Evaluation of AGV routeing strategies using hierarchical simulation

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1 int. j. prod. res., 1998, vol. 36, no. 7, 1961± 1976 Evaluation of AGV routeing strategies using hierarchical simulation R. W. SEIFERT², M. G. KAY and J. R. WILSON * To analyse an automated guided vehicle (AGV) system operating under selected vehicle routeing strategies, we present a simulation model that can handle an arbitrary system layout as well as arbitrary numbers of AGVs and pedestrians causing congestion in the system. We introduce a dynamic vehicle routeing strategy based on hierarchical simulation that operates as follows: at the time of each AGV routeing decision in the main simulation, subordinate simulations are performed to evaluate a limited set of alternative routes in succession until the current routeing decision can be nalized and the main simulation resumed. A case study involving a prototype AGV system operating under the control of a global vision system illustrates the advantages not only of this strategy but also of global-vision-based control. 1. Introduction Automated guided vehicles (AGVs) constitute a major component of many automated material handling systems. AGVs are driverless vehicles that follow physical or virtual guidepaths under the control of a computer. Such vehicles play a key role in interconnecting all important locations on the factory oor for the horizontal movement of materials in a exible manner. Unlike other more conventional material handling devices, an AGV can select its own route to reach a designated work station or warehouse. To realize an AGV system s full potential for exibility, we must exercise careful planning and control of the design and operation of the system. The problem of assigning parts to vehicles and vehicles to parts has been the focus of several studies, and numerous authors have evaluated heuristic dispatching rules such as the random vehicle rule, the nearest vehicle rule, the longest idle vehicle rule, and the least utilized vehicle rule (Viswanadham and Narahari 1992). However, identifying the `nearest vehicle and the `shortest route involves signi cant di culties. We observe that the shortest travel-distance route may not be the shortest travel-time route. Along any given route, the actual travel speed of a vehicle depends on the amount of congestion encountered. This can have a substantial in uence on the vehicle s travel time and hence on the overall performance of the AGV system Problem statement To gain the full bene ts from an AGV system, we must exploit the exibility of the AGVs; in particular, we must take advantage of the possibility to choose between various routes to reach a selected destination. To nd the route with the shortest travel time, we must solve the well-known vehicle routeing problem. Beyond the Revision received July ² Department of Industrial Engineering and Engineering Management, Stanford University, Stanford, CA , USA. Department of Industrial Engineering, North Carolina State University, 2401 Stinson Drive, Raleigh, NC , USA. *To whom correspondence should be addressed. 0020± 7543/98 $ Ñ 1998 Taylor & Francis Ltd.

2 1962 R. W. Seifert et al. deterministic approach which simply follows the shortest travel-distance route, extensive research has been devoted to the development of algorithms for nding the shortest travel-time route (path) in a graph that has random weights on the arcs representing the times required to traverse those arcs. However, the complexity of the AGV routeing problem makes it di cult, if not impossible, to obtain e ective analytical solutions to this version of the stochastic shortest route problem. Computationally feasible analytical techniques are limited to graphs with stochastically independent arc weights. This is an unacceptable limitation in the routeing of AGVs because, for example, the tra c congestion encountered by a vehicle along each arc of its current route is generally dependent on the congestion encountered along the preceding arcs of that route: and thus the travel times for di erent arcs of the route are stochastically dependent. There is a clear need for a more realistic approach to the identi cation of the shortest travel-time route between a speci ed origin and destination that takes into account the present status of the system. Such an approach would provide further potential for improvements in the utilization of AGVs Terminology and problem representation According to Tanchoco and Taghaboni (1988), the primary vehicle management functions for an AGV system can be de ned as follows: Dispatching is the process of selecting and assigning tasks to vehicles. Routeing is the selection of the speci c paths taken by vehicles to reach their destinations. Scheduling is the determination of the arrival and departure times of vehicles at certain points along their prescribed routes to ensure collision-free journeys. The guidepaths of an AGV system can be modelled as a graph consisting of nodes (or points, or vertices) connected by a set of arcs (or lines, or branches). The nodes represent locations in the system such as intersection regions or `pickup and delivery (P & D) stations. The arcs connecting these nodes comprise the physical or virtual guidepaths to be followed by an AGV. This graph is the primary input to the routeing function of the AGV control system. Given the current location (origin node) of an AGV and its prescribed destination node, the vehicle router must select an appropriate path for the vehicle that consists of an alternating sequence of distinct nodes and arcs beginning with the origin node and ending with the destination node such that each arc is terminated by (incident with) the two nodes immediately preceding and following it in the sequence. Di erent routes can be evaluated based on an aggregate cost of traversing the corresponding paths, such as travel distance or expected travel time (Co and Tanchoco 1991). The evaluation of alternative routes and the actual routeing of a vehicle based on this evaluation can be either static or dynamic: When routeing is static, the path taken by an AGV between any two given nodes is always the sameð that is, the route does not vary over time as a function of the current congestion in the system. The most natural solution is always to select the path with the shortest travel distance. When routeing is dynamic, di erent paths can be taken by an AGV at di erent times when moving between two given nodes. Taking into consideration the current status of the system, the vehicle router selects a path for the AGV at

3 Evaluating AGV routeing strategies 1963 the time that the vehicle is dispatched (Hodgson et al. 1987) and if there is a communications link between the router and the vehicle, then the router modi- es the vehicle s path during travel. The primary objective of this paper is to evaluate the bene ts of dynamic vehicle routeing strategies versus conventional static strategies for controlling the operation of an AGV system. The experimental tool for performing this comparison is a exible, hierarchical simulation model that can be used to simulate an arbitrary AGV system con guration operating under an arbitrary vehicle routeing strategy. This model is hierarchical in the following sense: at the time of each routeing decision for an AGV in the main simulation, subordinate simulations (subsimulations) are performed sequentially for selected alternative routes between the AGV s current location and its assigned destination; and the performance observed for the latest route in the corresponding subsimulation is used to determine whether additional subsimulations should be performed before nalizing the current routeing decision and resuming the main simulation. We present a case study involving a prototype AGV system operating under the control of a global vision system; and the results of this case study indicate that signi cant, cost-e ective improvements in performance can be achieved by the use of dynamic vehicle routeing strategies in conjunction with global-vision-based control. 2. Review of previous work The following material brie y summarizes previous research on the vehicle routeing problem. It is by no means comprehensive but is intended to show some alternative approaches to the problem. Moreover, in this section we introduce the concept of global vision, a technology that we expect to provide the information necessary for dynamic vehicle routeing as proposed in this study Analytical models In the classical shortest route problem for a given graph with deterministic arc lengths, the objective is to determine a minimum-length path between given origin and destination nodes, where the length of each path in the graph is the sum of the lengths of the arcs comprising the path. This problem can be solved e ciently by Dijkstra s algorithm (Eiger et al. 1985). Throughout the rest of this section, the term arc length (respectively, path length) is always understood to mean a relevant weight assigned to an arc (respectively, path). For shortest route problems de ned on the stochastic networks (directed graphs) that typically arise in transportation studies, there are no procedures that are both generally applicable and comparable in computational e ciency to Dijkstra s algorithm. In such networks, the arc weights often represent travel times that are subject to pervasive random e ects due to tra c congestion; and thus the arc weights are dependent random variables. Since the pioneering work of Frank (1969), various approaches have been used to determine key properties of the shortest path in a stochastic network. Starting with the joint cumulative distribution function (cdf) of the arc lengths in the network, Frank (1969) derived the characteristic function of the shortest path length as a complicated multidimensional integral; and he suggested that the corresponding cdf of the shortest path length could be computed using the inversion formula for characteristic functions (Gnedenko 1968). However, Frank s approach is prohibitively expensive in terms of computation time even for stochastic

4 1964 R. W. Seifert et al. networks of moderate size. To compute the expected value of the shortest path length in a stochastic network, Mirchandani (1976) developed a computationally e cient algorithm based on converting the network to an `emergency equivalent network whose expected shortest path length can be readily computed by an iterative scheme. Unfortunately, Mirchandani s algorithm is limited to stochastic networks in which all arc lengths are mutually independent, discrete random variables. Some authors have proposed and investigated the stochastic shortest path problem with special optimality criteria. Sigal et al. (1980) introduced an `optimality index for a given path, which is de ned as the probability that the length of the given path is shorter than that of any other path. Sigal, Pritsker, and Solberg concentrated on the problem of nding a path that maximizes this optimality index. Eiger et al. (1985) de ned a `traveller s utility for each path in a stochastic network as a function of the path weight. Assuming that the traveller s utility function is linear or exponential and that the arc weights are stochastically independent, Eiger et al. (1985) showed that a variant of Dijkstra s algorithm can be used to nd the path with the maximal expected utility. To design optimal ow paths for an AGV system, Gaskins and Tanchoco (1987) formulated and solved a zero-one integer programming problem. The objective of Gaskins and Tanchoco was to construct a vehicle routeing plan that minimizes the total distance travelled by loaded vehicles to satisfy a given set of transportation requirements. This formulation was extended by Kaspi and Tanchoco (1990) to apply to the problem of optimal ow path design for unidirectional AGV systems. Kaspi and Tanchoco developed a branch-and-bound procedure to determine the direction of ow for each arc in the ow path network as well as the optimal vehicle routeing plan. The common drawback of all the analytical models discussed previously is that they allow only a static vehicle routeing for a prespeci ed layout. The mathematicalprogramming approaches of Gaskins and Tanchoco (1987) and Kaspi and Tanchoco (1990) are limited to AGV systems with deterministic travel times for all routes. The more general analytical approaches to the stochastic shortest route problem are either computationally infeasible in practice or limited to graphs with stochastically independent arc weights; and as explained in 1.1, these limitations preclude applying such techniques to AGV systems of realistic complexity Computer simulation models Many researchers have used the technique of computer simulation to address the problem of dynamic vehicle routeing. The main motivation is that using a simulation model provides a system-wide view of the e ect of a local change in the AGV system. In the following discussion, two successful approaches are explained. Tanchoco and Taghaboni (1988) developed a LISP-based controller for freeranging AGV systems. In the rst phase of this research, the authors performed a simulation-based performance evaluation of a job shop, where transportation was critical. It was shown that increasing the number of vehicles improved the throughput of the system up to a point; however, beyond that point, the throughput started to decrease. This decrease was found to be due to vehicle blockage (that is, selfcongestion), causing unit loads to spend more time on vehicles travelling to workstations. After having shown that self-congestion can have a signi cant e ect on AGV system performance, Taghaboni and Tanchoco (1988) developed an intelligent

5 Evaluating AGV routeing strategies 1965 supervisory controller in the second phase of their work. The controller was designed for dynamic vehicle routeing to address the problem of vehicle blockage at intersections. Initially, the best route is assumed to be the one that results in a minimum travel distance. The vehicle controller then provides a timetable of occupation times for each node along the vehicle s route. The times for the new journey are compared with the previously scheduled journey times, and thereby con icts are identi ed between the newly selected route and the nodes reserved occupation times for all the other journeys. If a con ict is detected, then the con ict resolver will explore alternate routes with the objective of nding a route that will minimize delay time. The objective is realized either by slowing down the vehicle on a certain route or by selecting an alternative route without con icts. Gaskins and Tanchoco (1989) introduced the vehicle simulator AGVSim2, which was intended to be a development tool for testing the performance of an AGV supervisory controller. Rather than modelling the control logic, AGVSim2 was designed to be linked directly to the supervisory controller software. The simulator models the environment in which the supervisory controller software operates, generating the events to which the controller responds. By altering the environment and other components of the AGV system, the user can test the performance of the supervisory controller software under a variety of conditions. To enhance the evaluation procedure, the simulator is designed to be linked to an animation module that graphically displays the vehicle s location Global vision as information support To achieve the most e cient path selection, we must be able to route vehicles dynamically over uncongested routes or to avoid obstacles in the way of an AGV. Although vehicle self-congestion can be avoided as long as the controller knows the position of each vehicle (Taghaboni and Tanchoco 1988), avoiding other possible sources of congestion (for example, pedestrians) requires that additional information be provided to the controller. This basically means that we must have not only a more sophisticated control scheme for the AGVs but also a system feedback mechanism. Both tasks may be realized by using free-ranging AGVs operating under the control of a global vision system. The global vision system enables the control system to detect congestion or unexpected obstacles and thus provides the necessary feedback for globally e cient path planning. Global vision refers to the use of cameras (or other types of sensors) placed at xed locations in a work space to extend the local sensing available on board each vehicle in a free-ranging AGV system (Kay 1992, Kay and Luo 1993). Information from the cameras is used to (1) monitor the work space to detect and track potential obstacles in the immediate vicinity of each AGV and over its intended path; (2) track each AGV along its intended path to bound errors in the vehicle s dead-reckoning sensors; (3) monitor the load aboard each AGV to detect positioning errors; and (4) provide video images of the entire work space so that a human operator can monitor the status of operations throughout the facility. The status of the AGV system is available as input to high-level transport control functions. Given that this system information (in particular, item (1) in the previous paragraph) can be provided in the present study, we seek to evaluate the use of a computer simulation model as a short-term decision tool for AGV routeing that accounts for the current system status and determines the current optimal path with

6 1966 R. W. Seifert et al. the minimum travel time to reach a certain destination. This cannot be accomplished by routeing strategies that do not utilize a system feedback mechanism. 3. Model description 3.1. Model overview The simulation model developed in this research is a discrete-event, mixed-language software package written in SLAM II (Pritsker 1995) with all event-processing routines written in the C programming language (Kernighan and Ritchie 1988). The model has a exible design and can handle an arbitrary user-speci ed layout for an AGV system. By collecting and summarizing key statistics on system performance, the model provides a complete bottleneck analysis at the end of each simulation experiment. Pedestrians and the other AGVs are the two possible causes of congestion for each vehicle as modelled at the current stage of the research. While requiring a minimum of user input, the model allows the user to: (1) specify an arbitrary number of AGVs and pedestrians in the system as well as di erent speeds for loaded and unloaded vehicles; (2) set node-speci c parameters (such as the time delay at intersections caused by the need for vehicles to slow down in order to detect and avoid possible collisions); and (3) study the e ect on the system throughput of the loading and unloading times at speci c P & D stations. Furthermore, the model is capable of evaluating the potential improvement in the performance of an AGV system that can be achieved with a dynamic vehicle routeing strategy versus a conventional static vehicle routeing strategy. A complete technical description of the structure and operation of this simulation model is given in Seifert (1994) Detailed model description General information structures The user speci es the layout and operating characteristics of the target AGV system by means of two plain text (ASCII) les. This information is read and stored in SLAM II les called layout les, with a unique layout le for each node (Pritsker 1974, pp. 265± 275). The rst entity in each layout le describes the characteristics of the corresponding node (such as the time required for pick-up and delivery of unit loads at a P&D station, the current status of load/unload operations at a P & D station, the slowdown time required for an AGV approaching an intersection, and the numbers of AGVs and pedestrians currently moving through an intersection). The second and subsequent entities in a layout le respectively describe the characteristics of each arc emanating from the corresponding node (such as the arc s destination node, its physical length, and the number of AGVs and pedestrians currently travelling on the arc). These attributes of the entities in the layout les are used rst to create an array of structures (Kernighan and Ritchie 1988) describing the paths in the network and then to regulate the operation of the AGV system simulation. During the course of the simulation, the status of the system is re ected by the changing values of (1) the attributes of the entities in the layout les, and (2) the members of the structures describing the paths in the network.

7 Evaluating AGV routeing strategies 1967 The AGVs and pedestrians are represented by entities that are placed on the event calendar and are processed at the corresponding event times. Arriving at or departing from the latest node in its currently assigned route, an AGV or pedestrian entity retrieves from that node s layout le the attributes of the node entity and the arc entities de ning the current conditions at the associated location in the system. Continued movement of the AGV or pedestrian entity into or out of the relevant node depends on the current local conditions; and as explained in the next subsection, this movement may be blocked (suspended) until certain conditions are achieved Modelling AGV system operations The congestion encountered by AGVs and pedestrians is modelled by using SLAM II les for intermediate storage of AGVs and pedestrians whose current activities must be blocked temporarily. If the movement of an AGV along an arc is blocked, then all other AGVs travelling behind the blocked AGV on the same arc are also blocked in order to maintain the user-speci ed minimum physical distance between successive AGVs travelling on the same arc. To model the interactions between AGVs and pedestrians in the system, we speci ed the logic for movement of pedestrians based on the following assumptions. (1) The routeing of pedestrians is deterministicð that is, all pedestrians follow the shortest travel-distance path between their origin and destination nodes. (2) Pedestrians do not overtake an AGV travelling on an arc unless the AGV is currently blocked. (3) During the time that an AGV is traversing a node, pedestrians who attempt to traverse that node must wait for the AGV to exit the node and enter the next arc on the AGV s currently assigned route. (4) A pedestrian traversing a node causes the blockage of all AGVs attempting to arrive at that node. (5) After a pedestrian enters the next arc on its currently assigned route, any AGV that immediately follows the pedestrian on to the same arc must maintain a minimum safety time-distance separation from the pedestrian. (6) Pedestrians do not interact with an AGV currently undergoing a load or unload operation at a nodeð that is, stationary AGVs do not in uence the movement of pedestrians. (7) Pedestrians do not interact with each otherð that is, they can pass each other on an arc or in a node without slowing down, and they do not block each other when arriving at or departing from a node. (8) After a pedestrian reaches its current destination node, the pedestrian will stay at this location for an exponentially distributed holding time with a userspeci ed mean before being assigned a new destination node as well as a route for walking to that node. Although these assumptions clearly do not capture the full complexity of the behaviour of pedestrians as they move around an AGV system, our preliminary sensitivity analyses with the simulation model revealed that these assumptions give rise to at best second-order e ects in the comparison of alternative vehicle routeing strategies. A more complete characterization of the e ect of pedestrians on the performance of AGV systems will be the subject of a follow-up study.

8 1968 R. W. Seifert et al. To improve the accuracy of the results of each simulation experiment, the model has been carefully constructed to take advantage of the variance reduction technique of common random numbers (Law and Kelton 1991). This means that in each vehicle routeing scenario to be compared, the same pattern of demands (destinations) is generated for the same AGV (while di erent demand patterns are generated for di erent AGVs); and a similar approach is used to generate destination patterns for pedestrians. Thus we obtained an e cient approach for studying the e ect of varying the numbers of AGVs and pedestrians in the system, and we sharpened the comparison of di erent routeing and sensing strategies. The functions used to generate and return the next demand (destination) for each AGV and pedestrian are modular so that they may be easily replaced or modi ed, for example, to read the next demand from an external scheduler Model veri cation and validation In addition to the standard trace reports available in SLAM II, we implemented several special output reports to provide a means for: (1) verifying the usage of path information during the course of the simulation experiment; (2) keeping track of the movements and the blockage of the AGVs and the pedestrians; and (3) recording the number of subsimulations that were performed at each decision epoch as well as the route that was nally selected at each decision epoch. Customized trace reports provide the means for verifying the correct operation of the simulation model. During the course of the simulation experiment, the movements of each individual AGV and each individual pedestrian are traced and the corresponding event-times are listed. To verify the implemented logic for modelling the congestion resulting from interactions not only between individual AGVs but also between AGVs and pedestrians, we provided the appropriate status messages to trace the disposition of the entities in the system as they are processed at their discrete-event times (that is, their node-arrival and node-departure times). Furthermore, we listed the current attributes of each entity and the current travel route that each entity follows. In the case study described in 5, validation of the accuracy of the simulation-generated system performance statistics was based on careful inspection of these customized output reports. 4. Vehicle routeing strategies In this section, we detail the static and dynamic vehicle routeing strategies that were implemented in the simulation model Static deterministic vehicle routeing A static vehicle routeing strategy generally assigns to each dispatched AGV the shortest travel-distance path between the AGV s origin and destination nodes, regardless of the current degree of congestion along the di erent routes connecting those nodes. This purely deterministic approach is widely used in practice, and the results obtained by this method will serve as the baseline scenario for our evaluation of di erent routeing strategies. However, this approach re ects the lowest level of

9 Evaluating AGV routeing strategies 1969 routeing sophistication in the sense that the vehicle router does not dynamically account for any feedback that is provided on the current status of the AGV Dynamic stochastic vehicle routeing based on hierarchical computer simulation A major disadvantage of static deterministic vehicle routeing is that the lack of responsiveness to changes in system status makes the AGV system prone to tra c congestion and the resulting congestion is exacerbated by breakdowns of vehicles or P & D stations. To implement dynamic vehicle routeing strategies in the AGV system simulation, we employ a hierarchical approach. At the time of each vehicle routeing decision in the main simulation, we perform up to N subsim short-term subsimulations to predict the vehicle s travel times for selected alternative routes, where N subsim is a prespeci ed upper bound on the number of subsimulations that may be performed at each decision epoch. (In the case study described in the next section, we took N subsim = 8 based on preliminary experimentation indicating that in the target system, this value for N subsim will generally yield most of the potential performance improvement achievable with a dynamic vehicle routeing strategy while keeping the overall simulation execution time within acceptable bounds.) For a given vehicle following a selected route, the corresponding subsimulation starts with the current system conditions inherited from the main simulation, stops when the given vehicle arrives at its destination node, and uses shortest travel-distance routeing for all AGVs except the given vehicle. When a subsimulation is to be started, a snapshot of the current status of the main simulation is written to unformatted (binary) les that are then read by the subsimulation to initialize its operation. As explained in the next paragraph, a sequential procedure is used to control the number of subsimulations that are performed at each decision epoch. Once all of these subsimulations have been performed, the travel times observed for the given vehicle on each of the selected alternative routes are then passed back to the main simulation and these subsimulation-generated statistics are used to nalize the current vehicle routeing decision. This approach enables the user to make better routeing decisions because it is based on the current status of the system, but the computational feasibility of this approach depends critically on the procedure that controls the number of subsimulations performed at each decision epoch. Figure 1 depicts the sequential procedure that controls the execution of subsimulations at each decision epoch. It is important to notice that the number of alternatives evaluated by separate subsimulations depends on the results observed in those subsimulations. First, the AGV is routed on the shortest travel-distance path, and a subsimulation is performed for this path. This routeing decision is evaluated by comparing (1) the actual travel time to the assigned destination that is observed in the subsimulation with (2) the theoretical minimum travel time for travelling on the next best alternative route as determined by the current vehicle s maximum speed and the physical length of each alternative route. If the actual travel time (1) observed on the shortest travel-distance path is less than the theoretical minimum travel time (2) on the next best alternative route, then we do not need to perform another subsimulation to support the routeing decision for the current AGV. In this situation we route the AGV on the shortest travel-distance path in the main simulation, since the AGV would be routed on the shortest travel-distance path in the real AGV system. On the other hand, if the alternative route has the potential to yield a reduced travel time for the given AGV, then we perform a second subsimulation to evaluate

10 1970 R. W. Seifert et al. Figure 1. Limiting the number of simulated alternatives. the travel time on this alternative route. After this second subsimulation terminates, we compare (1) the smaller observed travel time from the two subsimulations performed so far with (2) the theoretical minimum travel time for the next best remaining alternative route. By this means, we determine whether we have obtained su cient decision support to select the most promising route for minimizing the travel time of the given AGV. We continue to evaluate additional alternative routes for the given AGV until one of the following stopping criteria is satis ed: (1) the theoretical minimum travel time for the next best alternative route is greater than the smallest travel time observed in all of the subsimulations performed so far; (2) all possible routeing alternatives have already been investigated; or (3) a total of N subsim subsimulations have been performed. When one of these conditions is satis ed, we send the AGV along the route with the smallest estimated travel time based on the subsimulations performed and then we resume the main simulation.

11 Evaluating AGV routeing strategies 1971 Using this sequential procedure to control the execution of subsimulations, we try to minimize the total number of subsimulations that are required to yield the nal routeing decision. Furthermore, we record in a customized output report the number of subsimulations performed at each decision epoch along with the alternative route that was nally selected. This information can be used to specify a smaller value of N subsim in future experimentation while still being able to enjoy most of the potential improvement that can be achieved with a dynamic vehicle routeing strategy based on hierarchical simulation. While the computational overhead of this approach to dynamic vehicle routeing may be substantially improved by enhancements to the current software implementation, our experience strongly indicates that hierarchical AGV system simulation can be a feasible means of evaluating and applying dynamic vehicle routeing strategies in practice. In the case study described below, the execution time required to determine the best route based on hierarchical simulation was usually negligible in comparison to the AGV load/unload times; and thus in real-time applications of dynamic vehicle routeing, subsimulations could be performed in parallel with an AGV s load/unload operations without delaying the departure of that AGV from a P & D station. This approach still allows us to accurately account for the current system status, since the other AGVs move at a relatively slow pace. In the rare case of having to perform decision support for two AGVs at the same time, we can avoid delaying the departure of an AGV due to a computational bottleneck by simply deciding on a route to follow based on all the subsimulation-generated travel times that have been observed up to that point of time. 5. Case study In this section, we brie y present a case study of a prototype AGV system operating under the control of a global vision system and we perform formal statistical comparisons of the di erent vehicle routeing strategies with a varying number of AGVs and a varying number of pedestrians in the system. Figure 2 depicts the layout of the AGV system used in the case study. The system contains ten P & D Figure 2. Layout of the AGV system for the case study.

12 1972 R. W. Seifert et al. stations, numbered 1 to 10, as well as seven intersection region nodes, numbered 11 to 17. In gure 2 each arc is labelled with its distance (in feet). This layout was used in Kay (1992) to demonstrate global-vision-based AGV system control, and it represents a portion of a former textiles research facility. The layout is divided into two departments with combined oor space of 2318 square ft. Five wide-angle cameras mounted 21 ft overhead are su cient to cover the unshaded region in the layout where the AGVs travel. The departments are connected by a ve-foot-wide passageway (intersection region node 12) and many of the aisles are narrow enough (5 ft) so that a single vehicle or pedestrian can block the aisle. These characteristics of the layout were designed to allow realistic routeing bottlenecks to occur as a result of congestion Formulation of main performance measure To evaluate the performance of the AGV system, we formulated a speci c performance measure referred to as the `relative delay of an AGV. Statistics are collected on the relative delay of an AGV when it reaches its assigned destination. To calculate the relative delay of an AGV, we compute the di erence between (1) the AGV s actual travel time to its current destination, and (2) the corresponding theoretical minimum travel time of the AGV as determined by its maximum speed and the physical length of the shortest-travel-distance path between the AGV s current origin and destination nodes. The relative delay of an AGV is used to compare the di erences in the system performance that are caused by applying di erent vehicle routeing strategies, since it is our objective to minimize the travel time between all pairs of nodes in the network. With the current system con guration and vehicle routeing strategy, the AGV system s throughput is the ratio of (1) the number of observed relative delays, which re ects the total number of completed assignments, to (2) the total simulated time for operation of the AGV system. Notice that the idle times for AGVs performing unloading and loading operations are automatically taken into account in this calculation of the number of transport requests serviced per unit of time. The relative delay experienced by an AGV goes up as we increase the tra c intensity by increasing the total number of AGVs in the system; and as the relative delay of an AGV increases, the throughput realized by the AGV system decreases. If we increase the level of system disturbance, modelled as pedestrians walking around the system and causing dependent arc disturbances, then we can further see that an increased level of system disturbance leads to an increase in the relative delay of the AGVs Experimental comparison of routeing strategies To evaluate the performance of the di erent vehicle routeing strategies implemented in the simulation model for selected numbers of AGVs and pedestrians in the system, we performed a formal statistical analysis of the results based on the method of common random numbers. Figures 3 and 4 depict 90% con dence intervals for the reduction in the expected relative delay of AGVs that is achieved by using the dynamic stochastic vehicle routeing strategy based on hierarchical simulation as compared to the static deterministic strategy based on the shortest travel-distance path. The results graphed in gures 3 and 4 are based on 10 independent replications each of length 480 min. We see from gures 3 and 4 that as the number of pedestrians in the system increases, the superiority of the hierarchical simulation approach becomes more

13 Evaluating AGV routeing strategies 1973 Figure 3. 90% con dence intervals on reduction in expected relative delay for static and dynamic stochastic AGV routeing strategies with no pedestrians. Figure 4. 90% con dence intervals on reduction in expected relative delay for static and dynamic stochastic AGV routeing strategies with 5 pedestrians. pronounced. Moreover, the average reduction in the relative delay of AGVs appears to be signi cant even if the level of system disturbance is fairly low. However, since the layout used in the study did not show a particularly high level of routeing exibility, it is not clear that these conclusions can be extrapolated to other AGV systems with di erent layouts.

14 1974 R. W. Seifert et al Economics of a global-vision-based feedback system Any potential bene t associated with using hierarchical simulation for dynamic vehicle routeing has to be weighed against the additional cost associated with providing system feedback information. In order to implement global-vision-based feedback for the layout used in the case study, a total of ve overhead cameras would be required. These cameras and their associated image-processing hardware represent additional xed costs that depend only on the total area to be monitored, not the number of AGVs travelling in the area. If there are relatively few pedestrians in the area of AGV travel in a facility, then vehicle self-congestion can be included in routeing decisions as long as vehicle locations can be transmitted to the controller; additional feedback information is unlikely to be cost e ective. With a larger number of pedestrians, global-vision-based feedback would still not be cost e ective if the AGV system has relatively few vehicles operating in a large area; for these systems, it would be most cost-e ective to place additional collision-detection sensors on board each vehicle. Global vision is most likely to be cost e ective for AGV systems having a relatively large number of vehicles and pedestrians. Kay (1992) developed a simple economic model to compare di erent methods of providing the information necessary for the control of free-ranging AGV systems. Two types of vehicles were assumed: a basic AGV, and a higher cost AGV equipped with additional on-board collision-detection sensors. Three di erent methods were considered: basic AGVs without global vision, basic AGVs with global vision, and AGVs equipped with additional on-board sensors. For each method, Maxwell and Muckstadt s (1982) transportation model was used to determine a lower bound on the number of vehicles required to meet a given transport demand. The total cost determined for each method included total vehicle costs plus, for global vision, the cost of overhead cameras. Both global vision and the use of additional on-board sensors were assumed to enable an AGV to travel faster, eliminating the need for the vehicle to slow down when traversing uncongested intersection regions. Since the number of vehicles required for each method depended on their average speed, which in turn depended on collision detection capabilities, the cost trade-o s between the di erent methods could be modelled. For the speci c operating characteristics of the AGV system considered in our case study, Kay (1992) found that the expected equipment cost for the global vision system (vehicles and overhead cameras) was 31% lower than the expected equipment cost for AGVs equipped with additional on-board sensors and 25% lower than the expected equipment costs for basic AGVs without a global vision system. The cost of each overhead camera required for global vision and the cost of additional on-board sensors for each vehicle were assumed to equal 25% of the cost of a basic AGV. Although these results are highly system-speci c, they show how the increased throughput of a global-vision-controlled AGV system can lead to a su ciently large reduction in the number of required AGVs so that the resulting cost savings substantially exceed the cost of the additional equipment required to support the global vision system. 6. Conclusions and recommendations In this research, we have demonstrated the potential advantages of dynamic AGV routeing strategies based on hierarchical simulation. The results of the case study indicated the superiority of this approach in comparison to the usual static vehicle routeing strategy based on the deterministic shortest travel-distance path.

15 Evaluating AGV routeing strategies 1975 However, these results cannot be generalized without much more extensive experimentation. Moreover, to enjoy the full bene ts one can gain from the dynamic vehicle routeing approach, we have to account for the capabilities of this approach during the design phase of the AGV system by including more exibility in AGV system design. Speci cally, the AGV system design should: (1) provide a su cient number of alternative paths that can be chosen so that critical bottlenecks can be bypassed dynamically; (2) allow for dynamic selection of P & D stations corresponding to the same work centre and (3) allow for varying degrees of sensing capabilities to provide information concerning the congestion status of the system, ranging from purely local, vehicle-based sensing to full global vision capabilities. Enhancements to our method for exchanging information between the main simulation and the subsimulations should enable the user to implement dynamic vehicle routeing strategies as a real-time decision support tool for controlling the operation of an AGV system. In particular, the use of shared memory may eliminate much of the input/output overhead required by our approach to hierarchical simulation of AGV systems. Finally, the underlying approach of hierarchical simulation naturally lends itself to implementation on parallel processors and might prove bene cial for a variety of applications. Acknowledgments The authors thank the editor and the anonymous referee for several suggestions that improved this paper. The work reported in this paper was supported by the Fulbright Commission, Germany. This work was also supported in part by the National Science Foundation under Grant DMI References Co, C. G., and Tanchoco, J. M. A., 1991, A review of research on AGVS vehicle management. Engineering Costs and Production Economics, 21, 35± 42. Eiger, A., Mirchandani, P. B., and Soroush, H., 1985, Path preferences and optimal paths in probabilistic networks. Transportation Science, 19 (1), 75± 84. Frank, H., 1969, Shortest paths in probabilistic graphs. Operations Research, 17, 583± 599. Gaskins, R. J., and Tanchoco, J. M. A., 1987, Flow path design for automated guided vehicle systems. International Journal of Production Research, 25 (5), 667± 676. Gaskins, R. J., and Tanchoco, J. M. A., 1989, AGVSim2Ð a development tool for AGVS controller design. International Journal of Production Research, 27(6), 915± 926. Gnedenko, B. V., 1968, The Theory of Probability (New York: Chelsea Publishing). Hodgson, T. J., King, R. E., and Monteith, S. K., 1987, Developing control rules for an AGVS using Markov decision processes. Material Flow, 4, 85± 96. Kaspi, M., and Tanchoco, J. M. A., 1990, Optimal ow path design of unidirectional AGV systems. International Journal of Production Research, 28 (6), 1023± Kay, M. G., 1992, Global vision for the control of free-ranging automatic guided vehicle systems. PhD thesis, Department of Industrial Engineering, North Carolina State University, USA. Kay, M. G., and Luo, R. C., 1993, Global vision for the control of free-ranging AGV systems. Proceedings of the 1993 IEEE International Conference on Robotics and Automation (Los Alamitis, CA: IEEE Computer Society Press), 2, 14± 19. Kernighan, B. W., and Ritchie, D. M., 1988, The C Programming Language, 2nd edn (Englewood Cli s, NJ: Prentice Hall). Law, A. M., and Kelton, W. D., 1991, Simulation Modeling and Analysis, 2nd edn (New York: McGraw-Hill). Maxwell, W. L., and Muckstadt, J. A., 1982, Design of automatic guided vehicle systems. IIE Transactions, 14, 114± 124.

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