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retrieval systems
Computers ind. Engng Vol. 28, No. 1, pp. 71-79, 1995
Pergamon
0360-8352(94)00027-1
Copyright© 1995ElsevierScienceLtd Printed in Great Britain. All rights reserved 0360-8352/95 $9.50+ 0.00
SIMULATION-BASED DESIGN EVALUATION OF UNIT LOAD A U T O M A T E D STORAGE/RETRIEVAL SYSTEMS SABAH U. RANDHAWAI and RAJ SHROFF2 ~Departmentof Industrial and Manufacturing Engineering, Oregon State University,Corvallis, OR 9733l, U.S.A. and 2KI Associates, 5121 Villagegreen, Los Angeles, CA 90016, U.S.A. (Received for publication 11 May 1994)
A~tract--The focus of this paper is unit load automated storage/retrieval (AS/R) systems. Two of the more important factors affecting the design of AS/R systems are system configuration and policies used for storing and retrieving items to and from the warehouse. Simulation results are obtained for six different single-dock layouts using three different scheduling policies. The results are compared using system throughput as the primary criterion; other performance measures investigated are storage and retrieval waiting times, and rejects due to the rack or input/output queues being fully utilized.
INTRODUCTION This paper extends the work on automated storage and retrieval (AS/R) systems reported by R a n d h a w a et al. [1]. R a n d h a w a et al. [1] evaluated a single-dock layout with the dock at the end of the aisle and two different configurations of dual-dock layouts. Four different scheduling policies were examined. A scheduling policy is a combination of a storage rule and a retrieval rule. The storage rule in all cases was first-come-first-serve (FCFS), closest open location to the dock. The retrieval rules examined were FCFS, nearest neighbor (NN) which minimizes the expected travel time from the current location to the target location and from that location to the dock, and two variations of N N that set limits on m a x i m u m waiting time for items. The results showed that the throughput for all systems was maximized using a scheduling policy where items were stored on a first-come-first-serve, closest open location (to dock) basis, and retrieved using the nearest neighbor rule. The throughput o f an AS/R system depends on m a n y factors including the dimensions of the storage rack, the horizontal and vertical speed of the crane, whether the crane performs single or dual cycles, initial loading of the system, and the sequencing of storage and retrieval operations. The primary objective of this research is to evaluate the effect of different storage and sequencing scheduling rules on various configurations of single dock layouts. Background
In a unit load AS/R system, typically, each aisle is assigned its own automatic stacker crane. The stacker crane that stores and retrieves warehoused materials can move horizontally and vertically, simultaneously; thus the crane can travel diagonally resulting in reduction of travel time. A conveyor system provides the link between the warehouse and incoming and outgoing pallets from a source or to a destination. The dock is located where the pallets are exchanged between the conveyors and the cranes. The most important measure of performance for the system is its throughput, i.e. the number of storage and retrieval requests performed by the system during a specified time period. T h r o u g h p u t depends on the time required for the stacker crane to perform both single-command and dual-command cycles. In the unit-load system, a single-command cycle consists of either a storage or retrieval, but not both. A single-command crane storage cycle time is the sum of the times required to pick the load at the dock, travel to the storage location, place the load in the rack, and return to the dock. A single-command retrieval cycle is similar, operating in the reverse direction. A dual-command cycle involves both storage and retrieval to pick the load at the dock, travel to the storage location, place the load in the rack, travel empty to the retrieval location, retrieve a load, and return to the dock. CAIE2S/I--.V
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SABAHU. RANDHAWAand RAJ SHROFF
Prior research in unit load AS/R systems has focused on maximization of system throughput through minimization of crane travel time [2-6]. For a review of this research, see Randhawa et al. [1]. A primary result of previous research is that sequencing of storage and retrieval requests can result in substantial improvements in system throughput. In general, storage items can be assigned to the closest open location and processed on a FCFS basis. This is realistic for storage since there is little opportunity to change the physical order in which items are input to the system. On the other hand, retrievals are simple messages and can be arranged in a sequence that would reduce the crane travel time between the storage and retrieval locations and the dock during system operation. Optimizing retrieval requests is a complex problem, equivalent to the well known traveling salesman problem in dynamic programming, an NP-hard combinatorial optimization problem [7]. Another problem with the optimization of retrieval sequencing is the dynamic nature of the retrieval list, i.e. new retrieval requests arriving when prior requests are being performed. One alternative is to do batch processing by selecting a set of retrievals at a time and complete their processing before selecting a new set. A second alternative is to maintain a retrieval list by resequencing the list each time a new retrieval request arrives. This research uses the second alternative, that of maintaining a continuous retrieval list. DESIGN SPECIFICATIONS In the systems analyzed a single crane serves a single aisle with storage racks placed on one side of the aisle. There are two sources of storage pallets (e.g. from two different production departments), SI and $2, respectively. Similarly, there are two sources of retrieval requests, R 1 and R2, respectively. The exchange between the crane and the conveyor occurs at the dock. The results of the study can be generalized to a multi-aisle system with identical assumptions for each aisle, i.e, an N-aisle system with one crane per aisle may be viewed as N-independent single-aisle systems. The AS/RS designs and scheduling policies analyzed in this study are briefly described below.
A S / R S layouts Each of the single-dock layout is characterized by three parameters: location of dock (end-ofaisle vs mid-aisle), configuration of rack (square-in-time vs nonsquare-in-time), and turnover distribution of each location in the rack (uniform vs class-based). In a square-in-time rack design, the crane takes the same amount of time to reach the most distant row on the rack as it takes to reach the most distant column. This condition is not satisfied in the nonsquare-in-time rack. A uniform distribution represents the situation where each rack location has the same turnover frequency. In the class-based arrangement, the rack is partitioned into various classes; items in each class have a different turnover frequency with the highest turnover class located closest to the dock. For all arrangements, the crane operation is subject to the dual command rule as long as both the storage and retrieval queues are nonempty; otherwise, requests from the nonempty queue are performed.
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The dock is located at one end of the aisle. The layout is square-in-time with uniform turnover frequency for each location (Fig. 1). Layout 2: The dock is located at the middle of the aisle. The layout is square-in-time with uniform turnover frequency for each location (Fig. 2). Layout 3: The dock is located at the end of the aisle. The layout is square-in-time with class-based arrangement. Two classes are used with a 80: 20 turnover ratio (Fig. 3). Layouts 4a, 4b and 4c: All three layouts are end-of-aisle layouts with uniform turnover frequency for each rack location. However, the three layouts represent nonsquare-intime arrangements. The total number of rack openings remain the same as with the square-in-time arrangement, but the rack dimensions change. Racks with three different shape parameters are analyzed (Table 1). The six layouts are summarized in Table 1. Table 1. Layout arrangements Layout I
2 3 4a 4b 4c
Dock arrangement
Item distribution
Rack configuration
End-of-aisle Mid-aisle End-of-aisle End-of-aisle End-of-aisle End-of-aisle
Uniform Uniform Class-based Uniform Uniform Uniform
Square-in-time Square-in-time Square-in-time Nonsquare-in-time Nonsquare-in-time Nonsquare-in-time
Rack dimensions 5x 5x 5x 10 x 4x 2x
20 20 20 10 25 50
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SABAH U. RANDHAWA a n d RAJ SHROFF
Scheduling policies As stated earlier, a scheduling policy is a combination of a storage rule and a retrieval rule. Storage rule. Storage items are processed on a FCFS basis and are assigned to the closest open location (COL) from the dock. The COL is defined as an open storage location from among all available open locations which has the smallest sum of storage travel time from the dock to the open location and expected retrieval time from that open location to the dock. Retrieval rules. Three retrieval rules are used in conjunction with the FCFS, COL storage rule. These are: (1) Random retrieval with a maximum waiting time limit: When the crane initiates a retrieval cycle, a target retrieval location is selected randomly from all retrieval requests waiting to be served. The maximum time limit is introduced to avoid having retrieval requests wait for an unnecessarily long time before being served. Based on results of prior research [1], a time limit of 60 min (for the arrival and service rates used in this study) was selected to be used in conjunction with the random retrieval rule. (2) Nearest neighbor rule: The target location is determined based on the shortest operation time from the current crane location to the target location and from the target location to the dock. (3) Relief nearest neighbor rule: The FCFS rule is used as the primary sequencing criterion. If the queue length exceeds a specified maximum, then the nearest neighbor rule is used for selecting a request for retrieval. Rules such as relief nearest neighbor that consist of a combination of simpler rules have been shown to work quite well in machine scheduling. The scheduling policies resulting from the combination of storage and retrieval rules are summarized in Table 2.
Modeling assumptions Since there are numerous factors that must be analyzed and compared in the study of AS/R systems, some assumptions are necessary to simplify the problem and to allow focus on the system components being analyzed. The assumptions made in the analyses are listed below. (1) Each pallet contains one part number or item type and the size of all pallets are equal. Each storage or retrieval job consists of a single pallet assignment. This removes pallet assignment as an independent factor in the study. (2) All storage locations are identical in size, and any pallet load may be stored in any storage location. The only exception is in the class-based arrangement where items belonging to a particular class must be stored in the rack area designated for that class. (3) The maximum capacity of the crane is one pallet and the crane is capable of simultaneous horizontal and vertical movement. (4) When the crane is idle, its location is referred to as the dwell point. The dwell point for the crane is at the dock. (5) The pick-up and deposit (P/D) time is generally independent of the crane travel velocity and shape of the rack. Furthermore, given the crane load and unload characteristics, P/D time is usually deterministic. Hence, it is useful to include P/D time only after average travel time is computed. Consequently, the P/D time may be ignored as it will not affect the relative performance of the scheduling policies. Similarly, the crane acceleration and deceleration is ignored as it will not effect the relative performance of the scheduling policies [2]. Table 2. Scheduling policies Scheduling Policy
Storage Rule
COL/RNN
First-come-first-serve, closest open location First-come-first-serve, closest open location First-come-first-serve, closest open location
COL/NN COL/RNN
Retrieval Rule Random retrieval, wait limit = 60 min Nearest neighbor Relief nearest neighbor
Automated storage/retrievalsystems
75
Performance measures The following performance measures were used to analyze AS/R systems: (1) Throughput, defined as the total number of storage and retrieval requests performed in a specified time period. (2) Mean storage and mean retrieval waiting times. (3) Maximum retrieval waiting time. (4) Number of storage and retrieval requests rejected due to the rack, or storage or retrieval queue being full. SIMULATION MODEL Discrete event simulation was used to model different AS/R design configurations. The simulation models were developed using the SIMAN simulation language [8]. The programs utilize the built-in library routines available in SIMAN for creating and scheduling requests, file manipulation, attribute value assignment and statistics collection. In addition to the SIMAN library, a set of programs were also developed in FORTRAN and integrated with the SIMAN functions and subroutines. The primary function of the user written subroutines was to model sequencing requests and to produce output reports. The simulation models can be executed on any IBM compatible microcomputer. For the development of simulation models, see Shroff [9].
Parameter specification In the square-in-time design, a storage rack of 5 rows by 20 columns (100 storage locations) is located on one side of the aisle. To accomplish the square-in-time rack design with these dimensions, the horizontal and vertical crane velocities are set at 4 s per column and 20 s per row, respectively. For the nonsquare-in-time designs, three different rack designs are evaluated by varying the number of rows and the number of columns but holding the total number of storage locations constant. These dimensions are given in Table I. To analyze the different AS/R systems, the interarrival times are taken from an exponential distribution with a mean of four minutes for sources Sl and $2, and for retrieval requests from R1 and R2. The maximum queue size for storage and retrieval is restricted to l0 for random retrieval and NN retrieval policies. For the relief NN policy a critical queue specification is required. The critical queue length is where the switch is made from FCFS to NN; this is assumed to be ten. Additionally, the initial rack loading is assumed to be 90%; this utilization level has been shown to represent a nontrivial system in scheduling literature. For comparison, some of the systems are also evaluated at initial rack utilization level of 75%. RESULTS The simulation results are based on steady state behavior of the system. The results for each design level are based on five replications. Each design level used common random numbers, or synchronization, to achieve an ideal degree of blocking for the simulation experiments. The results are evaluated statistically using two-factor ANalysis Of VAriance (ANOVA), where the two independent factors are the layout arrangements (Table 1) and the scheduling policies (Table 2). Of specific interest are the following pairwise comparisons: end-of-aisle vs mid-aisle, uniform vs class-based, and square-in-time vs nonsquare-in-time. The discussion below is organized around the performance measures used for evaluating AS/R systems.
Throughput analysis Throughput results for one dock layouts at an initial rack loading of 90% are shown in Fig. 4. The maximum throughput for all three scheduling policies is obtained with the class-based layout (Layout 3). In the class-based arrangement, items with higher turnover are located close to the dock resulting in reduced crane travel times, and subsequently higher throughput.
76
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Of the two uniform, square-in-time rack layouts (Layouts I and 2), Layout 2 (with dock in the middle of the rack) produced consistently higher results than Layout 1 (dock at one end of the aisle). In Layout 2, the expected horizontal travel time to go to certain location would be half the distance expected in Layout 1. The result is a reduction in the crane travel time. The ANOVA results for pairwise comparison between Layouts 1 and 2 and between Layouts 1 and 3 show the interaction between layouts and scheduling policies to be significant at significance levels of 0.01 and 0.05. The performance of the other nonsquare layouts is inferior to the square-in-time layout, with throughput decreasing as dimensions deviate from the square-in-time arrangement. Since the crane can travel diagonally, the travel time to any cell ~ is defined as: [maximum {time to row i, time to column j}]. As the dimensions of the rack deviate from the square-in-time dimensions, the maximum travel distance increases, resulting in decreased throughput. Figure 4 shows that the relief NN (COL/RNN) scheduling policy produced better throughput results for all layouts, except in the class-based layout where there was no statistical difference in throughput for the three scheduling policies. Since the primary criterion in the COL/RNN policy is FCFS, items stored closest to the dock are first served. This results in smaller crane travel times and increased throughput. As the storage and retrieval rates increase, COL/RNN will approach the COL/NN policy as COL/RNN uses the NN rule most of the time. The random retrieval policy results in minimum throughput; items may be randomly selected for retrieval that are in locations far away from the dock, resulting in increased crane travel times. Effect of initial rack utilization on throughput. The throughput performance of the two single-dock layouts with uniform turnover frequency (Layouts 1 and 2) was also evaluated at initial rack utilization level of 75%. The results for both 75% and 90% rack utilizations are summarized in Table 3. Table 3. Effect of initial rack utilization on throughput Throughput Layout 1 Layout 2 Scheduling Policy 75% 90% 75% 90% COL/RR 737 660 958 840 COL/NN 777 715 1000 927 COL/RNN 868 777 1255 1143
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The trend for the two utilization levels is similar with the COL/RNN policy resulting in highest throughput for both layouts. The throughput decreases as rack utilization increases. Throughput is inversely proportional to crane travel time; as rack utilization increases, the crane spends a greater proportion of the time traveling to store and retrieve requests.
Storage waiting times Figure 5 shows that the best results for mean storage waiting times are obtained with the COL/RNN scheduling policy. The ANOVA results for pairwise comparison between Layouts ! and 2, 1 and 3, and 1 and 4a show the interaction between layouts and scheduling policies to be significant at significance levels of 0.01 and 0.05. Of the three square-in-time layouts (Layouts 1, 2 and 3), the mean storage waiting times for Layout 1 was the longest for all three scheduling policies. Due to the increased crane travel time with this layout arrangement, items had to wait longer to be served. On the other hand, with Layout 3 the highest frequency items were located close to the dock, expediting the storage-retrieval cycle. As explained in the throughput section, crane travel time increases with deviations from square-in-time dimensions, resulting in increased waiting times for requests before they are served.
Retrieval waiting times The mean and maximum retrieval waiting time comparisons are shown in Figs 6 and 7, respectively. It should be pointed out that whereas retrieval time results for the COL/RR and the COL/NN scheduling policies can be compared, the results from these two policies are not comparable to the COL/RNN policy. This is because both COL/RR and COL/NN used retrieval queues of size ten; retrieval requests were rejected from the system if ten requests were waiting to be served. In contrast, COL/RNN uses no queue limit due to the nature of the scheduling policy. Consequently, there are no rejects, though rejects may occur if the rack is fully utilized when requests arrive to the system. The mean retrieval time results (Fig. 6) show that: (1) Comparing COL/RR and COL/NN scheduling policies, COL/NN performed better for all square-in-time layouts. This is an expected result since the throughput for COL/NN was higher than the throughput for COL/RR.
78
SABAH U. RANDHAWA
and
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(2) The high mean retrieval times for COL/RNN is because all requests wait until satisfied, there being no queue limit. (3) Of the square-in-time layouts, the class-based layout seems to perform the best. The maximum retrieval times for the COL/RR policy are considerably shorter than those for the C O L / N N policy. Whereas a pallet located away from the dock can be selected at random or 4000
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Automated storage/retrieval systems
79
is selected after the waiting time limit with the C O L / R R policy, with the C O L / N N policy its selection is based on minimizing the expected distance from the dock. Thus, with the N N rule an item m a y have to wait a long time before being selected for retrieval. Storage and retrieval rejects
The trend for storage and retrieval rejects follows the throughput results. Higher throughput translates to smaller rejects and vice versa. For a detailed discussion, see [9]. CONCLUSIONS The objective of this study was to evaluate the effect of layout arrangement and scheduling policies on the performance of unit-load AS/R systems. The important results from the simulation and statistical analysis are summarized below: (l) Uniform vs class-based, square-in-time layouts: the throughput for the class-based layout was higher than that o f the uniform arrangement for all three scheduling policies with the C O L / R N N policy producing consistently better results. (2) End-of-aisle vs mid-aisle, uniform, square-in-time layouts: again, the C O L / R N N scheduling policy produced the best throughput results with the mid-aisle being the superior arrangement. (3) In comparing square-in-time with a number of non-square configurations, the square-intime arrangement produced the best combination of results. The performance of AS/RS is a function of several variables or system specifications. The choice of a specific layout depends on the level of activity demanded by the system and the structure of the production facilities. For a one-dock layout, a balance o f improved throughput and reduced waiting times can be achieved by sequencing of retrieval requests using the relief nearest neighbor rule, and by using class-based turnover arrangement, if possible. Furthermore, locating the dock at the middle of the storage aisle results in higher throughput as compared to the dock located at the end of the aisle. REFERENCES I. S. U. Randhawa, W. Wang and E. D. McDowell. Evaluation of scheduling rules for single- and dual-dock automated storage/retrieval systems. Computers ind. Engng. 20, 401~,10 (1991). 2. W. H. Hausman, L. B. Schwarzand S. C. Graves. Optimal storage assignmentin automatic warehousing systems. Mgmt Sci. 22, 629-638 0976). 3. S. C. Graves, W. H. Hausman and L. B. Schwarz. Storage-retrieval interleaving in automatic warehousing systems. Mgmt Sci. 23, 935-945 (1977). 4. L. B. Schwarz, S. C. Graves and W. H. Hausman. Scheduling-policy for automatic warehousing systems: simulation results. AIIE Trans. 10, 260-270 (1978). 5. M. Han, L. F. McGinnis, J. S. Shieh and J. A. White. On sequencing retrievals in an automated storage/retrievalsystem. AIIE Trans. 19, 55-66 0987). 6. Y. A. Bozer and J. A. White. Traveling-timemodels for automated storage/retrieval systems. AIIE Trans. 16, 329-338 0984). 7. R. A. Conway, W. L. Maxwell and L. W. Miller. Theory of Scheduling Addison-Wesley, Reading, Mass. 0967). 8. C. D. Pegden. Introduction to SIMAN. Systems Modeling Corp. State College, Pa. (1987). 9. R. Shroff. Simulation-based design evaluation of automated storage/retrieval systems. M.S. thesis, Department of Industrial and Manufacturing Engineering, Oregon State University, Corvallis, Ore. (1992).
Pergamon
0360-8352(94)00027-1
Copyright© 1995ElsevierScienceLtd Printed in Great Britain. All rights reserved 0360-8352/95 $9.50+ 0.00
SIMULATION-BASED DESIGN EVALUATION OF UNIT LOAD A U T O M A T E D STORAGE/RETRIEVAL SYSTEMS SABAH U. RANDHAWAI and RAJ SHROFF2 ~Departmentof Industrial and Manufacturing Engineering, Oregon State University,Corvallis, OR 9733l, U.S.A. and 2KI Associates, 5121 Villagegreen, Los Angeles, CA 90016, U.S.A. (Received for publication 11 May 1994)
A~tract--The focus of this paper is unit load automated storage/retrieval (AS/R) systems. Two of the more important factors affecting the design of AS/R systems are system configuration and policies used for storing and retrieving items to and from the warehouse. Simulation results are obtained for six different single-dock layouts using three different scheduling policies. The results are compared using system throughput as the primary criterion; other performance measures investigated are storage and retrieval waiting times, and rejects due to the rack or input/output queues being fully utilized.
INTRODUCTION This paper extends the work on automated storage and retrieval (AS/R) systems reported by R a n d h a w a et al. [1]. R a n d h a w a et al. [1] evaluated a single-dock layout with the dock at the end of the aisle and two different configurations of dual-dock layouts. Four different scheduling policies were examined. A scheduling policy is a combination of a storage rule and a retrieval rule. The storage rule in all cases was first-come-first-serve (FCFS), closest open location to the dock. The retrieval rules examined were FCFS, nearest neighbor (NN) which minimizes the expected travel time from the current location to the target location and from that location to the dock, and two variations of N N that set limits on m a x i m u m waiting time for items. The results showed that the throughput for all systems was maximized using a scheduling policy where items were stored on a first-come-first-serve, closest open location (to dock) basis, and retrieved using the nearest neighbor rule. The throughput o f an AS/R system depends on m a n y factors including the dimensions of the storage rack, the horizontal and vertical speed of the crane, whether the crane performs single or dual cycles, initial loading of the system, and the sequencing of storage and retrieval operations. The primary objective of this research is to evaluate the effect of different storage and sequencing scheduling rules on various configurations of single dock layouts. Background
In a unit load AS/R system, typically, each aisle is assigned its own automatic stacker crane. The stacker crane that stores and retrieves warehoused materials can move horizontally and vertically, simultaneously; thus the crane can travel diagonally resulting in reduction of travel time. A conveyor system provides the link between the warehouse and incoming and outgoing pallets from a source or to a destination. The dock is located where the pallets are exchanged between the conveyors and the cranes. The most important measure of performance for the system is its throughput, i.e. the number of storage and retrieval requests performed by the system during a specified time period. T h r o u g h p u t depends on the time required for the stacker crane to perform both single-command and dual-command cycles. In the unit-load system, a single-command cycle consists of either a storage or retrieval, but not both. A single-command crane storage cycle time is the sum of the times required to pick the load at the dock, travel to the storage location, place the load in the rack, and return to the dock. A single-command retrieval cycle is similar, operating in the reverse direction. A dual-command cycle involves both storage and retrieval to pick the load at the dock, travel to the storage location, place the load in the rack, travel empty to the retrieval location, retrieve a load, and return to the dock. CAIE2S/I--.V
71
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SABAHU. RANDHAWAand RAJ SHROFF
Prior research in unit load AS/R systems has focused on maximization of system throughput through minimization of crane travel time [2-6]. For a review of this research, see Randhawa et al. [1]. A primary result of previous research is that sequencing of storage and retrieval requests can result in substantial improvements in system throughput. In general, storage items can be assigned to the closest open location and processed on a FCFS basis. This is realistic for storage since there is little opportunity to change the physical order in which items are input to the system. On the other hand, retrievals are simple messages and can be arranged in a sequence that would reduce the crane travel time between the storage and retrieval locations and the dock during system operation. Optimizing retrieval requests is a complex problem, equivalent to the well known traveling salesman problem in dynamic programming, an NP-hard combinatorial optimization problem [7]. Another problem with the optimization of retrieval sequencing is the dynamic nature of the retrieval list, i.e. new retrieval requests arriving when prior requests are being performed. One alternative is to do batch processing by selecting a set of retrievals at a time and complete their processing before selecting a new set. A second alternative is to maintain a retrieval list by resequencing the list each time a new retrieval request arrives. This research uses the second alternative, that of maintaining a continuous retrieval list. DESIGN SPECIFICATIONS In the systems analyzed a single crane serves a single aisle with storage racks placed on one side of the aisle. There are two sources of storage pallets (e.g. from two different production departments), SI and $2, respectively. Similarly, there are two sources of retrieval requests, R 1 and R2, respectively. The exchange between the crane and the conveyor occurs at the dock. The results of the study can be generalized to a multi-aisle system with identical assumptions for each aisle, i.e, an N-aisle system with one crane per aisle may be viewed as N-independent single-aisle systems. The AS/RS designs and scheduling policies analyzed in this study are briefly described below.
A S / R S layouts Each of the single-dock layout is characterized by three parameters: location of dock (end-ofaisle vs mid-aisle), configuration of rack (square-in-time vs nonsquare-in-time), and turnover distribution of each location in the rack (uniform vs class-based). In a square-in-time rack design, the crane takes the same amount of time to reach the most distant row on the rack as it takes to reach the most distant column. This condition is not satisfied in the nonsquare-in-time rack. A uniform distribution represents the situation where each rack location has the same turnover frequency. In the class-based arrangement, the rack is partitioned into various classes; items in each class have a different turnover frequency with the highest turnover class located closest to the dock. For all arrangements, the crane operation is subject to the dual command rule as long as both the storage and retrieval queues are nonempty; otherwise, requests from the nonempty queue are performed.
I SOURCE 1
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I
s2
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R2
A u t o m a t e d storage/retrieval systems
I s°°"cE ' s,L
73
t s°U"c 2 I AS2
)ESTINATION 1 I
Fig. 2. Square-in-time, uniform, mid-aisle layout.
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Fig. 3, Square-in-time, class-based, end-of-aisle layout.
Layout 1:
The dock is located at one end of the aisle. The layout is square-in-time with uniform turnover frequency for each location (Fig. 1). Layout 2: The dock is located at the middle of the aisle. The layout is square-in-time with uniform turnover frequency for each location (Fig. 2). Layout 3: The dock is located at the end of the aisle. The layout is square-in-time with class-based arrangement. Two classes are used with a 80: 20 turnover ratio (Fig. 3). Layouts 4a, 4b and 4c: All three layouts are end-of-aisle layouts with uniform turnover frequency for each rack location. However, the three layouts represent nonsquare-intime arrangements. The total number of rack openings remain the same as with the square-in-time arrangement, but the rack dimensions change. Racks with three different shape parameters are analyzed (Table 1). The six layouts are summarized in Table 1. Table 1. Layout arrangements Layout I
2 3 4a 4b 4c
Dock arrangement
Item distribution
Rack configuration
End-of-aisle Mid-aisle End-of-aisle End-of-aisle End-of-aisle End-of-aisle
Uniform Uniform Class-based Uniform Uniform Uniform
Square-in-time Square-in-time Square-in-time Nonsquare-in-time Nonsquare-in-time Nonsquare-in-time
Rack dimensions 5x 5x 5x 10 x 4x 2x
20 20 20 10 25 50
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Scheduling policies As stated earlier, a scheduling policy is a combination of a storage rule and a retrieval rule. Storage rule. Storage items are processed on a FCFS basis and are assigned to the closest open location (COL) from the dock. The COL is defined as an open storage location from among all available open locations which has the smallest sum of storage travel time from the dock to the open location and expected retrieval time from that open location to the dock. Retrieval rules. Three retrieval rules are used in conjunction with the FCFS, COL storage rule. These are: (1) Random retrieval with a maximum waiting time limit: When the crane initiates a retrieval cycle, a target retrieval location is selected randomly from all retrieval requests waiting to be served. The maximum time limit is introduced to avoid having retrieval requests wait for an unnecessarily long time before being served. Based on results of prior research [1], a time limit of 60 min (for the arrival and service rates used in this study) was selected to be used in conjunction with the random retrieval rule. (2) Nearest neighbor rule: The target location is determined based on the shortest operation time from the current crane location to the target location and from the target location to the dock. (3) Relief nearest neighbor rule: The FCFS rule is used as the primary sequencing criterion. If the queue length exceeds a specified maximum, then the nearest neighbor rule is used for selecting a request for retrieval. Rules such as relief nearest neighbor that consist of a combination of simpler rules have been shown to work quite well in machine scheduling. The scheduling policies resulting from the combination of storage and retrieval rules are summarized in Table 2.
Modeling assumptions Since there are numerous factors that must be analyzed and compared in the study of AS/R systems, some assumptions are necessary to simplify the problem and to allow focus on the system components being analyzed. The assumptions made in the analyses are listed below. (1) Each pallet contains one part number or item type and the size of all pallets are equal. Each storage or retrieval job consists of a single pallet assignment. This removes pallet assignment as an independent factor in the study. (2) All storage locations are identical in size, and any pallet load may be stored in any storage location. The only exception is in the class-based arrangement where items belonging to a particular class must be stored in the rack area designated for that class. (3) The maximum capacity of the crane is one pallet and the crane is capable of simultaneous horizontal and vertical movement. (4) When the crane is idle, its location is referred to as the dwell point. The dwell point for the crane is at the dock. (5) The pick-up and deposit (P/D) time is generally independent of the crane travel velocity and shape of the rack. Furthermore, given the crane load and unload characteristics, P/D time is usually deterministic. Hence, it is useful to include P/D time only after average travel time is computed. Consequently, the P/D time may be ignored as it will not affect the relative performance of the scheduling policies. Similarly, the crane acceleration and deceleration is ignored as it will not effect the relative performance of the scheduling policies [2]. Table 2. Scheduling policies Scheduling Policy
Storage Rule
COL/RNN
First-come-first-serve, closest open location First-come-first-serve, closest open location First-come-first-serve, closest open location
COL/NN COL/RNN
Retrieval Rule Random retrieval, wait limit = 60 min Nearest neighbor Relief nearest neighbor
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Performance measures The following performance measures were used to analyze AS/R systems: (1) Throughput, defined as the total number of storage and retrieval requests performed in a specified time period. (2) Mean storage and mean retrieval waiting times. (3) Maximum retrieval waiting time. (4) Number of storage and retrieval requests rejected due to the rack, or storage or retrieval queue being full. SIMULATION MODEL Discrete event simulation was used to model different AS/R design configurations. The simulation models were developed using the SIMAN simulation language [8]. The programs utilize the built-in library routines available in SIMAN for creating and scheduling requests, file manipulation, attribute value assignment and statistics collection. In addition to the SIMAN library, a set of programs were also developed in FORTRAN and integrated with the SIMAN functions and subroutines. The primary function of the user written subroutines was to model sequencing requests and to produce output reports. The simulation models can be executed on any IBM compatible microcomputer. For the development of simulation models, see Shroff [9].
Parameter specification In the square-in-time design, a storage rack of 5 rows by 20 columns (100 storage locations) is located on one side of the aisle. To accomplish the square-in-time rack design with these dimensions, the horizontal and vertical crane velocities are set at 4 s per column and 20 s per row, respectively. For the nonsquare-in-time designs, three different rack designs are evaluated by varying the number of rows and the number of columns but holding the total number of storage locations constant. These dimensions are given in Table I. To analyze the different AS/R systems, the interarrival times are taken from an exponential distribution with a mean of four minutes for sources Sl and $2, and for retrieval requests from R1 and R2. The maximum queue size for storage and retrieval is restricted to l0 for random retrieval and NN retrieval policies. For the relief NN policy a critical queue specification is required. The critical queue length is where the switch is made from FCFS to NN; this is assumed to be ten. Additionally, the initial rack loading is assumed to be 90%; this utilization level has been shown to represent a nontrivial system in scheduling literature. For comparison, some of the systems are also evaluated at initial rack utilization level of 75%. RESULTS The simulation results are based on steady state behavior of the system. The results for each design level are based on five replications. Each design level used common random numbers, or synchronization, to achieve an ideal degree of blocking for the simulation experiments. The results are evaluated statistically using two-factor ANalysis Of VAriance (ANOVA), where the two independent factors are the layout arrangements (Table 1) and the scheduling policies (Table 2). Of specific interest are the following pairwise comparisons: end-of-aisle vs mid-aisle, uniform vs class-based, and square-in-time vs nonsquare-in-time. The discussion below is organized around the performance measures used for evaluating AS/R systems.
Throughput analysis Throughput results for one dock layouts at an initial rack loading of 90% are shown in Fig. 4. The maximum throughput for all three scheduling policies is obtained with the class-based layout (Layout 3). In the class-based arrangement, items with higher turnover are located close to the dock resulting in reduced crane travel times, and subsequently higher throughput.
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Of the two uniform, square-in-time rack layouts (Layouts I and 2), Layout 2 (with dock in the middle of the rack) produced consistently higher results than Layout 1 (dock at one end of the aisle). In Layout 2, the expected horizontal travel time to go to certain location would be half the distance expected in Layout 1. The result is a reduction in the crane travel time. The ANOVA results for pairwise comparison between Layouts 1 and 2 and between Layouts 1 and 3 show the interaction between layouts and scheduling policies to be significant at significance levels of 0.01 and 0.05. The performance of the other nonsquare layouts is inferior to the square-in-time layout, with throughput decreasing as dimensions deviate from the square-in-time arrangement. Since the crane can travel diagonally, the travel time to any cell ~ is defined as: [maximum {time to row i, time to column j}]. As the dimensions of the rack deviate from the square-in-time dimensions, the maximum travel distance increases, resulting in decreased throughput. Figure 4 shows that the relief NN (COL/RNN) scheduling policy produced better throughput results for all layouts, except in the class-based layout where there was no statistical difference in throughput for the three scheduling policies. Since the primary criterion in the COL/RNN policy is FCFS, items stored closest to the dock are first served. This results in smaller crane travel times and increased throughput. As the storage and retrieval rates increase, COL/RNN will approach the COL/NN policy as COL/RNN uses the NN rule most of the time. The random retrieval policy results in minimum throughput; items may be randomly selected for retrieval that are in locations far away from the dock, resulting in increased crane travel times. Effect of initial rack utilization on throughput. The throughput performance of the two single-dock layouts with uniform turnover frequency (Layouts 1 and 2) was also evaluated at initial rack utilization level of 75%. The results for both 75% and 90% rack utilizations are summarized in Table 3. Table 3. Effect of initial rack utilization on throughput Throughput Layout 1 Layout 2 Scheduling Policy 75% 90% 75% 90% COL/RR 737 660 958 840 COL/NN 777 715 1000 927 COL/RNN 868 777 1255 1143
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The trend for the two utilization levels is similar with the COL/RNN policy resulting in highest throughput for both layouts. The throughput decreases as rack utilization increases. Throughput is inversely proportional to crane travel time; as rack utilization increases, the crane spends a greater proportion of the time traveling to store and retrieve requests.
Storage waiting times Figure 5 shows that the best results for mean storage waiting times are obtained with the COL/RNN scheduling policy. The ANOVA results for pairwise comparison between Layouts ! and 2, 1 and 3, and 1 and 4a show the interaction between layouts and scheduling policies to be significant at significance levels of 0.01 and 0.05. Of the three square-in-time layouts (Layouts 1, 2 and 3), the mean storage waiting times for Layout 1 was the longest for all three scheduling policies. Due to the increased crane travel time with this layout arrangement, items had to wait longer to be served. On the other hand, with Layout 3 the highest frequency items were located close to the dock, expediting the storage-retrieval cycle. As explained in the throughput section, crane travel time increases with deviations from square-in-time dimensions, resulting in increased waiting times for requests before they are served.
Retrieval waiting times The mean and maximum retrieval waiting time comparisons are shown in Figs 6 and 7, respectively. It should be pointed out that whereas retrieval time results for the COL/RR and the COL/NN scheduling policies can be compared, the results from these two policies are not comparable to the COL/RNN policy. This is because both COL/RR and COL/NN used retrieval queues of size ten; retrieval requests were rejected from the system if ten requests were waiting to be served. In contrast, COL/RNN uses no queue limit due to the nature of the scheduling policy. Consequently, there are no rejects, though rejects may occur if the rack is fully utilized when requests arrive to the system. The mean retrieval time results (Fig. 6) show that: (1) Comparing COL/RR and COL/NN scheduling policies, COL/NN performed better for all square-in-time layouts. This is an expected result since the throughput for COL/NN was higher than the throughput for COL/RR.
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(2) The high mean retrieval times for COL/RNN is because all requests wait until satisfied, there being no queue limit. (3) Of the square-in-time layouts, the class-based layout seems to perform the best. The maximum retrieval times for the COL/RR policy are considerably shorter than those for the C O L / N N policy. Whereas a pallet located away from the dock can be selected at random or 4000
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Automated storage/retrieval systems
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is selected after the waiting time limit with the C O L / R R policy, with the C O L / N N policy its selection is based on minimizing the expected distance from the dock. Thus, with the N N rule an item m a y have to wait a long time before being selected for retrieval. Storage and retrieval rejects
The trend for storage and retrieval rejects follows the throughput results. Higher throughput translates to smaller rejects and vice versa. For a detailed discussion, see [9]. CONCLUSIONS The objective of this study was to evaluate the effect of layout arrangement and scheduling policies on the performance of unit-load AS/R systems. The important results from the simulation and statistical analysis are summarized below: (l) Uniform vs class-based, square-in-time layouts: the throughput for the class-based layout was higher than that o f the uniform arrangement for all three scheduling policies with the C O L / R N N policy producing consistently better results. (2) End-of-aisle vs mid-aisle, uniform, square-in-time layouts: again, the C O L / R N N scheduling policy produced the best throughput results with the mid-aisle being the superior arrangement. (3) In comparing square-in-time with a number of non-square configurations, the square-intime arrangement produced the best combination of results. The performance of AS/RS is a function of several variables or system specifications. The choice of a specific layout depends on the level of activity demanded by the system and the structure of the production facilities. For a one-dock layout, a balance o f improved throughput and reduced waiting times can be achieved by sequencing of retrieval requests using the relief nearest neighbor rule, and by using class-based turnover arrangement, if possible. Furthermore, locating the dock at the middle of the storage aisle results in higher throughput as compared to the dock located at the end of the aisle. REFERENCES I. S. U. Randhawa, W. Wang and E. D. McDowell. Evaluation of scheduling rules for single- and dual-dock automated storage/retrieval systems. Computers ind. Engng. 20, 401~,10 (1991). 2. W. H. Hausman, L. B. Schwarzand S. C. Graves. Optimal storage assignmentin automatic warehousing systems. Mgmt Sci. 22, 629-638 0976). 3. S. C. Graves, W. H. Hausman and L. B. Schwarz. Storage-retrieval interleaving in automatic warehousing systems. Mgmt Sci. 23, 935-945 (1977). 4. L. B. Schwarz, S. C. Graves and W. H. Hausman. Scheduling-policy for automatic warehousing systems: simulation results. AIIE Trans. 10, 260-270 (1978). 5. M. Han, L. F. McGinnis, J. S. Shieh and J. A. White. On sequencing retrievals in an automated storage/retrievalsystem. AIIE Trans. 19, 55-66 0987). 6. Y. A. Bozer and J. A. White. Traveling-timemodels for automated storage/retrieval systems. AIIE Trans. 16, 329-338 0984). 7. R. A. Conway, W. L. Maxwell and L. W. Miller. Theory of Scheduling Addison-Wesley, Reading, Mass. 0967). 8. C. D. Pegden. Introduction to SIMAN. Systems Modeling Corp. State College, Pa. (1987). 9. R. Shroff. Simulation-based design evaluation of automated storage/retrieval systems. M.S. thesis, Department of Industrial and Manufacturing Engineering, Oregon State University, Corvallis, Ore. (1992).