A multiple-attribute method for concurrently solving the pickup-dispatching problem and the load-selection problem of multiple-load AGVs

Journal of Manufacturing Systems 31 (2012) 288–300

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Journal of Manufacturing Systems journal homepage: www.elsevier.com/locate/jmansys

Technical paper

A multiple-attribute method for concurrently solving the pickup-dispatching problem and the load-selection problem of multiple-load AGVs Ying-Chin Ho a,∗ , Hao-Cheng Liu a , Yuehwern Yih b a b

Institute of Industrial Management, National Central University, Chung-Li 32001, Taiwan School of Industrial Engineering, Purdue University, West Lafayette, IN 47907, USA

a r t i c l e

i n f o

Article history: Received 7 October 2010 Received in revised form 8 October 2011 Accepted 20 March 2012 Available online 30 April 2012 Keywords: Multiple-load AGVs Pickup dispatching Load selection Multiple-attribute

a b s t r a c t The pickup dispatching and the load selection are two control problems in multiple-load AGVs. Although they affect each other and are affected by various attributes, many researchers have solved them as separate problems and adopted single-attribute methods for them. In this paper, we propose a multipleattribute method that can solve them simultaneously. The proposed method has four stages: preparation, clustering, evaluation and execution. At the preparation stage, we calculate the weights for three attributes (i.e., slack time, waiting time and distance) that are important to our problems based on the system’s current status. These weights will be useful at the second and third stages. At the clustering stage, parts needing vehicle service are clustered into part groups based on their similarity in these three attributes. At the evaluation stage, part groups are evaluated by considering these three attributes. The part group with the greatest evaluation value will be served by the AGV. At the execution stage, a procedure is proposed to assist the AGV in picking up parts efficiently. Simulations were conducted to test the performance of the proposed method in throughput, flow time, and tardiness. The results show that the proposed method outperforms not only single-attribute methods, but also methods that solve pickup dispatching and load selection separately. © 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved.

1. Introduction Automatic Guided Vehicles (AGVs) are battery-powered and driverless vehicles that are controlled by computers. They move along wire, magnetic or optic guide paths that are laid on the shop floor. Since their guide paths can be easily modified, AGVs have been adopted in different environments, e.g., flexible manufacturing systems, warehouses, sea ports, semiconductor plants, and TFT-LCD production systems. Researchers have been studying various AGV-related problems. The vehicle dispatching problem is one of the problems that have received a lot of attentions from researchers (e.g., [1–10]). Although there have been many studies focusing on the vehicle dispatching problem, the majority of them are for single-load AGVs. However, as multiple-load AGVs are becoming more and more common in factories, the number of studies on them has been increasing. Some of these studies include [7,9–13]. It has been shown by researchers (e.g., [3,7,13]) that multiple-load AGVs have many advantages (e.g., smaller fleet size, better utilization of vehicle and greater throughput) over their single-load counterparts. However, multiple-load AGVs are known to have more difficult dispatching problems than single-load ones, since they have to consider several loads (including the loads that

∗ Corresponding author. E-mail address: [email protected] (Y.-C. Ho).

are currently on them and the loads that they are going to pick up) instead of only one load (as in single-load AGVs) when performing their pickup and delivery tasks [9,10]. Ho and Chien [9] define four multiple-load AGV control problems: task determination, delivery dispatching, pickup dispatching and load selection. Fig. 1 gives the flow chart of the control process proposed by them. This control process has also been adopted by Ho and Liu [10,14]. The task-determination problem occurs when a multiple-load AGV is ready for the next task. If it is partially loaded, its next task can be a delivery task or a pickup task. Determining a multiple-load AGV’s next task is the task-determination problem. The delivery-dispatching problem occurs when a multiple-load AGV with a delivery task as its next task must determine which delivery point it should visit next to deliver the load or loads currently on it. The pickup-dispatching problem occurs when a multiple-load AGV with a pickup task as its next task must determine which pickup point it should visit next to perform its pickup task. As for the load-selection problem, it occurs when a multipleload AGV (with a pickup task as its next task) has arrived at a pickup point. At this moment, it must select and pick up the load or loads (if there is more than one empty space on the vehicle and there is more than one load waiting at the pickup point) from the pickup point. In this study, we focus on the pickup-dispatching problem and the load-selection problem. Ho and Liu [10,14] have treated these two problems as separate problems despite the fact that they are

0278-6125/$ – see front matter © 2012 The Society of Manufacturing Engineers. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jmsy.2012.03.002

Y.-C. Ho et al. / Journal of Manufacturing Systems 31 (2012) 288–300

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Fig. 1. The multiple-load AGV control process [9,10,14].

mutually affected. Furthermore, simple single-attribute rules are used in Ho and Liu [10,14] for solving these two problems. Simple single-attribute rules are easy to use, but may not be enough for finding good decisions for the pickup-dispatching problem and the load-selection problem which can be affected by various attributes. In this study, we propose a multiple-attribute method that can solve these two problems simultaneously. The purpose of this study is twofold. First, we would like to see whether the proposed method can outperform traditional methods that solve the pickupdispatching problem and the load-selection problem separately. Second, we would like to see if the proposed method can outperform single-attribute methods. We summarize the assumptions of this study as follows:

just completed and is currently waiting at the queue of its pickup point. The NV rule has been shown to perform well in throughput by Egbelu and Tanchoco [1]. The remainder of this paper is organized as follows. In Section 2, previous studies that are relevant to our study are reviewed. In Section 3, the proposed method is presented. In Section 4, we conduct simulation experiments to understand the performance of the proposed method. The simulation results are analyzed and discussed in Section 5. Finally, we summarize this study and its findings in Section 6. 2. Literature review

• • • • •

All AGVs are multiple-load vehicles. The number of AGVs in the system is known. The layout of guide paths and workstations has been determined. A load is made up of only one part. The delivery point and the pickup point of every workstation are arranged in a way so that when an AGV is approaching a workstation, it will reach the workstation’s delivery point (i.e., input queue) first. • Every workstation has a waiting place nearby. Idle AGVs can stay at this place to wait for pickup requests from workstations. • The Nearest Vehicle (NV) rule is the workstation-initiated rule adopted in the system. If NV rule is used, a workstation will request the nearest vehicle to come and pick up the load it has

The majority of early studies on vehicle dispatching were for single-load AGVs. Egbelu and Tanchoco [1] divided vehicle dispatching rules into two categories: vehicle-initiated rules and workstation-initiated rules. Vehicle-initiated rules select a workstation from a set of workstations that are requesting for the service of vehicles. Workstation-initiated rules select a vehicle from a set of idle vehicles and assign the vehicle to a pickup task at a workstation. Russell and Tanchoco [2] proposed four rules and used simulations to understand the performance of these rules. King et al. [15] developed different AGV control strategies under different demand arrival patterns. The characteristics of their proposed strategies include: (1) dynamic assignment of vehicles, (2) minimizing vehicle deadheading, and (3) considering demand arrival

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rates. Egbelu [16] developed a demand-driven rule that was based on a pull concept. This demand-driven rule was then compared with several source-driven rules that were based on a push concept through simulation experiments. Bartholdi and Platzman [17] proposed a decentralized dispatching rule that enabled a fleet of automated guided vehicles to deliver unit loads quickly on a simple loop track. Sabuncuoglu and Hommertzheim [18] proposed an on-line dispatching algorithm for the FMS (Flexible Manufacturing System) scheduling problem. The algorithm scheduled the jobs on a machine or an AGV one at a time as the scheduling deci˜ and sion was needed or as the system status changed. Occena Yokota [19] modeled a multiple-load AGV system in a JIT (JustIn-Time) environment. They proposed a new dispatching rule – the maximum demand (MD) rule – that performed well in lowering inventory and improving transporting efficiency. Srivastava et al. [20] presented an intelligent agent-based controller for an FMS. They addressed the operational control of AGVs by integrating different activities (e.g., path generation, journey time enumeration, collision and deadlock identification, etc.) on the selection of the conflict-free shortest feasible path. Desaulniers et al. [21] presented an exact solution approach for the problem of the simultaneous dispatching and conflict-free routing of AGVs in an FMS. Smolic-Rocak et al. [22] presented a dynamic routing method for the supervisory control of AGVs within a warehouse. Koo and Jang [23] presented stochastic vehicle travel time models for AGVs with emphasis on the empty travel times of vehicles. Rajotia et al. [24] addressed the issue of vehicle route planning in an AGV system. Their simulation results showed that the proposed routing strategy was able to reduce vehicle blocking time and improve the system’s throughput. Some researchers have used Petri net for their studies on AGVs. For example, Yim and Linnt [5] developed a Petri-netbased simulation to investigate the effect of different dispatching rules (pull-based and push-based) on the FMS performance. Nishi and Maeno [25] proposed a Petri Net (PN) decomposition approach for the route planning problem of AGVs in semiconductor fabrication bays. Tiwari et al. [26] modeled the AGV system of an FMS by using timed Petri net and Activity Cycle Diagrams (ACDs) as basic tools. Some researchers have proposed multiple-attribute dispatching rules or bidding-based dispatching rules for dispatching AGVs. Klein and Kim [27] demonstrated the superiority of multipleattribute dispatching rules by conducting simulation experiments to compare single-attribute dispatching rules (proposed by other researchers) and multiple-attribute dispatching rules (proposed by them) in different performance measures, e.g., queue length and load-waiting time in each department, vehicle travel time, and job completion time. Bozer and Yen [28] presented two dispatching rules – the modified shortest rule and the bidding-based dynamic dispatching rule – to improve the efficiency of trip-based material handling systems. Hwang and Kim [29] also proposed a bidding-based AGV dispatching algorithm that utilized the relevant information, e.g., the work in process (WIP) in the buffer of a workstation and the travel time of AGVs. Kim and Hwang [30] proposed an adaptive dispatching algorithm based on bidding functions which considered the WIP level in incoming buffer, the WIP level in outgoing buffer and the travel distance of vehicles. Jeong and Randhawa [8] developed a multiple-attribute dispatching rule that used an additive weighting method and considered three system attributes. Tan and Tang [31] developed a fuzzy decision-making system that emulated the human behavior necessary for multiple-objective decision making in a dynamically evolving environment. Bilge et al. [32] examined responsiveness in AGV dispatching. They proposed an additive multiple-attribute dispatching rule that employed two attributes – output buffer length and travel time to pick-up – to prioritize tasks based on the current system status.

The number of studies for multiple-load AGVs has been increasing as more and more multiple-load AGVs are being adopted in real-life manufacturing systems. Ozden [3] studied the effects of several multiple-load AGV-related factors on the performance of an FMS. Gaskins and Tanchoco [33] reported a development tool’s capability in modeling multiple-load vehicles for the controller ˜ and Yokota [19] extended the work of design of AGVs. Occena ˜ and Yokota [4] by modeling an AGV system with multipleOccena load vehicles under a JIT environment. Tanchoco and Co [34] reviewed various control problems in multiple-load AGVs. They proposed two control procedures to sequence the stations in a vehicle’s task list. Bilge and Tanchoco [7] extended the work of Tanchoco and Co [34] by implementing the most promising control policies, considering issues such as network congestion and guidepath design, and assessing the degree of flexibility and robustness offered by multiple-load AGVs. Ho and Shaw [12] studied the performance of multiple-load AGVs under different guide-path configurations and vehicle control strategies. They found that a control strategy’s performance can be affected by the guide-path configuration. Ho and Chien [9] identified four control problems (i.e., task determination, delivery-dispatching, pickup dispatching and load selection) in the control process of multiple-load AGVs and investigated two of them – task-determination and delivery-dispatching. Ho and Liu [10] used the multiple-load AGV control process proposed by Ho and Chien [9] to study the pickupdispatching problem. They proposed nine pickup-dispatching rules and studied their performance with computer simulations. They also investigated the effects that load-selection rules have on the performance of pickup-dispatching rules. Lee et al. [11] studied the load-selection problem of multipleload AGVs in a flexible manufacturing system. They proposed five heuristic rules and evaluated these rules with the aid of computer simulation. Ho and Liu [14] extended the work of Ho and Liu [10] by proposing more load-selection rules and studied their performance. They also investigated the mutual effects between load-selection rules and pickup-dispatching rules. Their simulation results indicated load-selection rules and pickup-dispatching rules affected each other’s performance. Lee and Srisawat [35] referred to the load-selection problem as the load pick-up problem. They investigated the interaction between manufacturing system constructs and the operations strategies in a multiple-load AGV system. They proposed rules for the load pick-up problem and the dropoff problem and tested their performance in two manufacturing system constructs: the job shop and the FMS.

3. The control process Fig. 2 shows the control process adopted by us. The control process is similar to the one (see Fig. 1) adopted by Ho and Liu [10,14]. The main difference between them is the way they handle the pickup-dispatching problem and the load-selection problem. Ho and Liu [10,14] solve these two problems separately, while the proposed method solves them simultaneously. Furthermore, since the task-determination problem and the delivery-dispatching problem are not the focus of this study, methods developed by other researchers are adopted by us. As shown in Fig. 2, the DTF rule and the SD rule are used to solve the task-determination problem and the delivery-dispatching problem respectively. In the following sections, we first explain why the DTF rule and the SD rule are adopted by us to solve the task-determination problem and the delivery-dispatching problem respectively in our multiple-load AGV control process. After that, the method proposed by us for simultaneously solving the pickup-dispatching problem and the load-selection problem is presented in Section 3.3.

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A multiple-load AGV, V, has completed a pickup task or a delivery task and is ready for the next task.

Are the following two conditions both true? First, V is empty. Second, there are no loads waiting to be picked up in the system. Taskno

yes

Determination Problem

V becomes idle and goes to the nearest waiting place. It will stay there until it receives a pickup request from a machine. V will perform the pickup request after receiving it .

Use the Delivery-Task First (DTF) rule to determine the next task of V is a pickup task or a delivery task.

The next task is a delivery task Use the Shortest Distance (SD) rule to determine which delivery point that V should visit next to perform its delivery task.

The next task is a pickup task

DeliveryDispatching Problem

PickupDispatching Problem

Use the proposed method to solve the pick-up dispatching problem and the load-selection problem together.

Dispatch V to the delivery point.

V arrives at the delivery point and unloads the loads that need to get off at this delivery point.

Load-Selection Problem

Fig. 2. The multiple-load AGV control process adopted in this study.

3.1. The method for the task-determination problem Ho and Chien [9] proposed three task-determination rules (i.e., Delivery-Task First (DTF), Pickup-Task First (PTF), and Load-Ratio (LR)) and compared their throughput performance and the mean lateness of parts (MLP) performance. They found that the DTF rule outperformed the other two rules in both performance measures. Under the DTF rule, a multiple-load AGV will always perform delivery tasks first when delivery tasks and pickup tasks are both available. A multiple-load AGV will continue performing delivery tasks as long as there are loads on it. Because of its superior performance, the DTF rule is the task-determination rule adopted by us in this study. 3.2. The method for the delivery-dispatching problem We also adopt a delivery-dispatching rule proposed by Ho and Chien [9]. Ho and Chien [9] proposed ten delivery-dispatching rules and compared their throughput performance and the mean lateness of parts (MLP) performance. They found the Shortest Distance (SD) rule is better than the other delivery-dispatching rules in both performance measures. Under the SD rule, loads are delivered based on the distance between their destinations and the AGV’s current position. The load with the smallest distance will be delivered first. Because of its superior performance, the SD rule is the delivery-dispatching rule adopted by us in this study. 3.3. The proposed method for the pickup-dispatching problem and the load-selection problem As shown in Fig. 2, the proposed method is activated right after it has been decided that the next task of the multiple-load AGV, V, is a pickup task. Since the DTF rule is adopted by us to determine the next task of V, V’s next task will not be a pickup task unless it is empty, i.e., we will have an empty multiple-load AGV, V, at the

beginning of the proposed method. As shown in Fig. 3, there are four stages – preparation, clustering, evaluation and execution – in the proposed method. Fig. 3 also shows the section at which the details of each stage are explained. The task in each stage is explained as follows.

• Preparation stage: At this stage we calculate the weights for the three attributes (that are important to the pickup-dispatching and the load-selection decisions) based on the system’s current status. These three attributes are slack time of parts, waiting time of parts and the distance (e.g., the distance between parts and the travel distance of AGVs). The weights for these attributes will be useful at the second and the third stages. • Clustering stage: There are two main steps at this stage. First, use an equation (that is proposed by us and considers the three attributes mentioned above) to calculate the dissimilarity value between parts that need the service of AGVs. Second, cluster parts into different parts groups based on their dissimilarity values. • Evaluation stage: There are also two main steps at this stage. First, evaluate each of the part groups formed at the clustering stage with an evaluation function (proposed by us) that also considers the three attributes mentioned above. Second, select the part group with the greatest evaluation value as the part group to be served by the multiple-load AGV, V. • Execution stage: At this stage, the multiple-load AGV, V, follows a procedure (proposed by us) to pick up parts in the selected part group. The procedure is designed to help the multiple-load AGV, V, execute its tasks efficiently.

In the following subsections, the details of each stage will be presented. Table 1 summarizes the notation definitions appearing in the proposed method.

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Fig. 3. The four stages of the proposed method.

3.3.1. Preparation – the first stage of the proposed method At this stage, we calculate the values of three weights (i.e., ws , wt , and wd ) for the three attributes mentioned above (i.e., slack time, wait time and distance) based on the system’s current status. These three attributes will be considered at the second and third stages. Since these weights change with the system, thus every time the proposed method is activated, they must be updated. The first weight, ws , is for the slack time of parts. The equation for calculating ws is as follows:

 ˛· ROTi ws =  i ∈ IS & if ws > 1, ws = 1 i ∈ IS

ATi

(1)

In Eq. (1), the numerator is the estimation of the remaining time that parts in IS will spend in the system. The denominator is the sum of available time of parts in IS. A large ws indicates that the parts in IS do not have a lot of slack time, therefore the slack time criterion is considered as important. The greater ws is, the more important the slack time criterion becomes. The adjustment factor ˛ is Table 1 Notation definitions in the proposed method. V = the multiple-load AGV in the proposed method. ws = the weight for the slack time attribute. wt = the weight for the waiting time attribute. wd = the weight for the distance attribute. i,j = the part indices. IS = the set of parts currently waiting for the service of AGVs in the system. ROTi = the remaining operation time of part i (i ∈ IS). ˛ = an adjustment factor. ATi = max{(due time of part i − current time), 0}, i.e., the available time of part i. QS = the set of workstation output queues in the system. NIQm = the number of parts waiting in the workstation output queue m (m ∈ QS). QCm = the capacity of output queue m (m ∈ QS). c = the workstation at which the multiple-load AGV, V, is currently located. DISij = the dissimilarity between part i and part j (i,j ∈ IS). Si = the slack time of part i (i ∈ IS). Smax = max{Si |i ∈ IS}, i.e., the maximum slack time of all parts in IS. Smin = min{Si |i ∈ IS}, i.e., the minimum slack time of all parts in IS. Ti = the waiting time of part i (i ∈ IS) in its current output queue. Tmax = max{Ti |i ∈ IS}, i.e., the maximum waiting time of all parts in IS. Tmin = min{Ti |i ∈ IS}, i.e., the minimum waiting time of all parts in IS. / j). Dij = the distance between part i and part j (i,j ∈ IS & i = Dmax = max{Dij |i,j ∈ IS}, i.e., the maximum distance between parts in IS. GDISpq = the dissimilarity between part group p and part group / q). q (p,q ∈ PGS & p = PS(p) = the set of parts in part group p (p ∈ PGS). NPS(p) = the number of parts in part group p (p ∈ PGS). CPY(V) = the load capacity of the multiple-load AGV, V. EVp = the evaluation value of part group p (p ∈ PGS). TDp = the travel distance required for the multiple-load AGV, V, to pick up the parts in part group p. TDmax = max{TDp |p ∈ PGS}.

determined by the human designer. A large ˛ is needed for a busy system since parts will have to spend a lot of time on waiting in order to get the service of workstations, vehicles and other resources. In this study, preliminary experiments are conducted to find the best value of ˛. The second weight wt is for the amount of time that parts have been waiting in their current queues for the service of AGVs. The equation for calculating wt is as follows:

 NIQm m ∈ QS wt =  m ∈ QS

(2)

QCm

In Eq. (2), the numerator is the sum of the number of parts waiting in every output queue. The denominator is the sum of the capacity of every output queue. Eq. (2) indicates how congested the system is. The closer ww is to one, the more congested the system is. This implies parts will have to wait even longer for the service of AGVs. In other words, the waiting time of parts in their current output queues is becoming more important. The third weight wd is for the distance related attribute. The equation for calculating wd is as follows. In Eq. (3), c stands for the workstation at which the multiple-load AGV, V, is currently located. wd =

NIQc QCc

(3)

According to Eq. (3), the greater the number of parts in the output queue of workstation c, the greater wd becomes. We define wd in this way since we want that the chance for the following event to occur will increase as wd increases. The event is that the parts in the output queue of workstation c will be clustered into the same part group at the second stage and subsequently their part group will be chosen at the third stage. In this event, the multiple-load AGV, V, is able to pick up parts directly from the output queue of the workstation at which it is currently located. 3.3.2. Clustering – the second stage of the proposed method At this stage, we cluster parts into part groups. As explained earlier, there are two main steps at this stage (see Fig. 4). As shown in Fig. 4, at the first main step, we use Eq. (4) to calculate the dissimilarity value between any two parts in IS (i.e., the set of parts currently waiting for the service of AGVs in the system). Please note the greater DISij is, the less similar i and j are to each other. After that, at the second main step, we cluster parts into part groups using the proposed clustering method shown in Fig. 5.

  DISij =

ws

Si − Sj Smax − Smin

2

 + wt

Ti − Tj Tmax − Tmin

2

 + wd

Dij Dmax

2 1/2 (4)

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Fig. 4. The two main steps of the second stage of the proposed method.

Step 1: At the beginning, each part in IS forms its own part group, i.e., every part group contains only one part.

Let PGS stand for the set of part groups.

Step 2: Calculate the dissimilarity value, GDIS pq , between every two part groups, p and q, in PGS using the following equation. DISij

GDIS pq

i PS ( p ) j PS ( q )

NPS ( p ) NPS (q )

Step 3: Can we identify two part groups, r and s ( r, s PGS & r

s ), that meet the following

two criteria? a. NPS (r ) NPS ( s) CPY (V ) , and b. The dissimilarity value between r and s is the smallest. If yes, proceed to Step 4. If no, stop the clustering method.

The part groups in PGS are the part groups found

by the clustering method.

Step 4: Merge r and s into a new group. and s from PGS.

Add the new group into PGS and delete r

After that, proceed to Step 2.

Fig. 5. A clustering method for the second stage of the proposed method.

3.3.3. Evaluation – the third stage of the proposed method As shown in Fig. 6, there are also two main steps in this stage. At the first main step, we evaluate every part group formed at the second stage with an evaluation function Eq. (5). Eq. (5) also considers the same three attributes (i.e., slack time, waiting time and distance) considered in Eq. (4). With Eq. (5), a part group, p, containing parts with little overall slack time, large overall waiting time and a small travel distance (that is required for the multiple-load AGV, V, to pick them up) will have a large evaluation value, EVp . The greater the evaluation value of a part group, the higher its priority to be served by the multiple-load AGV, V. After that, at the second main step, the part group with the greatest evaluation value will be selected. Here G is used to denote the selected part group. The parts in the selected part group, G, will be served by the multiple-load AGV, V. EVp = ws

 Smax − S i i ∈ PS(p)

Smax − Smin

+ wt

 i ∈ PS(p)

TDp Ti − Tmin − wd (5) Tmax − Tmin TDmax

3.3.4. Execution – the fourth stage of the proposed method After the evaluation stage, the part group, G, with the greatest evaluation value has been identified. Please note that the parts in the part group, G, may not be at the same place. As a result, the multiple-load AGV, V, may have to visit different pickup points (i.e., output queues of workstations) to perform its pickup tasks. The purpose of the stage is to help the multiple-load AGV, V, pick

up these parts efficiently. A procedure (see the flow chart in Fig. 7) is proposed to achieve this purpose. As shown in Fig. 7, the multipleload AGV, V, follows two principles to perform its pickup tasks. These two principles are designed to further minimize the travel distance of AGVs so that parts can be picked up by AGVs more efficiently. The first principle is that the multiple-load AGV, V, uses the shortest distance rule to pick up parts. Parts nearest to the multipleload AGV, V, will be picked up first (see Fig. 7). The second principle is that when the multiple-load AGV, V, is approaching, L (i.e., the workstation that V is heading for to perform a pickup task), it will also perform a delivery task if there are parts on V needing to get off at L (see Fig. 7). In other words, no extra cost (i.e., extra travel distance of the vehicle) is incurred by performing this delivery task. The reason why the second principle can be followed by AGVs is because we have assumed the delivery point and the pickup point of every workstation have been arranged in a way so that when an AGV is approaching a workstation, it will reach the workstation’s delivery point (i.e., input queue) first. 4. Simulation experiments Simulation experiments were conducted to see if the proposed method can outperform methods that solve the pickup-dispatching problem and the load-selection problem separately, and to see if the proposed method can outperform single-attribute methods. Fig. 8 shows the layout of the manufacturing system. There are 15

Fig. 6. The two main steps of the third stage of the proposed method.

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From the parts in the part group, G, select the part, K, which is nearest to the multiple-load AGV, V. Let L stand for the workstation at which K is located.

The multiple-load AGV, V, proceeds to the pickup point (i.e. output queue) of L.

The multiple-load AGV, V, has completed its pickup task.

Check if the following is true as V is approaching L. Are there any parts currently on V that need to get off at L?

Is G empty?

yes

V arrives at the delivery point (i.e. input queue) of L.

V unloads those parts that need to get off at L.

yes

no

Delete those parts picked up by V from G.

no V arrives at the pickup point (i.e. output queue) of L.

V picks up K and the parts that are also in G and at the output queue of L.

V continues proceeding to the pickup point (i.e. output queue) of L. Fig. 7. The procedure for helping multiple-load AGVs pick up parts efficiently.

Fig. 8. The layout of the manufacturing system in the simulations experiments.

workstations in the system. Workstations 1 and 15 are input and output stations respectively. There are ten part types made in the system. Table 2 shows the mix ratio and the operation sequence of each part type. There are four multiple-load AGVs in the system and

Table 2 The mix-ratio and process sequence of each part type. Part type

Mix ratio

Operation sequence (in workstation #)

1 2 3 4 5 6 7 8 9 10

0.1 0.15 0.05 0.07 0.15 0.11 0.08 0.09 0.13 0.07

1-2-3-5-6-7-9-10-11-13-15 1-2-3-4-7-8-9-10-11-12-13-15 1-3-4-5-6-7-8-10-11-14-15 1-3-5-8-9-10-11-12-13-14-15 1-2-3-4-7-9-10-12-13-14-15 1-2-3-5-6-7-8-11-12-14-15 1-2-3-4-9-10-11-12-13-15 1-2-4-5-8-9-10-11-13-14-15 1-4-5-7-8-9-10-11-12-14-15 1-5-6-7-8-9-10-11-12-14-15

the load-carrying capacity of each AGV is four. This fleet size and this load-carrying capacity are enough for us to test the proposed method and the other methods in the simulation experiments. The average speed of AGVs is 42 (m/min), which is a real AGV speed obtained from a manufacturing company in Taiwan. We model the manufacturing system as a closed system with a fixed WIP, i.e., the number of parts in the system is fixed. WIP is set at 80 in the simulations. Preliminary experiments have shown that this level of WIP is sufficient to keep vehicles busy. Keeping vehicles busy is necessary in this study since the purpose of study is to understand the performance of the proposed method, which is a vehicle-initiated method (i.e., the decisions are made by vehicles). If vehicles are frequently idle, the machine-initiated method will take over and become the dominant factor in determining the system’s performance. Twenty-one simulations have been conducted. These simulations are different in their methods for solving the pickupdispatching problem and the load-selection problem. The number of replications in each simulation is 20. The warm-up time is

Y.-C. Ho et al. / Journal of Manufacturing Systems 31 (2012) 288–300

295

Table 3 Five categories of methods for solving the pickup-dispatching problem and the load-selection problem. No.

Category A

Category B

Category C

Category D

Category E

1 2 3 4 5 6 7 8 9 10 11 12 13

The proposed method

GQL + IDF

Traditional-Slack-Time Traditional-Waiting-Time Traditional-Distance

SA-Proposed-Slack-Time SA-Proposed-Waiting-Time SA-Proposed-Distance

FW-Proposed-1-1-1 FW-Proposed-2-1-2 FW-Proposed-2-2-1 FW-Proposed-2-1-1 FW-Proposed-1-2-1 FW-Proposed-1-1-2 FW-Proposed-1-2-2 FW-Proposed-10-1-10 FW-Proposed-10-10-1 FW-Proposed-10-1-1 FW-Proposed-1-10-1 FW-Proposed-1-1-10 FW-Proposed-1-10-10

2000 min and the simulation time of each replication is 10,000 min. The number of replications and the warm-up time are determined using the method described in Law and Kelton [36]. The simulation software package is Arena [37]. Values collected from the experiments include the system’s throughput, the Mean Flow Time of Parts (MFTP) and the Mean Tardiness of Parts (MTP). Table 3 summarizes the methods tested in the simulations. As shown in Table 3, they are divided into five categories. The following describes the methods in each category. • Category A: This category has only one method which is the method proposed by us. • Category B: There is also only method, i.e., GQL + IDF, in Category B. This method serves as the benchmark of this study, since it is the best combination of pickup-dispatching rule and the loadselection rule found by Ho and Liu [14]. Although two attributes (i.e., queue length and identical destination) are considered by the GQL + IDF method, they are considered separately in the pickupdispatching problem and the load-selection problem. In essence, the GQL + IDF method is a single-attribute method as only one attribute is considered in the pickup-dispatching problem and the load-selection problem. The pickup-dispatching rule in this method is the Greatest Queue Length (GQL) rule, while the loadselection rule in this method is the Identical Destination First (IDF) rule. According to Ho and Liu [14], among all the combinations of pickup-dispatching rule and the load-selection rule studied by them, this combination can result in the best throughput performance. With this method, the multiple-load AGV, V, selects the pickup point, P* , with the greatest number of parts waiting in the queue. After the multiple-load AGV, V, has arrived at the selected pickup point, V will first identify those parts whose next destinations are identical to the next destination of any load currently on the multiple-load AGV, V. These parts will have the higher priority to be picked up by V first. On the other hand, if no parts can be identified, the multiple-load AGV, V, will pick up the part with the longest waiting time in the queue of P* . • Category C: The methods in Category C are traditional methods that are similar to the ones seen in Ho and Liu [10,14]. Each Category C method considers only one (and the same) attribute in the pickup-dispatching problem and the load-selection problem. Category C methods solve the pickup-dispatching problem and the load-selection problem separately. Category C has three methods, i.e., Traditional-Slack-Time, Traditional-Waiting-Time and Traditional-Distance. We name each method based on the attribute it uses for selecting the pickup point in the pickupdispatching problem and the parts in the load-selection problem. The following describes each method in Category C. o Traditional-Slack-Time: The multiple-load AGV, V, selects the pickup point containing the part with the smallest slack time. After it has arrived at the selected pickup point, it picks up parts

from the pickup point based on a slack-time-based rule, i.e., the smaller a part’s slack time, the higher its priority to be picked up by V. o Traditional-Waiting-Time: The multiple-load AGV, V, selects the pickup point containing the part with the greatest waiting time in its current queue. After it has arrived at the selected pickup point, it picks up parts from the pickup point based on a waiting-time-based rule, i.e., the greater a part’s waiting time, the higher its priority to be picked up by V. o Traditional-Distance: The multiple-load AGV, V, selects the nearest pickup point. After it has arrived at the selected pickup point, it picks up parts from the pickup point based on a distance-based rule, i.e., the closer a part’s next destination is to V, the higher its priority to be picked up by V. • Category D: Category D methods are similar to the proposed method in the solution procedure (i.e., they also solve the pickup-dispatching problem and the load-selection problem simultaneously), except only one attribute is considered by them. In other words, the weight of the attribute considered by them is equal to one, while the weights of the other two attributes are equal to zero. Category D also contains three methods, i.e., SA-Proposed-Slack-Time, SA-Proposed-Waiting-Time, and SAProposed-Distance. The ‘SA’ in the names of these methods stands for ‘Single-Attribute’. The attribute adopted by a method can also be seen in its name. For example, the distance attribute is the only attribute considered in the SA-Proposed-Distance method. • Category E: The methods in Category E are also similar to the proposed method in the solution procedure (i.e., they also solve the pickup-dispatching problem and the load-selection problem simultaneously), except their weights for the three attributes (i.e., slack time, waiting time, and distance) are fixed. Category E has thirteen methods which have different weight values for the three attributes. These methods include FW-Proposed-1-1-1, FW-Proposed-2-1-2, FW-Proposed-2-2-1, FW-Proposed-2-1-1, FW-Proposed-1-2-1, FW-Proposed-1-1-2, FW-Proposed-1-2-2, FW-Proposed-10-1-10, FW-Proposed-10-10-1, FW-Proposed10-1-1, FW-Proposed-1-10-1, FW-Proposed-1-1-10, and FWProposed-1-10-10. Please note the ‘FW’ in the names of these methods stands for ‘Fixed Weights’. The three numbers in the name of each method are weights for slack time, waiting time, and distance respectively.

5. Analysis of simulation results Tables 4–6 give the ANOVA results of the throughput, MFTP, and MTP performance respectively. The main effects in these tables exhibit a statistical significance of less than 0.05. In the following subsections, we will compare the proposed method with the methods in other categories.

296

Y.-C. Ho et al. / Journal of Manufacturing Systems 31 (2012) 288–300

Table 4 The ANOVA on the throughput performance. Source

Sum of squares

df

Mean square

F

Sig.

Main effect Method Error Total Corrected total

23756985.8 78507.75 1,276,280,081 23835493.55

20 399 420 419

1187849.29 196.761

6037.007

0.000***

***

Method

Subset 1

Traditional-Distance The proposed method GQL + IDF Traditional-Slack-Time Traditional-Waiting-Time

Significance at the 5 percent level or below.

Table 5 The ANOVA on the MFTP performance.

2

3

4

379.6685 382.2595 480.6055 594.8785 692.635

Note: ˛ = 0.05.

Source

Sum of squares

df

Mean square

F

Sig.

Main effect Method Error Total Corrected total

2674714.051 6478.821 75771254.17 2681192.872

20 399 420 419

133735.703 16.238

8236.151

0.000***

***

Table 8 The Tukey test result on the MFTP performance of the proposed method, Category B method and Category C methods.

Table 9 The Tukey test result on the MTP performance of the proposed method, Category B method and Category C methods. Method

Subset 1

2

3

4

5

The proposed method 0.1505 20.4215 Traditional-Distance 149.4436 GQL + IDF 207.0277 Traditional-Slack-Time Traditional-Waiting-Time 296.0153

Significance at the 5 percent level or below.

Table 6 The ANOVA on the MTP performance. Source

Sum of squares

df

Mean square

F

Sig.

Note: ˛ = 0.05.

Main effect Method Error Total Corrected total

2569601.823 5309.827 3077689.2 2574911.65

20 399 420 419

128480.091 13.308

9654.468

0.000***

the difference between them is not significant (at an ˛ of 0.05). The GQL + IDF method, the Traditional-Slack-Time method, and the Traditional-Waiting-Time method are all significantly worse (at an ˛ of 0.05) than the proposed method in the MFTP performance. Furthermore, by comparing Table 7 with Table 8, one can see if a method does well in the throughput performance, it also does well in the MFTP performance. This observation agrees with the general principle that a shorter flow time leads to a greater throughput. Table 9 shows the Tukey test results on the MTP performance of the proposed method and the methods in Category B and Category C. According to Table 9, the proposed method has the best MTP performance. Its MTP performance is close to zero, which is very good. As shown in Table 9, the proposed method is significantly better (at an ˛ of 0.05) than every method in Category B and Category C in the MTP performance. From Tables 7–9, one can see although the Traditional-Distance method performs very well in throughput and MFTP, its MTP performance is much worse than that of the proposed method. These results prove the proposed method is a better method for us to adopt than Category B and Category C methods if we want good performance in throughput, MFTP, and MTP.

***

Significance at the 5 percent level or below.

5.1. The proposed method vs. Category B method & Category C methods The purpose of this comparison is to see whether the proposed method (which is a multiple-attribute method that solves the pickup-dispatching problem and the load-selection problem simultaneously) can outperform Category B and Category C methods (which are single-attribute methods and solve the pickupdispatching problem and the load-selection problem separately) in the throughput, MFTP and MTP performance. Table 7 shows the Tukey test results on the throughput performance of the proposed method and the methods in Category B and Category C. From Table 7, one can see that the proposed method is slightly worse than the Traditional-Distance method in the throughput performance, but the difference between them is not significant (at an ˛ of 0.05). Furthermore, the proposed method and the TraditionalDistance method are both significantly better (at an ˛ of 0.05) than the GQL + IDF method, the Traditional-Slack-Time method, and the Traditional-Waiting-Time method in the throughput performance. Table 8 shows the Tukey test results on the MFTP performance of the proposed method and the methods in Category B and Category C. Table 8 shows the proposed method is slightly worse than the Traditional-Distance method in the MFTP performance, but Table 7 The Tukey test result on the throughput performance of the proposed method, Category B method and Category C methods. Method

Subset 1

Traditional-Waiting-Time Traditional-Slack-Time GQL + IDF The proposed method Traditional-Distance Note: ˛ = 0.05.

2

3

4

5.2. The proposed method vs. Category D methods By comparing the proposed method with Category D methods, one will be able to see whether the proposed method (which is a multiple-attribute method) can outperform Category D methods (which are single-attribute methods) in the throughput, MFTP, and MTP performance. Table 10 shows the Tukey test results on the throughput performance of the proposed method and the methods in Category D. As one can see in Table 10, although the Table 10 The Tukey test result on the throughput performance of the proposed method and Category D methods. Method

Subset 1

998.4 1167.3 1441.3 1840.7 1851.5

SA-Proposed-Slack-Time SA-Proposed-Waiting-Time The proposed method SA-Proposed-Distance Note: ˛ = 0.05.

2

3

1515.3 1831 1840.7 1847.15

Y.-C. Ho et al. / Journal of Manufacturing Systems 31 (2012) 288–300 Table 11 The Tukey test result on the MFTP performance of the proposed method and Category D methods. Method

Subset 1

SA-Proposed-Distance The proposed method SA-Proposed-Waiting-Time SA-Proposed-Slack-Time

Table 13 The Tukey test result on the throughput performance of Category D methods and Category C methods. Method

2

380.641 382.2595

297

Subset

3

382.2595 384.103 462.747

Note: ˛ = 0.05.

1 Traditional-Waiting-Time Traditional-Slack-Time SA-Proposed-Slack-Time SA-Proposed-Waiting-Time SA-Proposed-Distance Traditional-Distance

2

3

4

5

998.4 1167.3 1515.3 1831 1847.15 1851.5

Note: ˛ = 0.05.

SA-Proposed-Distance method’s throughput performance is better than that of the proposed method, the difference between them is not significant at an ˛ of 0.05. Furthermore, both the proposed method and the SA-Proposed-Distance method are significantly better (at an ˛ of 0.05) than the SA-Proposed-Waiting-Time method and the SA-Proposed-Slack-Time method. Table 11 shows the Tukey test results on the MFTP performance of the proposed method and the methods in Category D. Table 11 shows that the SAProposed-Distance and the proposed method are in the first subset (at an ˛ of 0.05), while the SA-Proposed-Slack-Time is the last subset. By comparing Table 10 with Table 11, one can see the “a shorter flow time leads to a better throughput” principle also holds here. Table 12 shows the Tukey test results on the MTP performance of the proposed method and the methods in Category D. As shown in Table 12, the proposed method has the best MTP performance and is significantly better (at an ˛ of 0.05) than all Category D methods. These results indicate that considering all three attributes (as in the proposed method) is better than considering just one attribute (as in Category D methods) in obtaining good throughput, MFTP, and MTP performance. 5.3. Category D methods vs. Category C methods Category D methods and Category C methods are all singleattribute methods. Their difference is at the way they solve the pickup-dispatching problem and the load-selection problem. Similar to the proposed method, Category D methods solve the pickup-dispatching problem and the load-selection problem simultaneously, while Category C methods solve them separately. By comparing Category D methods with Category C methods, one will be able to see whether solving the pickup-dispatching problem and the load-selection problem simultaneously can result in better throughput, MFTP and MTP results than solving them separately. Table 13 shows the Tukey test results on the throughput performance of Category D methods and Category C methods. From Table 13, one can see that the SA-Proposed-Slack-Time method and the SA-Proposed-Waiting-Time method are significantly better (at an ˛ of 0.05) than the Traditional-Slack-Time method and the Traditional-Waiting-Time method respectively in the throughput performance. Furthermore, although the SA-Proposed-Distance is slightly worse than the Traditional-Distance method, the difference between them is not significant (at an ˛ of 0.05). Table 12 The Tukey test result on the MTP performance of the proposed method and Category D methods. Method

Note: ˛ = 0.05.

Method

Subset 1

2

2

3

2.9364 3.6131 16.9078

4

5

Note: ˛ = 0.05.

Table 14 gives the Tukey test results on the MFTP performance of Category D methods and Category C methods. By comparing Table 13 with Table 14, one can see that the “a shorter flow time leads to a better throughput” principle is also met here. Table 15 shows the Tukey test results on the MTP performance of Category D methods and Category C methods. As shown in Table 15, every SA-Proposed method is significantly better (at an ˛ of 0.05) than its traditional counterpart with the same attribute in the MTP performance. For example, the SA-Proposed-Slack-Time method is significantly better (at an ˛ of 0.05) than the Traditional-Slack-Time method, while the SA-Proposed-Waiting-Time method and the SAProposed-Distance method are significantly better (at an ˛ of 0.05) than the Traditional-Waiting-Time method and the TraditionalDistance method respectively. These results allow us to conclude that solving the pickup-dispatching problem and the load-selection problem simultaneously can lead to good performance in throughput, MFTP, and MTP. 5.4. The proposed method vs. Category E methods Category E methods are similar to the proposed method except their weights for the three attributes are fixed. The proposed method has a dynamic-weight strategy in which the weights for the three attributes are updated to reflect the current status whenever the proposed method is activated. By comparing the proposed method with Category E methods, one will be able to see whether Table 15 The Tukey test result on the MTP performance of Category D methods and Category C methods. Method

Subset 1

0.1505

3

Traditional-Distance 379.6685 380.641 380.641 SA-Proposed-Distance 384.103 SA-Proposed-Waiting-Time 462.747 SA-Proposed-Slack-Time 594.8785 Traditional-Slack-Time Traditional-Waiting-Time 692.635

Subset 1

The proposed method SA-Proposed-Waiting-Time SA-Proposed-Distance SA-Proposed-Slack-Time

Table 14 The Tukey test result on the MFTP performance of Category D methods and Category C methods.

SA-Proposed-Waiting-Time SA-Proposed-Distance SA-Proposed-Slack-Time Traditional-Distance Traditional-Slack-Time Traditional-Waiting-Time Note: ˛ = 0.05.

2

3

4

2.9364 3.6131 16.9078 20.422 207.0277 296.0153

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Y.-C. Ho et al. / Journal of Manufacturing Systems 31 (2012) 288–300

Table 16 The Tukey test result on the throughput performance of the proposed method and the methods in Category D. Method

Subset 1

FW-Proposed-10-1-1 FW-Proposed-1-10-1 FW-Proposed-10-10-1 FW-Proposed-1-2-1 FW-Proposed-2-2-1 The proposed method FW-Proposed-1-10-10 FW-Proposed-1-2-2 FW-Proposed-1-1-1 FW-Proposed-2-1-1 FW-Proposed-1-1-2 FW-Proposed-2-1-2 FW-Proposed-1-1-10 FW-Proposed-10-1-10

2

3

1664 1833.3 1837.45 1839.5 1840.65 1840.7 1840.75 1841.35 1843.55 1844.75 1844.95 1846.3 1846.6

1837.45 1839.5 1840.65 1840.7 1840.75 1841.35 1843.55 1844.75 1844.95 1846.3 1846.6 1848.05

Note: ˛ = 0.05. Table 17 The Tukey test result on the MFTP performance of the proposed method and the methods in Category D. Method

Subset

6. Summary

1 FW-Proposed-10-1-10 FW-Proposed-1-1-10 FW-Proposed-2-1-2 FW-Proposed-1-1-2 FW-Proposed-2-1-1 FW-Proposed-1-1-1 FW-Proposed-1-2-2 FW-Proposed-1-10-10 FW-Proposed-2-2-1 The proposed method FW-Proposed-1-2-1 FW-Proposed-10-10-1 FW-Proposed-1-10-1 FW-Proposed-10-1-1

throughput performance), since both of them are in the same subset. Table 17 shows the Tukey test results on the MFTP performance of the proposed method and Category E methods. As one can see, although the proposed method does not have the best MFTP performance, its MFTP performance is not significantly different (at an ˛ of 0.05) from that of the FW-Proposed-10-1-10 method (which is the method with the best MFTP performance). Furthermore, by comparing Table 16 with Table 17, one can see the “a shorter flow tine leads to a better throughput” principle also holds here. Table 18 shows the Tukey test results on the MTP performance of the proposed method and Category E methods. From Table 18, one can see that the proposed method has the best MTP performance and is significantly better (at an ˛ of 0.05) than all Category E methods in the MTP performance. One can also see that the MTP performance of the FW-Proposed-10-1-10 method (i.e., the method with the best throughput and the best MFTP performance) is rather poor. From the analysis above, one can conclude that the dynamicweight strategy is indeed a better strategy for the proposed method if one wants to have good throughput, MFTP, and MTP performance.

2

380.513 380.823 380.882 381.0785 381.1545 381.4335 381.8085 382.0235 382.047 382.2595 382.365 382.85

3

380.823 380.882 381.0785 381.1545 381.4335 381.8085 382.0235 382.047 382.2595 382.365 382.85 383.599 422.282

Note: ˛ = 0.05.

the dynamic-weight strategy is better for the proposed method than the fixed-weight strategy. Table 16 shows the Tukey test results on the throughput performance of the proposed method and the methods in Category E. There are three subsets in Table 16. As shown in Table 16, although the proposed method’s throughput performance is not the best, its throughput performance is not significantly different (at an ˛ of 0.05) from that of the FWProposed-10-1-10 method (which is the method with the best

In this paper, we study the pickup-dispatching problem and the load-selection problem. These two problems have been solved separately by traditional methods (e.g., those proposed by Ho and Liu [10,14]) despite the fact that they are mutually affected. Furthermore, traditional methods often use single-attribute decision rules to solve these two problems even though they can be affected by various attributes. Because of these two shortcomings, the results obtained by traditional methods can be undesirable. In this study, we propose a multiple-attribute method that can solve these two problems simultaneously. The proposed method contains four stages: preparation, clustering, evaluation and execution. At the preparation stage, we update the weights for the slack time, waiting time and distance attributes based on the system’s current status. At the clustering stage, we cluster parts that need the service of AGVs into different part groups based on their similarity in these attributes. At the evaluation stage, we evaluate these part groups. The part group with the greatest evaluation value will be served by the AGV. At the execution stage, a procedure is proposed to help the multiple-load AGV pick up parts in the selected part group more efficiently. Computer simulations were conducted to understand the performance of the proposed method. From the simulation results, we have the following findings.

Table 18 The Tukey test result on the MTP performance of the proposed method and the methods in Category D. Method

Subset 1

The proposed method FW-Proposed-10-1-1 FW-Proposed-10-10-1 FW-Proposed-2-1-1 FW-Proposed-10-1-10 FW-Proposed-2-2-1 FW-Proposed-2-1-2 FW-Proposed-1-1-1 FW-Proposed-1-2-1 FW-Proposed-1-10-1 FW-Proposed-1-1-2 FW-Proposed-1-2-2 FW-Proposed-1-10-10 FW-Proposed-1-1-10 Note: ˛ = 0.05.

2

3

4

5

6

7

8

9

0.1505 1.0887 1.3244

1.3244 1.4592 1.9302 1.9733 2.2231 2.4022

2.4022 2.567

2.567 2.7699

2.7699 2.8678 2.8859 3.2058 3.3658

Y.-C. Ho et al. / Journal of Manufacturing Systems 31 (2012) 288–300

• The proposed method is better than the GQL + IDF method, which is the best combination of pickup-dispatching rule and the loadselection rule found by Ho and Liu [14]. • The proposed method is a better method for us than traditional methods (which are single-attribute methods and solve the pickup-dispatching problem and the load-selection problem separately) if we want good performance in throughput, MFTP, and MTP. • Considering all three attributes (as in the proposed method) is better than considering just one attribute (as in the methods of Category D) in obtaining good throughput, MFTP, and MTP performance. • Solving the pickup-dispatching problem and the load-selection problem simultaneously (as in the proposed method) can lead to good performance in throughput, MFTP, and MTP. • The dynamic-weight strategy is a better strategy for the proposed method if one wants to have good throughput, MFTP, and MTP performance. Proposing a multiple-attribute method that can solve the pickup-dispatching and load-selection problems of multiple-load AGVs simultaneously and proving the proposed method can outperform not only single-attribute methods, but also methods that solve pickup dispatching and load selection separately are the main contribution of this study. The knowledge learned from the above findings is also the contribution of this study. It is hoped the proposed method and the knowledge learned from this study can be beneficial to industrial engineers in solving real-life multiple-load AGV control problems that are similar to the one studied here. Finally, we would like to suggest two future research possibilities. First, we only consider three attributes in this study. It is believed that there may be other attributes that are also important to the pickup-dispatching and load-selection problems. Investigating other attributes and including those that are also important to these two problems into the proposed method is the first future research possibility suggested by us. Second, a simple clustering technique is proposed for the second stage of the proposed method. Although the proposed clustering technique is suitable for us, there may be other clustering techniques that can produce better clustering results. Investigating other clustering techniques and finding a better one for the proposed method is the second future research possibility suggested by us.

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[36] Law AM, Kelton WD. Simulation modeling and analysis. Boston: McGraw-Hill; 2000. [37] Rockwell Automation. Arena user’s guide. Milwaukee: Rockwell Software; 2004. Ying-Chin Ho is a professor in the Institute of Industrial Management at National Central University (NCU) in Taiwan. He received his BS degree in industrial management from National Cheng-Kung University (Tainan, Taiwan) in 1987, and MS and PhD degrees in industrial engineering from Purdue University in 1991 and 1995, respectively. He joined the faculty of NCU in 1995. His research and teaching interests include facilities layout design, material handling systems, group technology, and the design, analysis, operation, and control of production and logistics systems.

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Hao-Cheng Liu is a PhD student in the Institute of Industrial Management at National Central University (NCU) in Taiwan. He received a MS degree in industrial management from National Central University in 2004 and a BS degree in industrial engineering and enterprise information from Tunghai University in 2002. His primary research interests include facilities layout design, material handling systems and the design, analysis, operation, and control of production and logistics systems. Dr. Yuehwern Yih is a professor of the School of Industrial Engineering at Purdue University and the Director of Smart Systems and Operations Laboratory. She is the

Faculty Scholar of the Regenstrief Center for Healthcare Engineering. She received her Ph.D. in Industrial Engineering from the University of Wisconsin-Madison in 1988. Her expertise resides in system and process design, monitor, and control to improve its quality and efficiency. Her research work has been focused on dynamic process control and decision making for operations in complex systems (or systems in systems), such as healthcare delivery systems, manufacturing systems, supply chains, and advanced life support system for mission to Mars.