Map-Route: a GIS-based decision support system for intra-city vehicle routing with time windows

Transcription

1 Journal of the Operational Research Society (2002) 53, #2002 Operational Research Society Ltd. All rights reserved /02 $ Map-Route: a GIS-based decision support system for intra-city vehicle routing with time windows G Ioannou*, MN Kritikos and GP Prastacos Athens University of Economics and Business, Athens, Greece This paper presents a Decision Support System (DSS) that enables dispatchers schedulers to approach intra-city vehicle routing problems with time windows interactively, using appropriate computational methods and exploiting a custom knowledge base that contains information about traffic and spatial data. The DSS, named Map-Route, generates routes that satisfy time and vehicle capacity constraints. Its computational engine is based on an effective heuristic method for solving the underlying optimization problem, while its implementation is developed using MapInfo, a popular Geographical Information System (GIS) platform. Map-Route provides very efficient solutions, is particularly userfriendly, and can reach answers for a wide variety of what if scenarios with potentially significant cost implications. We have implemented Map-Route in an actual industrial environment and we report on the experience gained from this reallife application. Journal of the Operational Research Society (2002) 53, doi: /palgrave.jors Keywords: vehicle routing; distribution/logistics; decision support systems; heuristics; GIS Introduction The vehicle routing problem with time windows (VRPTW) arises in a variety of pick-up and delivery applications and can be described as the design of optimal delivery= collection routes from one or several depots to a number of customers, within a pre-specified time window, at minimum cost. Many papers in the literature have addressed the VRPTW problem, and substantial research effort has been devoted in developing efficient algorithms for solving a variety of VRPTW problems. We refer to Bodin, 1 Laporte 2 and Gendreau et al 3 for surveys of the VR literature and appropriate pointers to relevant research efforts. Since the mid-1980s, significant work has been performed in developing computerized routing software systems. 4 Examples are: Geo-route, 5 Fleet-Manager, 6 micro-alto, 7 Greentrip Toolkit, 8 MACS-VRPTW, 9 Dynamic Route Guidance, 10 and DRIVE. 11 Apart from general and=or dynamic VRPTW software, there have been several industry specific approaches such as the ones summarized in Campbell and Langevin 12 for roadway snow and ice control, and Road-net, Truck stops, and Micro Vehicle Plan, in the soft drink industry. 13 Commercial software is also available for various applications (see eg, and *Correspondence: G Ioannou, Management Sciences Laboratory, Graduate Program in Decision Sciences, Department of Management Science and Technology, Athens University of Economics and Business, 8th Floor, 47A Evelpidon Street and 33 Lefkados Street, Athens , Greece. ioannou@aueb.gr The majority of the systems to-date have been of help to enterprises; however for most of them a number of drawbacks have been reported: (a) they are quite expensive, thus not preferred solutions for Small and Medium Enterprises (SMEs) the majority of users; (b) they are based on proprietary software as opposed to popular GIS platforms with standardized user-interfaces, effective personnel training, and guaranteed maintenance and system upgrades; and (c) they need to incorporate more realistic assumptions, and to improve solutions graphically. As a result, distribution, pick-up and delivery SMEs still need suitable tools for supporting complex decisions related to route planning, in order to provide high level service to their customers and optimize their resources. The objective of this paper is threefold: first, to propose a framework for addressing VRPTW for intra-city networks in a user-friendly and effective manner via efficient solutions of the underlying optimization problem. Second, to develop a prototype DSS based on: (i) a popular GIS platform; and (ii) an optimization method coupled with a knowledge base. And third, to demonstrate the applicability of the approach through the results obtained from the implementation of the DSS to an actual industrial environment. The proposed DSS can assist logistics operations in a number of ways, eg: (a) enhance daily operational tasks of dispatchers schedulers; (b) provide flexibility in solving VRPTW by generating alternative solutions and reformulating problem conditions (eg, editing the underlying transportation network, adding or removing customers, defining alternative scenarios etc.), while keeping a good eye on the geographical reality of

2 G Ioannou et al Map-Route: a GIS-based decision support system 843 the problem; and (c) offer interactivity, ie, allowing users to employ visual techniques to formulate reformulate problems and derive solutions that can be easily implemented. The remainder of the paper is organized as follows: first, we present the architecture of our Decision Support System (DSS) and its constituent elements. Then we provide the overall framework of Map-Route and identify the interaction between all of its components. The report on an industrial application follows, and the conclusions of our work are finally presented. Map-Route architecture Map-Route is specifically designed for vehicle fleet routing for deliveries within a compact large city street network, rather than general VRPTW. It consists of four basic components, which are presented in detail below. Databases of Map-Route Map-Route s spatial database includes a digitized map with all relevant locations (depot and customers) and underlying network (streets, roads, intersections, etc.). The customer database includes, for each customer, the node identification number, the demand, and the time window restrictions and service time. The nodes database includes, for each node, the identification number and coordinates. Finally, the street database includes, for each street segment, name, length, and address ranges for both sides. The data files of Map- Route can be changeable or permanent. The former relate to the properties of the underlying transportation network and the coordinates of the depot location node. The latter may be modified by the scheduler through our DSS by, eg, inputting a new scenario via tables, entering new customers into a given problem, removing customers from a scenario, inputting a new scenario using the map under consideration, and entering data related to the problem using the browser table. Computational engine of Map-Route The computational engine of Map-Route can include any heuristic or mathematical programming method for solving the VRPTW. The selected method is very important since it determines the applicability of the solution scheme in reallife situations. The key factor for the appropriate selection is the efficiency of the method and its ability to provide in very short times high-quality solutions. In our approach, we use IMPACT, 14 the basic steps of which are: Algorithm IMPACT Step 0: Initialization. Read the number of customers, the vehicle capacity, the inter-customer and depot customer distances (or times, routing costs) and the earliest and latest service times (time window) for each customer. Step 1: Select a seed customer to start a route, finding the farthest customer from the depot. If there is no non-routed feasible customer to start a route, go to Step 6. Step 2: Find the feasible non-routed customer u that minimizes a composite criterion Impact(u), which includes functions of the relationship between the arrival time to customer u and the lower bound on the service time of u, the impact of customer s u insertion on non-routed customers, and the impact of customer s u insertion on customers already routed within the route under construction. The search procedure is as follows: Step 2a: Examine all possible feasible insertions of customer u into the current route. For each feasible insertion, calculate the criterion function Impact(u). Select the insertion location that results in minimum Impact(u) for this customer. Step 2b: Repeat Step 2a for all feasible non-routed customers. Step 2c: Select customer u with minimum Impact(u). Step 3: Insert the selected customer u, to the best insertion location on the current route (see Steps 2a and 2c). Update the route and set u as a routed customer. Step 4: If there are non-routed customers that are feasible for insertion into the current route, return to Step 2; otherwise proceed to Step 5. Step 5: If all customers have been scheduled, terminate. Otherwise, go to Step 1 initiating new route. The algorithm terminates by providing the number of routes (equal to active vehicles), the customers that are assigned to each vehicle, the sequence in which customers are visited, and the total time distance cost of the solution. IMPACT is very efficient and provides results comparable to meta-heuristics at a fraction of the computational effort. For a detailed description of IMPACT and the computational tests that support its effectiveness, the reader is referred to Ioannou et al, 14 while Table 1 provides a comparison of IMPACT with several heuristics (I-1, PARIS, HE) and metaheuristic (GRASP, Tabu search TABU-A and RTS, and genetic algorithms GENEROUS-20) methods to illustrate its efficiency ( * indicates that IMPACT outperforms other methods for the classical data sets R1, C1, RC1, R2, C2, and RC2 of Solomon 15 ). User-interface of Map-Route Map-Route s user-interface has been developed using the Map-Basic programming language and is based on pulldown menus to provide functionality related to solution methods, problem initialization (eg, defining the speed of

3 844 Journal of the Operational Research Society Vol. 53, No. 8 Table 1 Comparison between literature heuristics and new heuristic on average number of routes Data set I-1 PARIS HE GRASP TABU-A RTS GENEROUS-20 R1 * * * * * R2 * * * * * * * C1 * * * * * * * C2 * * * * * RC1 * * * * * * RC2 * * * * vehicles), data input, formation of local networks, design of accurate vehicle routes, etc. Furthermore, it allows the display of spatial maps allowing the user to zoom on a part of the map and evaluate the suggested solution or generate alternative solutions using logical inference. The user manuals of MapInfo 16 provide all the necessary functionality information. Knowledge base of Map-Route Deriving solutions that follow actual road networks and complying to traffic patterns that favour main city arteries, large streets and roads with light traffic and open structure is a very difficult task, especially when optimization approaches are employed. The latter are very sensitive to the route segments that characterize the underlying road street network and cannot handle logical attributes such as those described above. The solutions they produce comprise segments that may not be feasible in actual route planning, or may not be preferable to drivers. The above problems may be alleviated either by direct user interaction, ie, changes in the route structure that are performed manually by experienced users, or by appropriate knowledge bases that capture the logic in which such changes are made. The first approach requires high level of user involvement in the solution process and is very time consuming for large problems, since the user has to examine all parts of the network and make the necessary changes. The latter approach requires a strong set-up phase in which roads are coupled with specific prioritization attributes and routes are examined using a knowledge base containing all these attributes or additional information concerning preferences. The structure of the knowledge base we propose is simple: Rules and attributes are assigned to road segments and inference logic is designed in order to transform an optimisation solution into a feasible preferable solution with minor cost implications. The rules can have, eg, the following forms relevant to street characteristics, timerelated traffic and date peculiarities, respectively: IF MULTILINE IS {main, regular, narrow} street then label ¼ {PREFERRED, NONE, LOW} IF MULTILINE IS traffic loaded at time t then label ¼ LOW IF MULTILINE IS non-preferable on date then label ¼ LOW Labels characterize the priority for using a particular route segment (ie, segments with priority LOW will be used only when necessary to guarantee the connectivity of a sub-network). The rules are exhaustive for all appropriate road segments and time- and date-related information, and are implemented in conjunction with the Map-Basic routines using the experience of drivers and planners schedulers. The priorities associated with road segments are directly used when forming a transportation network over which vehicles are to be routed. 17 Solution framework The proposed solution framework follows a typical four-step process: (a) solve an approximation of the VRTPW using Euclidean distances; (b) break the region down into subnetworks, each corresponding to a vehicle route, and generate a travel path over each sub-network using shortest paths between customers, while preserving the order of customers in routes; (c) modify the solution via the knowledge base rules to better approach the actual vehicle paths; and (d) perform manual modifications, if necessary. The solution process iterates among these steps until a good solution is obtained. Subsequently the user accepts the solution or modifies some of its attributes in order to provide the final set of routes. The user can also modify problem parameters and reapply the four steps if the system proposed solution is not satisfactory. Visualization can play a critical role in this process, and the GIS platform is very helpful in this direction. Figure 1 provides an overview of Map-Route s infrastructure and organization. MapInfo is the centre of the approach. Databases include digitized maps and data concerning customers and depot. The knowledge base is represented as a database that is external but connected to MapInfo via an appropriate API. The user can interact with the spatial data and also provide adjustments graphically to the solutions provided by the computational engine. In Figure 1, lines connect sequentially evoked components, while arrows provide the direction of each sequence. Map-Route phases As mentioned before, Map-Route involves four interacting phases. During the first phase, the VRPTW is solved for a network where the customers and the depot are connected

4 G Ioannou et al Map-Route: a GIS-based decision support system 845 Figure 1 The architecture of Map-Route. with straight lines. This enables the solution of problems with a large number of customers, in short computational times. Standard MapInfo tools estimate the Euclidean distances between customers and between customers and the depot. During Phase 2, for every route of Phase 1, a connected sub-network is constructed by selecting areas (road sections) adjacent to the Euclidean routes. Sub-networks are adjusted through MapInfo tools that use proximity criteria for actual route segment inclusion. Furthermore, distances are reevaluated based on the priority rules of the knowledge base. On the new networks, accurate routes can be determined according to the following steps: Step 1: Renumber the nodes of the selected sub-network (assigning 1 to the depot) Step 2: Run the Floyd s Shortest Path algorithm 18 between customer locations (stops) and depot, in the same order as in the solution of Phase 1 Step 1: Display the final accurate route on the original map The above steps can be repeated for each sub-network, leading to accurate routes that incorporate actual road segments. Note that in Phase 2, the distance between customer locations is increased, since the multi-lines of Phase 2 replace the straight lines of Phase 1, and violations of customers time windows may occur. This problem can be addressed by: (a) selecting sub-networks more adjacent to specific trips; and (b) tightening time windows of specific customers and iterating the whole process of the two phases. Both approaches have been examined, and the results showed that multiple iterations with tighter time windows are preferable. 19 It is important to note that the two-step approach of determining Euclidean routes and transforming them into actual street segment-routes may not be necessary or even efficient for general VRPTW, especially in the case of large inter-city routing with significant obstacles and constraints, where severe problems may arise. Nevertheless, for a compact intra-city network such as the one we are handling via Map-Route, the approach can smoothly work. In Phase 3 the knowledge base rules are evoked and the solution is transformed to approach better the road segments employed by the vehicles. This is accomplished by feeding the solution to the knowledge base via the MapInfo interfaces. When Phase 3 is completed, the actual road network is determined based on proximity criteria and preferences residing within the rule constructs. Finally, Phase 4 is a pure user-driven phase. The user interacts with MapInfo via the solution of Phase 3 and provides final adjustments necessary to derive the schedule of each vehicle. Figure 2 illustrates the four-phase approach inherent in the Map-Route logic. Note that this is a discrete and time-including representation of the Map-Route architecture of Figure 1. The elements of each Phase are grouped in shaded boxes, while the sequence of the approach is depicted through the directional arcs that connect databases, applications, results and user adjustments. Before we proceed to the implementation aspects of Map- Route, we should mention that the optimal solution to intracity routing problems that we consider in this paper might include more than one daily trip per vehicle. However, the common policy in all distribution companies we have interacted with was to load only once the vehicles at the warehouse and perform all remaining activities the rest of the day. Furthermore, reaching near-truck load per vehicle was a key performance indicator. Thus, we did not proceed in exploiting this potential cost-saving application and constrained our DSS into single daily loading and single routes per day per vehicle. Nevertheless, an extension to

5 846 Journal of the Operational Research Society Vol. 53, No. 8 Figure 2 The Map-Route solution flow. Map-Route is possible through reduced time available per day, a factor that could be interactively modified within the DSS to produce various solutions. Map-Route implementation Map-Route has been implemented on a Pentium PC. The core of DSS has been written in Map-Basic, and the algorithms for the VRPTW in Fortran, appropriately integrated into MapInfo. The knowledge base uses a Lisp inference engine and is also integrated with MapInfo. The solution provided by Map-Route is depicted on a real city map, and generates informative output for the vehicle driver, while enabling the evaluation of alternative routes. It is important to restate the significance of user involvement in the solution procedure. No matter how, extensive and complete the knowledge base is, or effective and comprehensive the optimization solution is, the final set of routes is either accepted or modified by the scheduler planner, whose experience and flexibility in dynamic daily adjustments of the problem parameters is irreplaceable. Industrial application Background The company for which Map-Route was developed is a wholesaler and logistics service provider that supplies multiple packaged goods and beverages to a large number of local small supermarkets and other small retail outlets throughout the Central Athens area, in Athens, Greece on a daily basis. The company operates its own small-vehicle fleet from a central warehouse located at Pireus (noted as PIRAIVS at the map of MapInfo provided later in this section) Street, a main street connecting Pireus to Omonia Square in the centre of Athens. The company owns 26 delivery vehicles, which are operated by certified drivers. The overall fleet size though, necessary for satisfying all customers was approximately 35 vehicles, before the implementation of our DSS; thus, the company employed vehicles owned by individuals on a need-basis, a fact the created additional costs and resulted in severe problems with respect to quality of customer service and adherence to order fulfilment goals. The number of customers varies from 435 to 680, depending on the day of the week and the period of the year (higher number of demand points during the summer season, when additional points of sale are open to service the large tourist population that visits Athens). The customers are dispersed throughout central Athens, and are located at main arteries of the city (eg, Panepistimiou or Stadiou Street) as well as at small streets near the archaeological sites and particularly vibrant or densely populated city neighbourhoods. Figure 3 illustrates the distribution of the customer set on the map of Athens (circles), and the depot (square). Since a just-in-time approach is promoted as the competitive advantage of the company, the replenishment of goods follows daily orders from each customer; these orders may

6 G Ioannou et al Map-Route: a GIS-based decision support system 847 Figure 3 Customer distribution and depot location on the map of Athens. be zero for some Stock Keeping Units (SKU) in a day. Nevertheless, the overall demand is relatively constant, apart from peak seasons, and especially during the summer where beverage consumption increases significantly. The daily iterative operations start with customer orders, which are finalized every evening, and can be satisfied by the inventory held at the warehouse. Inventory availability is guaranteed by the large safety stock held for each SKU. The customers are geographically dispersed within a distance radius that allows for demand to be satisfied through daily deliveries, as shown in Figure 3. In addition, the time interval during which the delivery has to take place (time window) is also known (fixed for each customer according to a contract). The delivery process is performed as follows. Products are loaded on vehicles at warehouse docks up to (or sometimes below, according to customer requests) capacity and they are transported to the customers locations. At each location, quantities that equal customer demand for each SKU are unloaded, and paper work (shipping documents, bills and invoices) is filled and exchanged; this takes approximately 5 min. Then, vehicles travel to subsequent customers where the process is repeated, until all deliveries have been performed and return to the depot for the following daily cycle. It is important to note that before Map-Route s implementation, the sequence in which a vehicle visited customers was not determined when loading at the depot; drivers responsible for a particular area customer set were making sequencing decisions. This had a significant effect of the compliance to time windows, and affected cost, customer satisfaction and quality of service. Map-Route set-up To generate the problem within MapInfo, we have started with appropriate maps of the Central Athens area, and created 5137 node-objects for the 8231 road segments of the underlying map that model approximately 3000 different streets and covering almost 500 km of road network, using the configuration tools of MapInfo. This initialization is required for any subsequent task. Figure 4 provides a zoomed view around the depot of the road network modelled in MapInfo for the application. To input the customer location coordinates and the data concerning time windows, we used appropriate files for data entry into MapInfo. Furthermore, we have created special MapInfo screens to be available to the planners for adjustments, deletions and additions of customers and time windows. Figure 5 provides a sample screen that was constructed to give multiple points of access to the user (both graphical and in tabular form). The road segments (black lines in Figure 3) were characterized as preferred, unacceptable or non-labelled, and this information was included in the knowledge base. Filling up the knowledge base with rules and priorities was the most daunting and time-consuming task of the system

7 848 Journal of the Operational Research Society Vol. 53, No. 8 Figure 4 The zoomed map around the depot. Figure 5 Data manipulation screen.

8 G Ioannou et al Map-Route: a GIS-based decision support system 849 set-up process. We used data from the Greek Ministry of Transportation and Communications concerning traffic patterns and time-info for various dates of the year and times of the day. Furthermore, we interviewed the drivers of the company for routing preferences and considered their answers for labelling road segments. Drivers were requested to provide the most commonly used streets and estimates of travelling times at these segments during peak and off-peak hours. Finally, for each unacceptable road segment, we run a special MapInfo procedure to derive via proximity measures a preferable corresponding road segment, and included it in the knowledge base. It is important to note that the experience of drivers conflicted some times with official data; however the company s management insisted on adhering to drivers preferences, as more reliable information concerning actual routing paths. Apart from the initial setup of the knowledge base, we have provided screens within MapInfo, which allow users to adjust the labels according to new realities, as the system life cycle evolves, or on a daily basis, in line with expectations concerning congestion, road blocking (strikes and marches in the centre of Athens is commonplace), etc. The computational engine of Map-Route, ie, IMPACT, was integrated in the MapInfo menu. For the particular instances in the industrial case, IMPACT required less than 30 s to terminate (for the larger examples of more than 600 customers). We have also incorporated Floyd s algorithm within the DSS. Floyd s implementation uses dynamic tables in order to provide fast the optimal solutions; for the particular instances in the industrial case, the algorithm took less than 40 s to terminate, even in cases where the sub-network included a large number of node-objects due to alternative route segments induced by the knowledge base. The DSS in operation At the start of a shift, customer demand is already into the system and Phase 1 of Map-Route is initiated. The result is the sequence of customers visited by each vehicle based on Euclidean distances, which are automatically calculated by MapInfo. Euclidean routes appear on the screen with lines connecting customers and depot; such a screen from the actual application is provided in Figure 6. Note that the user can make adjustments to time windows, demand and customer attributes (existence, location, etc.) before running IMPACT, if necessary, through appropriate selections in the MapInfo menu (that invoke the previously discussed screens). Subsequently, the user proceeds to the second phase of Map-Route to determine the actual road path of each vehicle using the shortest paths on the real road network. The procedure is repeated for each vehicle and is as follows: An initial sub-network is formed through the knowledge base rules of proximity; this sub-network, which includes various road segments, is expanded or adjusted by the user that can include additional segments or remove some segments based on experience and daily data. Given the sub-network, a routine incorporated in MapInfo produces the necessary shortest path matrix. Figure 7 presents a sample sub-network associated with one route of the Euclidean solution of Phase 1 presented in Figure 6 (includes all route segments depicted by the thick lines). Given the distance matrix, the next step is to apply Floyd s algorithm to determine the actual vehicle paths by invoking a resident MapInfo routine for calculating shortest paths and displaying the results on the MapInfo interface. Figure 8 provides the actual road path for the sub-network of Figure 7, and Figure 9 a zoomed view. The procedure is repeated for each initial Euclidean route of Phase 1. This loop constitutes the most time consuming part of the application, since it is directly linked to the number of vehicles employed. If this number remains at the present level (ie, order of 30 vehicles), then it is possible to complete the routing procedure and derive schedules for each vehicle in less than 1 h. This time is acceptable, and allows the company to smoothly employ the DSS. However, future plans include the addition of several more SKUs and customers locations, a fact that would add further delay to the application. Thus, we were asked to automate a combined Phase 1 2 of Map-Route. This provided full solutions (actual road networks for all vehicles) that could be further examined and improved a posteriori by the users, if necessary. The automated procedure allowed the completion of the daily tasks in less than 0.5 h. However, planners who desired their direct intervention and drivers who felt that their flexibility was compromised did not deem the total automation appropriate. Thus, the operational version of Map-Route runs with individual route construction and adjustments, and performs the routing procedure sequentially for each vehicle. The results of Map-Route are provided to the drivers, who are requested to follow the prescribed routes (customer sequences and road segments) in their daily delivery schedule. Appropriate forms that include the sequence of customers to be visited and the expected time of arrival at each customer s location are employed to check the delivery schedule; customers are required to sign the form when paperwork is exchanged. Results and discussion of the application Map-Route was deployed to two PCs of the company, located at the office of the warehouse. The DSS was standalone, ie, it was not connected to any other Information Systems (eg, the warehouse and inventory management systems). Two planners, who were involved in all stages of the finalization deployment of the DSS, were responsible for data entry and running Map-Route on a daily basis. The system was tested using demand data from previous time periods and covered all peak seasons and several traffic loading scenarios. The key result that impressed the company s

9 850 Journal of the Operational Research Society Vol. 53, No. 8 Figure 6 Sample Euclidean routes. Figure 7 A sub-network for a route.

10 G Ioannou et al Map-Route: a GIS-based decision support system 851 Figure 8 The accurate route. Figure 9 A zoomed view of the accurate route.

11 852 Journal of the Operational Research Society Vol. 53, No. 8 management was the possibility of serving all customers even during the peak seasons under heavy traffic loading conditions. This was attributed to the fact that optimizing the routes at the planning stage was indeed better than the intuitive schedules followed by the drivers. The second aspect of Map-Route that was in-line with the company s expectations was the simplicity of the user-interface and the power that the DSS left in the hands of the users, who were key decision-makers in the daily operations of the logistics plan. The third positive reaction came from the drivers, who were asked for a trial period of one week to follow the schedules produced by Map-Route. They were all able to finish their delivery routes on-time and served the customers within the contractual time windows. Thus, even the drivers bought-in the new application. Apart from the positive views above, there were some negative comments by some drivers that apart from full-time employment also owned their own vehicles that used to rent to the company during peak seasons. Nevertheless, the obvious savings that the DSS offered to the company overcame their negative reactions. Table 2 provides a summary of Map-Route implementation details. It is evident from the results presented in Table 2 that minimal investment is required to deploy Map-Route, and the cost is affordable even for SMEs. Furthermore, for the particular application, Map-Route resulted in effective route planning by allowing the use of the existing fleet of the company (26 vehicles), even during peak season. The quality of the solution can be inferred by the significant reduction of both violated time windows and lost sales; note that these two percentages are different due to the acceptance of some off-time window deliveries by several customers. Finally, user training on MapInfo and the Map-Route components was straightforward and was completed during the system development (since the two users were involved from the initial development stages). Unfortunately, we did not have access to commercial software in order to compare our results. After the full-scale deployment of Map-Route, several additional functionalities were requested for implementation. Most of these add-ons are related to reports that help reviews and managerial control=decision making. All requests were implemented using standard MapInfo tools and for each route, Map-Route can now generate various reports that can be accessed by the user interactively. Figure 10 provides such a report that includes the components of all routes with respect to arrival times at customer locations, waiting times until service begins, and demand, as well as all the names of the streets in the sequence that vehicles visit them. There are several such reports that MapInfo can generate, based on which the user can modify the solution, alter the problem parameters and rerun Phases 1 and 2 of Map-Route, or return to Phase 2 and reconfigure the set of road segments produced by the knowledge base in order to derive better solutions. A final point that should be noted relates to the distances times produced at the various phases of Map-Route. The distances between delivery points would generally be different when comparing solutions between Phase 1 (straight lines), Phase 2 (accurate routes), or Phase 3 (user adjustments). These differences may cause violations of time window constraints, which can be overcome by a combination of the following rules: (a) select another sub-network adjacent to the route of Phase 1; (b) move earlier the start time of scheduling; (c) reduce the length of the time window through dummy time windows in the first phase; and (d) split the problem into smaller ones. Thus, the selected sub-network plays an essential role in the feasibility of the solution. Conclusions In this paper we developed a DSS for the VRPTW for intracity fleet planning. Map-Route, is based on the popular GIS platform MapInfo instead of proprietary software, and is at the right cost for SMEs. The computational engine is IMPACT, a heuristic that provides high quality results in short computational times, coupled with Floyd s shortest path algorithm and a knowledge base to allow for efficient transformation of the Euclidean solutions into effective trips on the actual street network. The DSS is developed with a Table 2 Summary of DSS implementation results Parameter Status before Map-Route implementation Status after Map-Route implementation Required number of vehicles Optimized routes No Yes Violated time windows 20% <5% Lost sales 10% <2% IMPACT running time (>600 customers) <30 s Final route construction (time) Ad hoc (Driver) Near optimal (<1h) Cost of two MapInfo user licenses C= 6000 Cost of digitized maps (city of Athens) C= 5000 Software maintenance cost (yearly) 12% of licences Cost of solution algorithms C= 0 (freeware) Training C= 1000

12 G Ioannou et al Map-Route: a GIS-based decision support system 853 Figure 10 Map-Route report on the actual routes. user-centric philosophy, bringing vehicle routing algorithms into the hands of planners schedulers, whose vast experience and common sense can be the determinant success factors for the GIS-based DSS implementation in real environments. The experiences from the deployment of Map-Route to an actual case in the Greek market were presented to demonstrate the phases of the methodology inherent in the DSS and reveal several open issues that need to be handled on an exception basis by the users and=or the knowledge base. Through this case, the flexibility and ease of adaptation of the DSS were also illustrated. Via the four-phase approach offered by Map-Route, a user can easily find a schedule as well as alternative schedules on intra-city transportation networks for VRPTW. The use of visualization along with the availability of GIS can help users in making improved decisions when solving real world routing problems, which are everyday reality in logistic operations, and become even more critical due to the expansion of third-party logistics. Thus, developing and deploying effective DSSs is a key prerequisite for the successful operation of logistics groups. Further extensions of Map- Route include: (a) integrating modern meta-heuristics to further improve the quality of the final solutions; (b) enhancing the approach to handle inter-city networks with additional constraints and route complications; and (c) integrating the DSS with warehouse management systems (eg, MANTIS) or Enterprise Resource Planning Systems (eg, SAP or Oracle Apps) for seamless information technology applications to distribution problems. Acknowledgements The authors would like to thank the two anonymous referees for their constructive comments and pointers to archival literature that helped improve the content and the presentation of the paper. References 1 Bodin L (1990). Twenty years of routing and scheduling. Opns Res 38: Laporte G (1992). The vehicle routing problem: an overview of exact and approximate algorithms. Eur J Opl Res 59: Gendreau M, Laporte G and Potvin J (1997). Vehicle routing: modern heuristics. In: Aarts E and Lenstra JK (eds). Local Search in Combinatorial Optimisation. John Wiley & Sons: Chichester, UK. 4 Keen PB (1998). Spatial decision support systems for vehicle routing. Dec Support Syst 22: Lapalme G, Rousseau JM, Chapleau S, Cormier M, Cossette P and Roy S (1992). Geo-route: a geographic information system for transportation applications. Commun ACM 35: Basnet C, Foulds L and Igbaria M (1996). Fleet-Manager: a microcomputer-based decision support system for vehicle routing. Dec Support Syst 16: Potvin JY, Lapalme G and Rousseau JM (1994). A microcomputer assistant for the development of vehicle routing and scheduling heuristics. Dec Support Syst 12: Concialini A and Hasle G (1997). The Greentrip toolkit sustainable transportation via intelligent routing.

13 854 Journal of the Operational Research Society Vol. 53, No. 8 9 Gambardella LC, Taillard E and Agazzi G (1999). MACS- VRPTW: a multiple ant colony system for vehicle routing problems with time windows. In: Corne D, Dorigo M and Glover F (eds). New Ideas in Optimization. McGraw-Hill: London, UK, pp Wahle J, Annen O, Schuster C, Neubert L and Schreckendberg M (2001). A dynamic route guidance system based on real traffic data. Eur J Opl Res : Savelsberg M and Sol M (1998). DRIVE: dynamic routing of independent vehicles. Opns Res 46: Campbell JF and Langevin A (2000). Arc routing applications for roadway snow and ice control. In: Dror M (ed). Arc Routing: Theory, Solutions and Applications. Kluwer: Amsterdam. 13 Golden BL and Wasil EA (1987). Computerized vehicle routing in the soft drink industry. Opns Res 35: Ioannou G, Kritikos M and Prastacos G (2001). A greedy lookahead heuristic for the vehicle routing problem with time windows. J Opl Res Soc 52: Solomon MM (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Opns Res 35: MapInfo (2000). MapInfo Professional: User s Guide. MapInfo Corporation: Troy, NY. 17 Taylor MA (1990). Knowledge-based systems for transport network analysis: a fifth generation perspective on transport network problems. Transport Res A 24: Cormen TH, Leiserson CE and Rivest RL (1992). Introduction to Algorithms. MIT Press: Cambridge, MA. 19 Kritikos MN (1997). Mathematical models and algorithmic approaches for transportation problems using Geographical Information Systems. PhD dissertation, Athens University of Economics and Business. Received September 2001; accepted January 2002 after one revision