the greatest weights belong to ST and MQW and the lowest one belongs to AGVI criterion. It should be noticed that the number of criteria in the experiments is 10 to create robust results. It is an important factor specially, when one compares the total criteria used by [21] with just 3 criteria. Then, TOPSIS was applied to rank the 20 strategies and the results were shown in Figure 6. According to the results, the best strategy is T1P3D2L1 since it has the lowest rank. Now the simulation model is ready to be started. After considering the warm-up period, the simulation replications ran and the results were shown in Table 7. According to the results, the best strategy for ST criterion is T1P2D3L1 and the worst one is T1P1D5L1, since it uses GQL as pickup-dispatching rule and SD as delivery-dispatching rule so these strategies have the greatest influence on the system throughput. Regarding MQW as the second important criterion, the best strategy is T1P1D4L1 and the worst one is T1P4D2L1. Maximum queue length happens when it uses T1P4D2L1 and the shortest length belongs to the strategy T1P1D4L1. The main contribution of this paper is using TOPSIS and fuzzy weights for selecting the best control strategies by mixing them with mentioned weights; therefore, by applying TOPSIS on the simulation results, we can rank and find the best control strategy; the related results were shown in Table 8. According to the final results, the best strategy is T1P3D2L1 and the worst one is T1P4D1L1, that is, when we use EDT for pickup-dispatching and SD for delivery-dispatching activities. The results show the importance of due time for selecting the best control strategies. The role of due time in the current consuming market conditions where the market is full of different brands with suitable quality and services is a key factor to keep the customers satisfied by agreed delivery times.Table 5
Fuzzy comparison measures.
Linguistic termstriangular fuzzy numbersVery High(1.5,2,2.5)High(1,1.5,2)Equal(1,1,1)Low(0.5,0.67,1)Very Low(0.4,0.5,0.67)Table 6
Criteria comparison matrix.
Assessment criteria no.STMFTPMTPAGVIAGVTFAGVTEAGVLAGVULMQLMQWWeightST—VHVHVHVHVHVHVHEE0.158MFTP—VHVHVHVHVHVHLL0.144MTP—VHVHVHVHVHLL0.107AGVI—VHVHVHVHVlVl0.087AGVTF—VHVlVlVlVl0.045AGVTE—VlVlVlVl0.029AGVL—EVlVl0.062AGVUL—VlVl0.062MQL—L0.150MQW—0.158Table 7
Simulation results.
CriterionSTMFTPMTPMQLMQWAGVIAGVTFAGVTEAGVLAGVULStrategyT1P1D1L1690.200001,419.62106511.3797111.159342,803.380510.000350.324560.494580.090250.09026T1P1D2L1688.400001,518.25473584.7827210.567342,737.494270.000420.327610.490750.089930.08994T1P1D3L1688.400001,462.67312518.6329711.019242,767.905810.000290.327610.492000.090040.09005T1P1D4L1687.800001,447.06987531.9604410.652392,733.410440.000400.328530.490570.090240.09026T1P1D5L1683.800001,481.42879551.4762710.809052,774.687430.000370.329430.489760.090200.09024T1P4D1L11,018.00000835.5426427.9031562.4680711,837.098830.241140.241140.218940.102910.10311T1P4D2L11,009.20000826.0996236.6437865.0388412,109.442200.210980.241890.340750.103070.10331T1P4D3L11,017.00000818.2683330.2817063.4045211,864.549270.229110.225340.338990.103180.10338T1P4D4L11,009.60000867.3222738.8943164.7381512,074.781630.218920.238440.336480.102960.10320T1P4D5L11,011.20000845.4139631.3979063.2275911,900.352910.228960.230710.334260.102960.10311T1P2D1L11,011.20000769.3457718.2164651.6763810,565.671970.241180.223000.330840.102350.10263T1P2D2L11,009.60000805.5070623.1852854.5224411,201.577890.198280.274510.322290.102300.10262T1P2D3L11,032.60000765.6473419.0224751.4475810,561.233270.243220.226130.325690.102330.10263T1P2D4L11,022.60000790.7099725.5395153.5262511,060.930080.214660.262750.317670.102320.10260T1P2D5L11,020.40000791.5186925.9519653.1975710,958.525950.212330.259910.322800.102350.10261T1P3D1L1923.20000846.9285587.6946843.476078,380.358120.172210.243280.378430.102970.10311T1P3D2L11,013.20000830.1388699.1874435.922608,020.678150.090580.286320.422340.100380.10039T1P3D3L1966.60000827.92455117.1265340.770308,546.091540.167370.248620.379240.102310.10247T1P3D4L1930.60000783.1837875.0486537.891607,859.486340.156330.259430.379240.102420.10258T1P3D5L1944.80000800.3171664.4504538.296248,057.845770.176670.252400.364580.103110.10324Table 8
Strategies ranking by TOPSIS method.
criteriaSTMFTPMTPMQLMQWAGVIAGVTFAGVTEAGVLAGVULd-d+CiRankStrategyW0.15785320.14354260.10721620.14988980.15785320.08672460.04498830.02855560.06166830.0616683T1P3D2L10.05418590.02619700.00865800.02606970.03090320.00994390.01064530.00697120.01375590.00138080.091330.066350.579201T1P3D4L10.05210810.02471520.00655090.02749860.03028210.01716170.00964560.00625980.01403560.00143750.091930.067970.574902T1P3D3L10.05673320.02612710.01022390.02958770.03292760.01837380.00924380.00625970.01402010.00143430.089050.065970.574453T1P1D3L10.02745220.04615810.04527090.00799690.01066460.00003220.01218080.00812100.01233910.00111100.085440.063820.572434T1P3D5L10.05093290.02525590.00562580.02779230.03104640.01939470.00938430.00601780.01413000.00145690.091640.068690.571555T1P1D4L10.02742830.04566570.04643430.00773060.01053170.00004400.01221480.00809740.01236630.00111590.085530.064220.571156T1P1D1L10.02622260.04479950.04463780.00809850.01080130.00003900.01206720.00816350.01236860.01236890.084560.064580.566997T1P3D1L10.05457100.02672680.00765480.03155140.03228900.01890430.00904540.00624650.01411080.00145300.089160.067560.568898T1P1D5L10.02724500.04674990.04813780.00784430.01069070.00004010.01224850.00808410.01236130.00111500.084860.064380.568619T1P1D2L10.02752400.04791210.05104510.00766890.01054740.00004570.01218080.00810040.01232440.00110850.084400.064890.5653510T1P2D3L10.06039170.02416180.00166050.03733640.04069180.02670030.00840770.00537580.01402330.00143500.092980.078560.5420511T1P2D1L10.05923380.02427850.00159010.03750250.04070890.02647660.00829130.00546090.01402610.00143560.092470.078270.5416012T1P2D5L10.06044660.02497820.00226530.03860640.04222250.02330890.00966360.00532830.01402630.00143560.091470.078150.5392813T1P2D4L10.06116930.02495270.00222930.03884500.04261710.02356510.00976920.00524350.01402150.00143460.091690.078640.5383314T1P2D2L10.05914010.02541970.00202380.03956790.04315900.02176640.01020640.00531980.01401970.00143430.090530.078340.5361015T1P4D3L10.05945570.02582240.00264330.04601380.04571340.02515130.00837810.00559540.01414000.00145900.088440.081420.5206616T1P4D5L10.05914010.02667900.00274070.04588540.04585130.02513470.00857790.00551740.01410990.00145280.087940.081100.5202317T1P4D2L10.05951420.02606950.00319860.04719990.04665690.02316130.00899340.00562450.01412470.00145580.087530.081560.5176718T1P4D4L10.05947930.02737040.00339500.04698170.04652340.02403270.00886540.00555400.01410990.00145280.086990.081090.5175419T1P4D1L10.04032480.02636750.00243560.04533420.04560760.02647170.00896560.00361390.01410300.00145140.083760.081310.5074320A+0.06116930.02416180.00159010.00766890.01053170.00003220.01224850.00361390.01232440.0011085A-0.02622260.04791210.05104510.04719990.04665690.02670030.00829130.00816350.01414000.0123689Figure 6
Strategies ranking by TOPSIS method.As mentioned before, for comparison purposes, we selected the study done by [21]. However, they did not mention the dimension of paths in their flow path. It is another strength point of this paper where the time needed for transportation time is included in the simulation model by defining the length of each path and the AGV speed like the real world. As well, since we used a random generator for due dates as same as [21], therefore, the results may change specially in Table 7, but the ranks of similar strategies are the same. They used 3 criteria and 18 different strategies but here we used 10 criteria and 20 different strategies. They used ANOVA analysis for ranking the strategies, but here we used TOPSIS together with fuzzy weighting method for ranking them. The approach used here is more close to the real applications where the top managers can change the strategies based on the production, market situation, and financial issues. The comparison made for final results in both studies is showen in Figure 7. The best strategy reported by [21] was T1P2D3L1 and the worst one was T1P1D3L1 while here the best one is T1P3D3L1 (on similar strategies) and the worst one is T1P4D3L1. But it should be mentioned that despite the approach used by [21], that is, ANOVA method which explains the effect of each rule like selection, pickup-dispatching, and the other rules on the system performances, we just focused on selecting the best control strategy since the effects were shown by [21] and it is not necessary to repeat them again. The focus in the present study was to create a more comprehensive framework for selection decision.Figure 7
TOPSIS method versus [21] results.Finally for optimizing the fleet size, we used the same approach for selecting the best number of AGVs in the system. For this reason, another criterion, costs, was added to the model for best evaluation. However, it is obvious that when the fleet size increases the system performances like ST, AGVUL, MQL, and MQW improve, but one should notice the costs of such a decision. Based on financial statements in the local auto part manufacturers, the annual average cost of handling an AGV (including the depreciation and maintenance) is $ 15,000, so the comparison matrix was reevaluated by the experts and the results were summarized in Table9; then the weights were calculated, the simulation model run by different fleet sizes such as 3, 4, 5, 6, 7, and 8 and the results were shown in Table 10. Finally by considering the weights and the simulation normalized results, the main index which is called Total Costwas calculated for the different fleet sizes. In Figure 8, this index is depicted against different fleet sizes. According to the results, the best fleet size is 7 units. It should be noticed that when the fleet size increases from 3 to 4 units, the ST increases by 3.65% in Table 10, but by further increases it keeps constant, because more AGVs get idle and the system throughput will not increase more. Such a conclusion can be got for other criteria.Table 9
Criteria comparison matrix.
EvaluatingSTMFTPMTPMQLMQWAGVIAGVTFAGVTEAGVLAGVULCosts ($)WightCriterionST—VHVHVHVHVHVHVHEEL0.13115MFTP—VHVHVHVHVHVHLLL0.12015MTP—VHVHVHVHVHLLL0.09239MQL—VHVHVHVHVIVIL0.07701MQW—VHVIVIVIVIL0.04589AGVI—VIVIVIVIL0.03376AGVTF—EVIVIL0.05846AGVTE—VIVIL0.05846AGVL—LL0.12503AGVUL—L0.13115Costs ($)—0.12652Table 10
Simulation results for different fleet size.
criteriaSTMFTPMTPMQLMQWAGVIAGVTFAGVTEAGVLAGVULCosts ($)Fleet size31013.2830.1499.19368020.680.0910.290.420.100370.1003845,00041050537.770.01934.27025.60.160.310.370.080.0860,00051050374.530.01033.616963.470.340.240.300.060.0675,00061050282.640.00523.894919.270.440.200.260.050.0590,00071050216.340.00516.953595.360.530.170.220.040.04105,00081050215.030.00516.953595.360.590.150.220.040.04120,000Figure 8
Total cost versus different fleet sizes.


## 4. Conclusions

In this paper, pickup-dispatching problem together with delivery-dispatching problem of a multiple-load automated guided vehicle (AGV) system has been studied. Several different rules of these problems were used to create the best control strategies. For selecting the best strategy, several important criteria were considered, such as System Throughput (ST), Mean Flow Time of Parts (MFTP), Mean Tardiness of Parts (MFTP), AGV Idle Time (AGVIT), AGV Travel Full (AGVTF), AGV Travel Empty (AGVTE), AGV Load Time (AGVLT), AGV Unload Time (AGVUT), Mean Queue Length (MQL), and Mean Queue Waiting (MQW) in a part manufacturing system where each part has a due date. The criteria were evaluated by a filed study with 10 experts who work in 5 local auto part manufacturing companies to make the results as applicable as possible. For evaluating each criterion, we used an MADM method with fuzzy triangular numbers to compute the importance weights. Meanwhile, several simulation experiments based on a flow path layout were conducted. Finally, for ranking and selecting the best control strategy, a TOPSIS method was applied to simulation results and the importance weights. Furthermore, the same approach was used for determining the optimal fleet size in the flow path layout. The results show that the best pickup-dispatching rule is EDT and the best delivery-dispatching strategy is SD while the best fleet size is 7 units. One of the contributions of this paper is combining several strategies together with 10 criteria by TOPSIS method to evaluate the best strategy which is carried out for the first time in the literature. The other one is the approach used in the field study to make the approach as close as possible to be applicable in related industries by using MADM to consider the top mangers’ views and finally some improvements were done in comparison with the similar work [21]. Here we defined the distances between workstations and calculated the warm-up period in order to make the simulation more practical while the total strategies examined were 20 strategies with 10 criteria which had been the biggest sets tested so far. The results show that the proposed algorithm is efficient and robust enough to be used in applications. However, in this study, we did not verify different flow path layouts to obtain better results. Some normal events which occur in a manufacturing system like machine/AGV break downs and the related repair time were not studied, as well. Moreover, we did not consider a battery management system for the AGVs. All these constraints can be considered in future works.



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*Source: 821701-2010-10-04.xml*