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Mathematical modeling of the AGVS capacity requirements planning problem
171
Engrneering Costs and Production Economics, 2 1 ( 199 1) 1I l- 17 5 Elsevier
Mathematical modeling of the AGVS capacity requirements planning problem R.G. Kasilingam Faculty of Engineering, University of Regina, Regina, Sask., Canada S4S 0A2 (Received March 1, 1990; accepted in revised form January 7, 199 1)
Abstract Determing the number and type of AGVs and the assignment of AGVs to transport parts between workstations is an important problem encountered in the design of an Automated Guided Vehicle System (AGVS). In this paper, an optimization model is proposed to solve this problem. The model minimizes the overall system cost defined as the sum of the annualized cost of operating the AGVs and the cost of transporting parts between workstations. The model is illustrated using a numerical example.
Introduction Material handling is an important, yet sometimes overlooked aspect of automation. The cost of material handling is a significant portion of the total cost of production. Estimates of handling cost run as high as two-thirds of the total manufacturing cost [ 11. This fraction to a great extent depends upon the degree of automation in the material handling function. An Automated Guided Vehicle System (AGVS) is a materials handling system that uses independently operated, self-propelled vehicles that are guided along defined pathways in the floor. With improved hardware and software, the AGVS has come a long way in terms of its acceptance as an effective material handling system in any manufacturing environment. AGVS can provide an economic solution to a material handling problem provided these systems are utilized with proper operating policies [ 2 1. The design of a material handling system using AGVs must address some of the critical issues such as guide path design, vehicle dispatching strategies and capacity requirements planning [ 3 1. The problem of guide path design has been addressed in detail in several research papers [ 4-7 1. The issue of vehicle dispatching rules has
0167-l 88X/9 l/$03.50 0 1991-Elsevier
Science Publishers B.V.
been dealt in [ 3, 8, 9 ]. Maxwell and Muckstadt [lo], Tanchoco et al. [ 111, Egbelu [ 121 and Mahadevan and Narendran [ 3 ] have studied the capacity requirements planning problem. Capacity requirements planning is an important problem encountered in the design of an AGVS. This is concerned with determining the number of AGVs required to meet given material handling requirements for a known manufacturing system layout. This decision is influenced by a large number of factors such as the flow of parts between workstations, the route by which parts are to be moved, the size of the unit load, and the scheduling of the moves between workstations. Maxwell and Muckstadt [ 10 ] used a transportation formulation to assign empty vehicles to various demand centers to estimate vehicle requirements. Mahadevan and Narendran [3] proposed an analytical model for vehicle requirements and performed a simulation analysis of the system under various dispatching rules. Tanchoco et al. [ 111 compared the effectiveness of CAN-Q to a simulation-based method ( AGVSim ) in determining the required number of vehicles for a specific application. They concluded that the results obtained through CAN-Q application provided a good starting search point
172 for a simulation-based technique. Egbelu [ 121 compared the performance of four analytical approaches to vehicle estimation with the results of detailed simulation under various vehicle dispatching strategies. He found that the analytical techniques underestimated the requirement under most of the dispatching strategies. Leung et al. [ 13 ] provided a means for calculating vehicle requirements by determining the total time of empty vehicle travel through solving an AGV assignment problem. In this paper, the combined problem of determining the number of AGVs required and the assignment of AGVs between pairs of workstations is addressed through a cost model. The model is quite general in nature. It may very well be used in situations where several different part types have to be transported between workstations and the transport requirements may be met by more than one vehicle type. The paper is organized as follows. The development of the integer programming model is presented in the next Section, followed by a numerical example. Finally conclusions are presented. Model development
Notation The following notation is used throughout. Parameters annualized cost of buying and maintaining vehicle type k C;,k cost of making an empty trip from workstation i to workstation j for vehicle type k f;i part flow rate between workstation i and workstation j FiJk cost of a loaded trip between workstation i and workstation j for vehicle type k Gr+ capacity of vehicle type k (in time units) loading time at workstation i L, number of parts that can be transported in nk one trip using vehicle type k Nk( i)net flow of vehicle type k at workstation i time to make an empty trip from workstari,k tion i to workstation j for vehicle type k ck
ti]k
Ui
time for a loaded trip from workstation workstationj for vehicle type k unloading time at workstation i
i to
Decision variables required number yak between w,jk number between
xk
number of vehicles of type k of loaded trips made by vehicle k workstation i and workstationj of empty trips made by vehicle k workstation i and workstationj
The development of the integer programming model to address the AGVS capacity requirements planning problem is explained in this section. The model is formulated under the following assumptions: ( 1) The layout of the manufacturing system is fixed and known, i.e., the location of the workstations and the AGVS guide pathways are known. (2) More than one vehicle type may be assigned to transport parts between any two workstations. (3) Time and cost of an empty trip are lower than that of loaded trip for any vehicle. (4) Effects of acceleration and deceleration on the velocity of the vehicle are negligible. ( 5) Information regarding part flow rates, loading and unloading times at workstations, time and cost of travel, etc. are available. The distance between any two workstations depends upon the manufacturing system layout and the AGVS guide pathways. The time to make a trip between any two workstations is a function of the distance between the workstations and vehicle velocity. The number of parts that can be transported by an AGV in one trip is computed based on the weight and volume requirements of the part. The capacity of an AGV denotes the availability of the vehicle after allowing for vehicle downtime and traffic congestion. Capacity planning model (CPM) Given the notation and assumptions as above, the AGVS capacity requirements planning problem can be formulated as the following integer programming model.
173
Minimize Z= C X, C,
(1)
k
+
c k
c
c j
i
( Y,kF,k
+
wi,kC*jk)
The objective function is the sum of two distinct, linear cost functions. The first cost term is the sum of the total annualized, depreciated costs of all AGVs required. The second term is the sum of the total material handling costs between all pairs of workstations, which includes the cost of loaded as well as empty trips of the vehicles. The material handling cost between any two workstations is a function of the vehicle type, distance travelled and whether the vehicle is loaded or empty. The material handling cost per unit distance is the variable cost of operating the vehicle [ 14,151. It typically includes the cost of power, lubricants, maintenance labor and parts, etc. [ 161. Some of these cost components are affected by the load carried by the vehicle. The objective function in ( 1) is subject to the following constraints: c
y,k
nk
a.hj
c
rljk
(2)
v (ild
k
+c
wi,k
c kjkihr,(i)sO
vk
(3)
V(i,k)
(4)
V (i,k)
(5)
j$i
C Wi,k+Nk(i) a0
Constraints (4) and ( 5 ) represent flow balance of the vehicles at any given workstation for any vehicle type [ 13 1. Nk( i), the net flow of vehicles for any vehicle type at workstation i is defined as the difference between the total number of trips made out of workstation i and the total number of trips made into workstation i by vehicle type k. This is represented in the form of eqn. (6)) in which Nk( i) > 0 implies that vehicle k will be making empty trips into workstation i. On the other hand, empty trips will be made by vehicle k from workstation i, if Nk( i) ~0. Due to the nature of the objective function, zJWJIk will be zero when Nk( i) -c 0 and 1, w,/k will be zero when Nk( i) > 0. Constraint (7 ) ensures integrality of the decision variables. A numerical example A numerical example of the CPM model is presented in this section. This is a slightly modified version of the example given in [ 131. A manufacturing system with five machines and two types of AGV is considered. The AGVS guide path layout is shown in Fig. 1. An estimate on the number of parts to be transported between workstations in a year is given in Table 1. The loading and unloading times are shown in Table 2. Information regarding the time of travel between workstations is given in Table 3. Material handling cost per unit time is assumed to be $7 and
where (6)
xk, YjJk, WiJk> 0 and integer V (i&k)
(7)
Constraint (2 ) ensures that trips are assigned to the various AGVs in order to meet the part flow requirements between all pairs of workstations. Constraint (3) represents the capacity restrictions of the vehicles. The first term in constraint (3 ) represents the time spent on loading/ unloading parts at workstations and transporting parts between workstations. The second term represents the time spent in making empty trips.
Fig. 1. AGVS guide path layout.
174 TABLE
1
TABLE
Part flow rate between
workstations
Optimal
4 trip assignment
To
1
for Vehicle
TO
From
1
2
3
4
5
From
1
2
3
4
5
1 2 3 4 5
_ 60 400 80 200
200 100 120 140
240 140 _ 180 260
160 240 200
100 80 180 260 _
1 2 3 4
_ 4 12 2
15 I 2
_ 20
4(l) 2
-
_ 4 2 _
5
2
2
3
-
-
TABLE
2
Loading
and unloading
200
TABLE times
(s.)
Optimal
Workstation
l_Jnload Load
TABLE Travel
trip assignment
1
2
3
4
5
From
10 20
20 30
10 20
20 30
10 20
1 2
_
3 4 5
11 3 9
time between
for Vehicle
2
To
3 workstations
1
1
2
3
(1) _
12
5 6
9 11
4
5
8 11 9(3) _ 10
2 4 8(l) 13(8)
(s. )
To Vehicle
5
Vehicle 2
From
1
2
3
4
5
1
2
3
4
5
1 2 3 4 5
300 240 180 120
60 180 120 60
120 60 180 120
180 120 60 180
240 180 120 60 -
225 180 135 90
45 135 90 45
90 4.5 135 90
135 90 45 135
180 135 90 45 -
$14, respectively for the two vehicle types. This is based on the material handling cost per unit distance and the velocity of the vehicle. In this example, the cost and time of travel are assumed to be the same for loaded as well as empty trips. The number of parts that can be transported in a single trip is assumed to be 15 and 20, respectively for the two AGVs and the annualized costs as $1000 and $1500, respectively. The availability of any vehicle is assumed to be 4.8 hours (i.e. 60% utilization of an g-hour shift). The example problem was formulated as a CPM model and solved using LINDO software on an IBM 438 1 computer. The optimal solution
requires 1 vehicle of each type. The optimal trip assignments for vehicle 1 and vehicle 2 are given in Table 4 and Table 5, respectively. In Tables 4 and 5, the values in parentheses denote the number of empty trips. Conclusions An integer programming model has been proposed to address the AGVS capacity requirements planning problem. The model minimizes the overall system cost defined as the sum of the annualized cost of operating the AGVs and the cost of transporting parts between workstations considering the required number of part movements between workstations and vehicle capacities. The model is very general in nature. For real life problems, commercially available integer programming software packages may be used to solve the model presented in this paper. The solution of this model will specify the required number of AGVs of each type and the assignment of AGVs to transport parts between workstations. However, it is to be noted that the model
175 will underestimate vehicle requirements since it is based on netflow of vehicles [ 121. The model presented in this paper may be generalized to consider movement of several different part types in the system by introducing an additional superscript p, an index for part type in some of the parameters and variables. For instance, YE, will indicate the number of loaded trips made by vehicle type k to transport part type p between workstations i and j andf P,will indicate the flow rate of part type p between workstation i and workstationj.
5
6
7
8
9
Acknowledgement 10
The author appreciates the useful comments of an anonymous referee. Major funding for this research work was provided by the Natural Sciences and Engineering Research Council of Canada.
11
12
References Groover, M.P., 1988. Automation, Production Systems, and Computer Integrated Manufacturing, McGraw-Hill Book Company, New York. Quinlan, J.C., 1980. The great AGVS race. Mater. Handling Eng., 35 (6): 56-64. Mahadevan, B. and Narendran, T.T., 1990. Design of an automated guided vehicle-based material handling system for a flexible manufacturing system. Int. J. Prod. Res.. 28(9): 1611-1622. Sharp, G.P. and Liu, F.F., 1990. An analytical method for configuring fixed-path, closed loop material handlingsystems. Int. J. Prod. Res., 28(4): 757-783.
13
14
15
16
Goetz Jr., G.W. and Egbelu, P.J., 1990. Guide path design and location of load pick-up/drop-off points for an automated guided vehicle system. Int. J. Prod. Res., 28(5): 927-941. Egbelu, P.J. and Tanchoco, J.M.A., 1986. Potentials for bidirectional guidepath for automatic guided vehicle based systems. Int. J. Prod. Res., 24(5): 1075-1097. Gaskins, R.J. and Tanchoco, J.M.A., 1987. Flowpath design for automated guided vehicle systems. Int. J. Prod. Res., 25( 5): 667-676. Ozden, M., 1988. A similation study of muhiple-loadcarrying automated guided vehicles in a flexible manufacturing system. Int. J. Prod. Res., 26( 8): 1353-I 366. Egbelu, P.J. and Tanchoco, J.M.A.. 1984. Characterization of automated guided vehicle dispatching rules in facilities with existing layouts. Int. J. Prod. Res., 22( 5): 359-374. Maxwell, W.L. and Muckstadt, J.A., 1982. Design ofautomated guided vehicle systems. IIE Trans., 14(2): 114124. Tanchoco, J.M.A., Egbelu, P.J. and Taghaboni, F., 1987. Determination of total number of vehicles in an AGVbased material transport system. Material Flow, 4( 3,4): 33-51. Egbelu, P.J., 1987. The use of non-simulation approaches in estimating vehicle requirements in an automated guided vehicle based transport system. Material Flow, 4(3,4): 17-32. Leung, L.C., Khator, SK. and Kimbler, D.L., 1987. Assignment ofAGVS with different vehicle types, Material Flow, 4: 65-72. Malmborg, C.J. and Deutsch, S.J., 1988. A Stock location model for dual address order picking systems. IIE Trans., 20( 1): 44-52. Hodgson, T.J. and Lowe, T.J., 1982. Production lotsizing with material handling cost considerations, IIE Trans., 14(I): 44-61. Apple, J.M.. 1972. Material Handling Systems Design. The Ronald Press Company, New York.
Engrneering Costs and Production Economics, 2 1 ( 199 1) 1I l- 17 5 Elsevier
Mathematical modeling of the AGVS capacity requirements planning problem R.G. Kasilingam Faculty of Engineering, University of Regina, Regina, Sask., Canada S4S 0A2 (Received March 1, 1990; accepted in revised form January 7, 199 1)
Abstract Determing the number and type of AGVs and the assignment of AGVs to transport parts between workstations is an important problem encountered in the design of an Automated Guided Vehicle System (AGVS). In this paper, an optimization model is proposed to solve this problem. The model minimizes the overall system cost defined as the sum of the annualized cost of operating the AGVs and the cost of transporting parts between workstations. The model is illustrated using a numerical example.
Introduction Material handling is an important, yet sometimes overlooked aspect of automation. The cost of material handling is a significant portion of the total cost of production. Estimates of handling cost run as high as two-thirds of the total manufacturing cost [ 11. This fraction to a great extent depends upon the degree of automation in the material handling function. An Automated Guided Vehicle System (AGVS) is a materials handling system that uses independently operated, self-propelled vehicles that are guided along defined pathways in the floor. With improved hardware and software, the AGVS has come a long way in terms of its acceptance as an effective material handling system in any manufacturing environment. AGVS can provide an economic solution to a material handling problem provided these systems are utilized with proper operating policies [ 2 1. The design of a material handling system using AGVs must address some of the critical issues such as guide path design, vehicle dispatching strategies and capacity requirements planning [ 3 1. The problem of guide path design has been addressed in detail in several research papers [ 4-7 1. The issue of vehicle dispatching rules has
0167-l 88X/9 l/$03.50 0 1991-Elsevier
Science Publishers B.V.
been dealt in [ 3, 8, 9 ]. Maxwell and Muckstadt [lo], Tanchoco et al. [ 111, Egbelu [ 121 and Mahadevan and Narendran [ 3 ] have studied the capacity requirements planning problem. Capacity requirements planning is an important problem encountered in the design of an AGVS. This is concerned with determining the number of AGVs required to meet given material handling requirements for a known manufacturing system layout. This decision is influenced by a large number of factors such as the flow of parts between workstations, the route by which parts are to be moved, the size of the unit load, and the scheduling of the moves between workstations. Maxwell and Muckstadt [ 10 ] used a transportation formulation to assign empty vehicles to various demand centers to estimate vehicle requirements. Mahadevan and Narendran [3] proposed an analytical model for vehicle requirements and performed a simulation analysis of the system under various dispatching rules. Tanchoco et al. [ 111 compared the effectiveness of CAN-Q to a simulation-based method ( AGVSim ) in determining the required number of vehicles for a specific application. They concluded that the results obtained through CAN-Q application provided a good starting search point
172 for a simulation-based technique. Egbelu [ 121 compared the performance of four analytical approaches to vehicle estimation with the results of detailed simulation under various vehicle dispatching strategies. He found that the analytical techniques underestimated the requirement under most of the dispatching strategies. Leung et al. [ 13 ] provided a means for calculating vehicle requirements by determining the total time of empty vehicle travel through solving an AGV assignment problem. In this paper, the combined problem of determining the number of AGVs required and the assignment of AGVs between pairs of workstations is addressed through a cost model. The model is quite general in nature. It may very well be used in situations where several different part types have to be transported between workstations and the transport requirements may be met by more than one vehicle type. The paper is organized as follows. The development of the integer programming model is presented in the next Section, followed by a numerical example. Finally conclusions are presented. Model development
Notation The following notation is used throughout. Parameters annualized cost of buying and maintaining vehicle type k C;,k cost of making an empty trip from workstation i to workstation j for vehicle type k f;i part flow rate between workstation i and workstation j FiJk cost of a loaded trip between workstation i and workstation j for vehicle type k Gr+ capacity of vehicle type k (in time units) loading time at workstation i L, number of parts that can be transported in nk one trip using vehicle type k Nk( i)net flow of vehicle type k at workstation i time to make an empty trip from workstari,k tion i to workstation j for vehicle type k ck
ti]k
Ui
time for a loaded trip from workstation workstationj for vehicle type k unloading time at workstation i
i to
Decision variables required number yak between w,jk number between
xk
number of vehicles of type k of loaded trips made by vehicle k workstation i and workstationj of empty trips made by vehicle k workstation i and workstationj
The development of the integer programming model to address the AGVS capacity requirements planning problem is explained in this section. The model is formulated under the following assumptions: ( 1) The layout of the manufacturing system is fixed and known, i.e., the location of the workstations and the AGVS guide pathways are known. (2) More than one vehicle type may be assigned to transport parts between any two workstations. (3) Time and cost of an empty trip are lower than that of loaded trip for any vehicle. (4) Effects of acceleration and deceleration on the velocity of the vehicle are negligible. ( 5) Information regarding part flow rates, loading and unloading times at workstations, time and cost of travel, etc. are available. The distance between any two workstations depends upon the manufacturing system layout and the AGVS guide pathways. The time to make a trip between any two workstations is a function of the distance between the workstations and vehicle velocity. The number of parts that can be transported by an AGV in one trip is computed based on the weight and volume requirements of the part. The capacity of an AGV denotes the availability of the vehicle after allowing for vehicle downtime and traffic congestion. Capacity planning model (CPM) Given the notation and assumptions as above, the AGVS capacity requirements planning problem can be formulated as the following integer programming model.
173
Minimize Z= C X, C,
(1)
k
+
c k
c
c j
i
( Y,kF,k
+
wi,kC*jk)
The objective function is the sum of two distinct, linear cost functions. The first cost term is the sum of the total annualized, depreciated costs of all AGVs required. The second term is the sum of the total material handling costs between all pairs of workstations, which includes the cost of loaded as well as empty trips of the vehicles. The material handling cost between any two workstations is a function of the vehicle type, distance travelled and whether the vehicle is loaded or empty. The material handling cost per unit distance is the variable cost of operating the vehicle [ 14,151. It typically includes the cost of power, lubricants, maintenance labor and parts, etc. [ 161. Some of these cost components are affected by the load carried by the vehicle. The objective function in ( 1) is subject to the following constraints: c
y,k
nk
a.hj
c
rljk
(2)
v (ild
k
+c
wi,k
c kjkihr,(i)sO
vk
(3)
V(i,k)
(4)
V (i,k)
(5)
j$i
C Wi,k+Nk(i) a0
Constraints (4) and ( 5 ) represent flow balance of the vehicles at any given workstation for any vehicle type [ 13 1. Nk( i), the net flow of vehicles for any vehicle type at workstation i is defined as the difference between the total number of trips made out of workstation i and the total number of trips made into workstation i by vehicle type k. This is represented in the form of eqn. (6)) in which Nk( i) > 0 implies that vehicle k will be making empty trips into workstation i. On the other hand, empty trips will be made by vehicle k from workstation i, if Nk( i) ~0. Due to the nature of the objective function, zJWJIk will be zero when Nk( i) -c 0 and 1, w,/k will be zero when Nk( i) > 0. Constraint (7 ) ensures integrality of the decision variables. A numerical example A numerical example of the CPM model is presented in this section. This is a slightly modified version of the example given in [ 131. A manufacturing system with five machines and two types of AGV is considered. The AGVS guide path layout is shown in Fig. 1. An estimate on the number of parts to be transported between workstations in a year is given in Table 1. The loading and unloading times are shown in Table 2. Information regarding the time of travel between workstations is given in Table 3. Material handling cost per unit time is assumed to be $7 and
where (6)
xk, YjJk, WiJk> 0 and integer V (i&k)
(7)
Constraint (2 ) ensures that trips are assigned to the various AGVs in order to meet the part flow requirements between all pairs of workstations. Constraint (3) represents the capacity restrictions of the vehicles. The first term in constraint (3 ) represents the time spent on loading/ unloading parts at workstations and transporting parts between workstations. The second term represents the time spent in making empty trips.
Fig. 1. AGVS guide path layout.
174 TABLE
1
TABLE
Part flow rate between
workstations
Optimal
4 trip assignment
To
1
for Vehicle
TO
From
1
2
3
4
5
From
1
2
3
4
5
1 2 3 4 5
_ 60 400 80 200
200 100 120 140
240 140 _ 180 260
160 240 200
100 80 180 260 _
1 2 3 4
_ 4 12 2
15 I 2
_ 20
4(l) 2
-
_ 4 2 _
5
2
2
3
-
-
TABLE
2
Loading
and unloading
200
TABLE times
(s.)
Optimal
Workstation
l_Jnload Load
TABLE Travel
trip assignment
1
2
3
4
5
From
10 20
20 30
10 20
20 30
10 20
1 2
_
3 4 5
11 3 9
time between
for Vehicle
2
To
3 workstations
1
1
2
3
(1) _
12
5 6
9 11
4
5
8 11 9(3) _ 10
2 4 8(l) 13(8)
(s. )
To Vehicle
5
Vehicle 2
From
1
2
3
4
5
1
2
3
4
5
1 2 3 4 5
300 240 180 120
60 180 120 60
120 60 180 120
180 120 60 180
240 180 120 60 -
225 180 135 90
45 135 90 45
90 4.5 135 90
135 90 45 135
180 135 90 45 -
$14, respectively for the two vehicle types. This is based on the material handling cost per unit distance and the velocity of the vehicle. In this example, the cost and time of travel are assumed to be the same for loaded as well as empty trips. The number of parts that can be transported in a single trip is assumed to be 15 and 20, respectively for the two AGVs and the annualized costs as $1000 and $1500, respectively. The availability of any vehicle is assumed to be 4.8 hours (i.e. 60% utilization of an g-hour shift). The example problem was formulated as a CPM model and solved using LINDO software on an IBM 438 1 computer. The optimal solution
requires 1 vehicle of each type. The optimal trip assignments for vehicle 1 and vehicle 2 are given in Table 4 and Table 5, respectively. In Tables 4 and 5, the values in parentheses denote the number of empty trips. Conclusions An integer programming model has been proposed to address the AGVS capacity requirements planning problem. The model minimizes the overall system cost defined as the sum of the annualized cost of operating the AGVs and the cost of transporting parts between workstations considering the required number of part movements between workstations and vehicle capacities. The model is very general in nature. For real life problems, commercially available integer programming software packages may be used to solve the model presented in this paper. The solution of this model will specify the required number of AGVs of each type and the assignment of AGVs to transport parts between workstations. However, it is to be noted that the model
175 will underestimate vehicle requirements since it is based on netflow of vehicles [ 121. The model presented in this paper may be generalized to consider movement of several different part types in the system by introducing an additional superscript p, an index for part type in some of the parameters and variables. For instance, YE, will indicate the number of loaded trips made by vehicle type k to transport part type p between workstations i and j andf P,will indicate the flow rate of part type p between workstation i and workstationj.
5
6
7
8
9
Acknowledgement 10
The author appreciates the useful comments of an anonymous referee. Major funding for this research work was provided by the Natural Sciences and Engineering Research Council of Canada.
11
12
References Groover, M.P., 1988. Automation, Production Systems, and Computer Integrated Manufacturing, McGraw-Hill Book Company, New York. Quinlan, J.C., 1980. The great AGVS race. Mater. Handling Eng., 35 (6): 56-64. Mahadevan, B. and Narendran, T.T., 1990. Design of an automated guided vehicle-based material handling system for a flexible manufacturing system. Int. J. Prod. Res.. 28(9): 1611-1622. Sharp, G.P. and Liu, F.F., 1990. An analytical method for configuring fixed-path, closed loop material handlingsystems. Int. J. Prod. Res., 28(4): 757-783.
13
14
15
16
Goetz Jr., G.W. and Egbelu, P.J., 1990. Guide path design and location of load pick-up/drop-off points for an automated guided vehicle system. Int. J. Prod. Res., 28(5): 927-941. Egbelu, P.J. and Tanchoco, J.M.A., 1986. Potentials for bidirectional guidepath for automatic guided vehicle based systems. Int. J. Prod. Res., 24(5): 1075-1097. Gaskins, R.J. and Tanchoco, J.M.A., 1987. Flowpath design for automated guided vehicle systems. Int. J. Prod. Res., 25( 5): 667-676. Ozden, M., 1988. A similation study of muhiple-loadcarrying automated guided vehicles in a flexible manufacturing system. Int. J. Prod. Res., 26( 8): 1353-I 366. Egbelu, P.J. and Tanchoco, J.M.A.. 1984. Characterization of automated guided vehicle dispatching rules in facilities with existing layouts. Int. J. Prod. Res., 22( 5): 359-374. Maxwell, W.L. and Muckstadt, J.A., 1982. Design ofautomated guided vehicle systems. IIE Trans., 14(2): 114124. Tanchoco, J.M.A., Egbelu, P.J. and Taghaboni, F., 1987. Determination of total number of vehicles in an AGVbased material transport system. Material Flow, 4( 3,4): 33-51. Egbelu, P.J., 1987. The use of non-simulation approaches in estimating vehicle requirements in an automated guided vehicle based transport system. Material Flow, 4(3,4): 17-32. Leung, L.C., Khator, SK. and Kimbler, D.L., 1987. Assignment ofAGVS with different vehicle types, Material Flow, 4: 65-72. Malmborg, C.J. and Deutsch, S.J., 1988. A Stock location model for dual address order picking systems. IIE Trans., 20( 1): 44-52. Hodgson, T.J. and Lowe, T.J., 1982. Production lotsizing with material handling cost considerations, IIE Trans., 14(I): 44-61. Apple, J.M.. 1972. Material Handling Systems Design. The Ronald Press Company, New York.