Algorithm for Time-Constrained Paths to Deliver Services

Algorithm for Time-Constrained Paths to Deliver Services

Raija Halonen

Olli Martikainen

Department of Information Processing Science University of Oulu Oulu, Finland [email protected]

Pikesta Oy Lönnrotinkatu 30 D, 4 krs Helsinki, Finland [email protected]

Valeriy Naumov

Ye Zhang

Pikesta Oy Lönnrotinkatu 30 D, 4 krs Helsinki, Finland [email protected]

PIKE Lönnrotinkatu 30 D, 4 krs Helsinki, Finland [email protected]

Abstract—In logistic services there often are pick-up and delivery time window constraints specified by logistics customers. Our study was to find a solution to manage huge amount of data to enable data processing when calculating shortest or most productive routes for vehicles. The solution allows different kinds of restrictions for the application area and it is adaptable in several services such as healthcare offered at home, postal services or carrying schoolchildren. Design science research was applied to build the output that relied heavily on mathematical approach. Logistic services; time-constrained path; shortest path; virtualization; time-window

I.

INTRODUCTION

The purpose of our study was to analyze the old problem of route optimization especially in cases when time is limited or otherwise pre-defined. The topic has connections with the famous ‘travelling salesman problem’ that at the time of the study had 234000 hits in Google.com. Christofides [1] was seeking a solution and he described a heuristic algorithm for the problem. Our study approaches the problem with a case that poses challenges with length of the route, number of customers, limited time-windows and capacities of the vehicles. Based on known algorithms we present a new solution, which is an extension to a time window constrained case. The motivation for our study origins from the lack of success in cases when there are several constrains that limit the possibility to identify the most productive or shortest or quickest way to deliver services in earlier defined areas. The constraints can be such as required or limited space and load capacity in the vehicles that are used. Our study reveals a solution that takes into account multiple services and vehicles in service, each service having their own given time intervals; and each vehicle having their capacities.

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So far, academic research has introduced several solutions in different environments to solve the old problem of routing in delivering services. Already Herstein [2] talked about the ‘travelling salesman’ problem and its potential solution that would lead to solving several other problems, too. Later, Sniezek and Bodin [3] note how most algorithms written to solve vehicle routing problem are focused on minimizing the total travelling time. Therefore their response is to use the most complex cost models when solving the problem. The travelling salesman problem has been an issue especially for postal business as verified by e.g. Bruns et al. [4], and Sebastian [5]. In addition, garbage disposal with its rollon-rolloff vehicles have fought with routing problems [6]. The problem has been solved in several ways, e.g. Sungur et al. [7] developed a heuristic called ‘Master And Daily Scheduler’ that they report to improve the similarity measure at the cost of increased time, thus adding the productivity of courier work. In our study we asked: How to identify the most productive route to deliver services in cases that are limited with time windows and delivery means? To find out the answer an algorithm called TCROWID was developed. The algorithm is able to calculate paths that need to be re-formed in limited time, and thus it has potential to be used also after the delivery shift is initiated. 3D virtual map is needed to provide information about the geography and streets and buildings. The developed solution is based on the TCROWID and software modules that carry out the required calculations. Design science research [8, 9] was applied to solve our research problem. Design science research appeared to be the most suitable because the research problem was significant and it required a viable solution that would help the organization to carry out its business more efficiently. Moreover, the solution was to be applicable in any other context that struggles with time-constrained routing problems.

II.

EARLIER KNOWLEDGE

The ‘travelling salesman problem’ is one of the trickiest problems that still in the 2010’s interests researchers as verified by 11,700 hits in Google Scholar. More than 60 years ago Herstein [2] pointed out the role of mathematics when seeking for efficiency and productivity especially in tasks that are related to the number of people acting under changing conditions. The travelling salesman problem is often referred to vehicle routing problem as was done by Sniezek and Bodin [3]. Instead of minimizing total travel time in solving the problem Sniezek and Bodin adopted use of more complex cost models. They built a function called the ‘Measure of Goodness’ to be used as a criterion when solving the problem. In their paper they present a dilemma of stops and the depot added with defined limitations. They want to find a set of routes to serve the known stops. They have identified two solutions and they need to know which is better. To find the answer they analyze the case with two settings: a homogeneous fleet and a non-homogeneous fleet. Sniezek and Bodin [3] draw to the conclusion that complex cost models allow route generation and analyzing of the solutions, but that they will give space for more research on the tradeoff between overtime and increased capital cost. Another approach was adopted by Baker and Ayechew [10] who remarked issues related to the vehicles such as their limit on the distance travelled and their weight limits. In their study Baker and Ayechew apply a generic algorithm (GA) that typically consists of a population of solutions that are used with the help of reproductive processes. They decided to apply two steps to keep their research setting manageable: consecutive customers were likely to be served by the same vehicle; and vehicles operated in about the same region for all population members. With this approach they applied the general reproductive process to the target population and generated solutions to share certain route structures with their parent structures. Based on their study Baker and Ayechew [10] believe that GAs are effective approaches to solve the vehicle routing problem. Vehicle routing problem is an issue especially in garbage collection as described by Baldacci et al. [11]. The garbage collection vehicles are typically large and the spots they visit are shopping centers, construction sites and neighborhoods where people are present. In their paper Baldacci et al. delineate that service times are scheduled according to the demand of the customers and other limitations such as size and weight of the vehicles are depending on the trailer they carry. Baldacci et al. propose a solution that they believe is adaptable to manage with other limitations such as time windows, capacity constraints or site dependencies. Routing was an issue also in Canada as reported by Duhaime et al. [12]. They analyzed how returnable containers were used by Canada Post and its customers. It appeared that the inventory balance between supply locations and demand locations caused problems and that it was challenging to produce benefits for both customers and Canada Post. To get a solution for the problems a value analysis was done and time lag between receiving empty

containers and returning full containers. The analysis also revealed the different tasks related to the full and empty containers. Duhaime et al. [10] conclude that the processes had to be changed before positive effects would be visible in the Canada Post case. In general, the delivery of services has been in focus during the past years and it continues to be a concern. Sebastian [5] investigated postal logistics especially from the letter mail and parcel mail point of view. He highlights the reduction in transportation and delivery time in his study and also addresses the need to minimize costs but keeping service quality. Sebastian lists four stages in a classical multistage distribution network: production sites, central warehouses, regional warehouses, and customers. The issue is to select the right nodes that will form the distribution network from the source (production site) to the destination (customers). From the postal logistics view, Sebastian lists mail collection (stage 0), long haul transportation (stage 1), distribution (stage 2), and delivery, also called The Last Mile (stage 3). The statistics from his cases realize the vast number of data: 40 million destinations, 72 million letters, 82 sorting centers, 3300 delivery stations, and 12000 branch offices. In all, the developed models act as prototypes of decision support systems in the challenging context of large postal services. Knowledge discovery and social network analysis benefits from low-cost paths as explained by Maier et al. [13] who developed an index of network structure that was built on the shortest-path tree, offering better performance than other indices. The aim of a network structure index was to provide applicable estimates of distances to allow efficient navigation. Maier et al. list four applications they performed to verify their research result, namely navigation, diameter approximation, centrality calculation, and clustering. In all applications they used three differing data sets. Finally Maier et al. [13] note the costs to work with large networks and they propose more research about network structure index that would be able to handle directed graphs. According to Densham [14], geographical information systems have been used to assist decision makers already for decades. Especially the way how expert knowledge is used to model procedures into decision support systems has gained attention. Densham reminds that such expert knowledge should contain environmental knowledge, procedural knowledge and structural knowledge. With time running, huge amounts of existing data have led to problems in analyzing the data and the role of data mining has increased especially in relation to decision support systems as reported by Rupnik et al. [15]. Recently Shcherbina and Shembeleva [16] published their research concerning decision making in the context of tourism planning and management. The authors point out the vast amount of problems caused by complex and versatile aims and goals in the business or tourism. Based on their literature study they list tour routing, reservation models, and planning urban recreational facilities as main topics to be considered when solving the problems in the tourism business. They also argue that pertinent decision making

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processes cannot be applied without utilizing newest ICT and operations research approaches. Besides tourism, healthcare is a good example of the need to seek for more efficiency and productivity. Halonen et al. [17] reported about improvements in service processes in healthcare, and they described how important it is to evaluate existing service processes and – if needed – modify the processes. In their study Halonen et al. utilized a special method called 3VPM [18]. Their study revealed that carefully analyzed processes can be modified to be more productive and that the improvement be as considerable as 35 %. Moreover, ability to use existing knowledge is essential for successful business as reported by Sedera and Gable [19]. To achieve the desired success, the required knowledge should be created, transferred, stored and applied. Sundgren [20] defines public information systems to be available for public use. Based on his study he elaborates that public information systems - among other tasks - provide services to people and organizations, and capture, preserve, and make available usable data for analysis, planning and research. Already earlier Komarkova et al. [21] had reported that the Internet and Web have provided readers easy, remote and fast access to information. Also geographic information, also known as spatial information, is increasingly available and it offers improving possibilities to solve spatially oriented problems. Komarkova et al. [21] highlight the importance of accessibility of spatial information in supporting decision making in both public and private sector. Besides solutions for vehicles and travelers, geographic data has benefited projects where a geographic information system was implemented for the city of Calhoun, Georgia. In their report Crawford and Hung [22] describe how the city acquired a utility geographic information system to cover its water, sewer, and electric management. Indeed, the role of available geographic data has offered new ways to think about ways and distances [23]. III.

IV.

THE CASE

Our case was about delivering services that required traveling or carrying things to customers. The service as such could be a service that was given on spot like washing or cooking or giving healthcare or bringing a letter. In this sense, all services that were not virtual or online belonged into the services under study. The services were delivered geographically in a limited area that we call Pinewood. Fig. 1 offers a simplified illustration about the research setting where the locations (marked with dots) waiting for services were all in fixed addresses and the services had to be delivered via the streets. The vehicle to deliver the service was dependent on the nature of the service. At another time there were more spots defined with timeslots or by the size of the delivery.

RESEARCH APPROACH

Design science research as described by Hevner et al. [8] was applied to produce the output in our study. Relying on interpretation of Peffers et al. [24] we applied design science research in a way that fit into our special context. Gregor and Hevner [9] addressed issues related to new knowledge that design science research should create and that should be revealed to be used by the scientific community. According to them, proposed design science research guidelines should be seen as guidelines but not as rules that should be blindly followed. The seven guidelines listed by Hevner et al. [8] were followed as reported here: The developed output was realizable, the problem was essential to the business of the organization, the output was implemented rigorously with scientific methods, the produced contribution offered new knowledge to the scientific society, the research applied approved methods both in construction and evaluation of the product, the solution was implemented after careful search for existing knowledge and methods, and the research results were published to audiences representing both business and theoretical knowledge.

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In the current design science study we first outlined the research problem. After that we carried out a limited literature study to provide us knowledge about existing solutions and possibilities. After having enough understanding about the context and desired output we finally paid more attention on the research methods that were necessary to provide the solution. In the next chapter the solution is described in detail.

Figure 1. Geographical area waiting for services.

As shown in Fig. 1, there were several spots to visit on a day. Some spots were time-constrained but not all. In addition, there were spots where the time of service delivery was not fixed even if informed beforehand. In other words, the planned timeslot could change. There were also different kinds of vehicles to deliver the services (by three different cars). The study was based on public maps such as Google and the information of the locations were based on GPS measures The problem was to plan the most effective and productive route to deliver services that were ordered either by the customer using the service or a special service provider. The problem had three dimensions such as length of the route, scheduled delivery time, and vehicle capacities. To note all three dimensions, a Three Dimensional Model was built. The model is illustrated in Fig. 2.

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In Fig. 2 the x-axis and y-axis depict for the planar map and they show the geographic position of the customers and service provider organization and road segments. The travelling time is illustrated by z-axis and it is drawn from one delivery spot to another.

Figure 2. TCROWID Design idea.

Due to the challenging research problem the solution includes several software modules that are linked to each other as illustrated by Fig. 3.

information about routes (see Fig. 3). After that, CYCLES calculates routes on a 3D virtual map and creates optimal modules and areas with area and time compactness for multiple services. CYCLES also creates new optimal routes with chosen delivery modules for each service vehicle. As illustrated in Fig. 3, CYCLES uses also information about orders and vehicles in this task. The functionality of the TCROWID algorithm can be simplified in three tasks: TCROWID calculates shortest paths database (SPDB), location graphs database (LGDB), and task graphs database (TGDB) as presented by Figs 4, 5, and 6, respectively. In Fig. 4 the straight lines pose for roads and we can see that there are several possibilities to go from one location to another (diamonds) similar to crossing roads between and around locations. Some of the roads are parallel and some crossing with other roads while others are not. In addition, Fig. 4 illustrates that a road segment depicts a stretch of a road that is measured by its length. The total up of stretches of the road segments reveal the distance between the locations (marked with diamonds) and they are further used in the calculations in the model.

Figure 4. Shortest Paths Database.

Figure 3. TCROWID Software Structure.

According to Fig. 3, five different information sources are needed to provide the required information for the algorithm: streets, locations, routes, orders and vehicles. The three dimensional shortest path database with respect to time and customer locations is created by TCTDB. As outputs there will be three databases: SPDB (shortest paths database), LGDB (location graphs database), and TGDB (task graphs database). These three databases include all information regarding the real visiting points and segments, all service locations and shortest virtual graphs between the services, and all pickups and deliveries with start and end times and shortest routes between them. After the database of SPDB, LGDB, and TGDB is built, TCROWE (time constrained route optimization with existing routes) optimizes existing routes with the help of it and

In the real environment, the number of road segments and locations waiting for services reaches hundreds of thousands and using them in the calculations would require huge resources measured by efficiency, storage and time, for example. Next, Fig. 5 illustrates the virtual segments that are formed when the distances between the locations are calculated based on their geographic locations.

Figure 5. Location Graphs Database.

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The use of virtual segments is needed to reduce the amount of data to be processed and stored as instead of thousands of road segments informing the distance between service locations (marked with diamonds) only one virtual segment is needed to inform the distance between two locations (Fig. 5). While Fig. 5 illustrates how the amount of data was reduced it is also a view about the environment described with one constraint, namely location. However, the delivery is often constrained with more than one requirement. Fig. 6 shows the same virtual environment with more restrictions.

Figure 6. Task Graphs Database.

Fig. 6 illustrates how both the shortest path database (SPDB) and location graphs database (LGDB) are combined with task graphs database (TGDB). In addition, time is shown as z-axis and the three lines depict for the timeslots that are limiting the spots. Finally, the calculations are based on only the piles of tasks that require actions and that, according to Fig. 6, meet the given restrictions. With the help of the virtualization the amount of data is decreased into thousandths or less and it is possible to calculate the most productive routes. After the route is recognized, the solution is turned back to reality and the service provider will get real-life information about which route to choose. Our algorithm applies Dijkstra [25] two times. First, shortest paths between all segment endpoints are calculated. This first calculation can be done once, and its results are applied always later. Recalculation is needed only when road segments are changed. The second calculation considers only virtual paths. The customer locations in x-y coordinates are now involved. These customer location maps are stacked so that every time slot (e.g. 5 min or 10 min) has its own layer w.r.t z-axis. In each layer only those locations, which are active in that time zone, are displayed. Hence we obtain a 3-dimensional map, which embeds the time constraints of all locations. Between each location we obtain the shortest path from the first calculation. This is now called the virtual path. When we apply Dijkstra second time in the 3-dimensional map with virtual paths, we obtain the time constrained shortest paths. The second calculation has to be done every time we reorganize the customer locations, e.g. daily. However, this approach may shorten the daily calculation time up to three orders of magnitude.

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V.

DISCUSSION

The purpose of the current study was to find a workable solution that would help a service organization to deliver services under several constraints such as time, nature of service, geographic distances and number of services. In logistic services there often are pick-up and delivery time window constraints specified by logistics customers. There may also be other constraints such as space and load in delivery vehicles that must be fulfilled. The optimization of such services so that the constraints are fulfilled and multiple customers can be served efficiently is a challenging problem. In this paper we present a new solution which extends known algorithms to the time window constrained case. The research problem was first viewed from the earlier knowledge point of view. It soon appeared that the ‘traveling salesman problem’ has gained interest for decades and the research reports offered a good background to our study. However, the old traveling salesman had only one restriction – he was not allowed to use any route more than once [2]. In our problematic context the restrictions added more challenges that differed from each other by nature. Since 1950's several researchers have tackled with the most productive route to deliver services [1-7] and the issue is topical also nowadays when people are aging and more services are expected to be offered at home or when ecommerce is extending to food delivery and wellness. The first problems were tied with timetable and timerelated restrictions [1, 7]. In our case time-related restrictions were among the first restrictions as productivity was perceived as one of the most important factors for productivity as was pointed out also Halonen et al. [17]. The earlier research reports describe solutions that are applicable under one or two constraints such as time when defined customers are carried with the same vehicle and where the size of the vehicle is significant e.g. [10]. The reports verify that the solution can be found and that it meets the given requirements. However, the solution is strongly context related and not applicable to other environments. In the current paper we show how the algorithms that utilize three context-related databases SPDB (shortest paths database), LGDB (location graphs database), and TGDB (task graphs database) it is possible to point out the most effective paths to deliver services. In all contexts, the three databases are formed case by case. Productivity is dependent on the chosen service process [17] and the current study introduced an approach to improve productivity especially in services where transport is the key functionality and bottleneck in the process. The size of vehicles has been identified in other studies as well [11] and on top of other restrictions such as time or travelled distance it can be seen as one of the restrictions that define the solution. The current solution does not pre-define the restrictions. Instead, the solution is adaptable for several contexts. Geographical data [14, 21, 22] has been utilized in studies that are focusing transport infrastructures and related issues. In particular, one of the latest papers introduces new ways to consider spatial analysis when studying geographical

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areas and distances [24]. As in tasks related to transport the geographical data form an important source for the available information it is also a cause for the need to manage enormous amounts of data. This was the case also in our study. In our study the service points were located in an area that consisted of streets, suburbs and roads connecting the suburbs. As illustrated in the simplified Fig. 1, the delivery spots were located partly scattered in the area, partly next to each other. According to the solution, the distances between the delivery spots were calculated based on the available geographical data and with the use of the developed algorithms that utilized the databased described in Section IV. The algorithms were functional only due to the virtual segments as virtualization decreases calculation load typically from one to three orders of magnitude. The value of this virtualization is significant as with the virtual approach the calculations could be carried out in real time and enable new routing during the working hours. Without the trick of virtualization the calculations would require computers running during every night and no modifications or changes into the services could be done. Further research is recommended especially in finding out application areas that lean on spatial data and that are looking for improvements in productivity and efficiency. There already are applications based on the introduced solution that take place in open air but it could be interesting to see if the solution can be applied in closed areas such as large and complex buildings. ACKNOWLEDGMENT The authors appreciate efforts from SIDI (Service Innovations for Developing Intelligent traffic) and Tekes (Finnish Funding Agency for Innovation) for funding, and the anonymous reviewers for their constructive comments.

[7]

[8] [9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

REFERENCES [1]

[2]

[3]

[4] [5]

[6]

N. Christofides, “Worst-case analysis of a new heuristic for the travelling salesman problem,” Management Sciences Reseach Report, 1976, No. 388. L. N. Herstein, “Some mathematical methods and techniques in economics,” Quarterly of Applied Mathematics (XI:3), pp. 249-262, 1953. J. Sniezek, and L. Bodin, “Cost models for vehicle routing problems,” in Proceedings of the 35th Annual Hawaii International Conference on System Sciences, HICSS 2002, pp. 1403-1414. A. Bruns, A. Klose, and P. Stähly, "Restructuring of Swiss parcel delivery services," OR Spectrum, (22:2), pp. 285-302, 2000. H.-J. Sebastian, "Optimization approaches in the strategic and tactical planning of networks for letter, parcel and freight mail," in D. Dolks et al. (Eds.) Decision Support Modeling in Service Networks, LNBIP 42, pp. 36-61, 2012. R. Baldacci, L. Bodin, and A. Mingozzi, "The multiple disposal facilities and multiple inventory locations rollon–rolloff vehicle

[20] [21]

[22]

[23]

[24]

[25]

routing problem," Computers & Operations Research, (33:9), pp. 2667-2702, 2006. I. Sungur, Y. Ren, F. Ordóñez, M. Dessouky, and H. Zhong,“A model and algorithm for the courier delivery problem with uncertainty,” Transportation Science, (44:2), pp. 193-205, 2010. A. R. Hevner, S. T. March, J. Park, and S. Ram, "Design science in information systems research," MIS Quarterly, 28(1), 75-105, 2004. S. Gregor, and A. R. Hevner, "Positioning and presenting design science research for maximum impact," MIS Quarterly (37:2), pp. 337-356, 2013. B. M. Baker., and M. A. Ayechew, "A genetic algorithm for the vehicle routing problem," Computers & Operations Research, (30:5), pp. 787-800, 2003. R. Baldacci, L. Bodin, and A. Mingozzi, "The multiple disposal facilities and multiple inventory locations rollon–rolloff vehicle routing problem," Computers & Operations Research, (33:9), pp. 2667-2702, 2006. R. Duhaime, D. Riopel, and A. Langevin, "Value analysis and optimization of reusable containers at Canada Post," Interfaces, (31:3), pp. 3-15, 2001. M. Maier, M. Rattigan, and D. Jensen, "Indexing network structure with shortest-path trees," ACM Transactions on Knowledge Discovery from Data (TKDD), (5:3), Article 15, 2011. P. J. Densham,. “Spatial decision support systems,” Geographical information systems: Principles and Applications, 1, pp. 403-412, 1991. R. Rupnik, M. Kukar, and M. Krisper, "Integrating data mining and decision support through data mining based decision support system," The Journal of Computer Information Systems, (47:3), pp. 89-104, 2007. O. Shcherbina, and E. Shembeleva, "Modeling recreational systems using optimization techniques and information technologies," Annals of Operations Research, (221:1), pp. 309-329, 2014. R. Halonen, O. Martikainen, K. Juntunen, and V. Naumov, "Seeking efficiency and productivity in health care," in Proceedings of the 20th Americas Conference on Information Systems, AMCIS-02512014.R1., 2014. O. Martikainen, “Productivity Improvements Enabled by ICT based Process Transformations”, Proceedings of the 3rd Balkan Conference in Informatics BCI’2007, pp. 1-8. D. Sedera, and G. G. Gable, "Knowledge management competence for enterprise system success," The Journal of Strategic Information Systems, (19:4), pp. 296-306, 2010. B. Sundgren, “What is a public information system? International Journal of Public Information Systems,” 1(1), 2012. J. Komarkova, M. Novak, R. Bilkova, O. Visek, and Z. Valenta,”Usability of GeoWeb sites: case study of Czech regional authorities web sites,” Business Information Systems, pp. 411-423, 2007. D. Crawford, and M. C. Hung, "Implementing a Utility Geographic Information System for Water, Sewer, and Electric: Case Study of City of Calhoun, Georgia," Journal of the Urban & Regional Information Systems Association, (26:1), pp. 25-34, 2015. Jiang, B., & Okabe, A. (2014). “Different ways of thinking about street networks and spatial analysis,” Geographical Analysis, 46(4), 341-344. K. Peffers, T. Tuunanen, M. A. Rothenberger, and S. Chatterjee, "A design science research methodology for information systems research," Journal of Management Information Systems, (24:3), pp. 45-77, 2007. Dijkstra. https://en.wikipedia.org/wiki/Dijkstra%27s_algorithm

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