As we mentioned earlier, our work is derived from an industrial problem, where an eective, easy-to-use and fast application is needed to oer a feasible and near-optimal solution for the redesign of supply of mobile mechanics. The system contains more than 500 mobile mechanics which supply is managed in star topology, wasting huge amount of resources. This topology should be replaced by a route system, where products are transported by minimal number of trucks, considering additional constraints like time-windows.
The activities of the mobile mechanics are controlled by a Field Ser-vice Management System (FSMS) with the target: dynamic optimization of planned/unplanned maintenance tasks in the power/gas network. Since the travel for material of mobile mechanics is a non-productive task within the FSMS, the supply of the more than 500 mobile mechanics from 20 warehouses (regional, central) represents a complex and economically important problem of the E.ON Network Services Kft. The new dynamic approach presented in this paper aims a signicant reduction of activities regarding material handling for the mobile teams with extending of serving locations from 20
to 100. The design of the supply system can be considered as a complex combinatorial optimization problem, where the goal is to nd a route plan with minimal route cost, which services all the demands from three central warehouses while satisfying other constraints like time windows.
In this section every steps of the methodology will be presented during a solution of the problem motivated our research. The necessity of the opti-mization is presented in Fig. 2.18. The company has a star topology which means that a truck transports the required materials from the Central De-pot to the Warehouses, while mechanics at the Bases transport the materials from the Warehouse to the bases. This topology produces high operational costs, thus the company wanted to replace this supply system with one truck which can serve the Warehouse and all the Bases with necessary materials.
Figure 2.18. Schematic view of the current status and the desired solution of the industrial problem. CD - Central Depot, WH - Warehouse, B - Base
We have developed a complete software package to solve this type of op-timization problems. The input data is given by a Google Maps map, which contains the locations (with the depot) and the nal output is a route system dened by a Google Maps map also. A complete, automated solution is freely available at our website3 as a web-based service. However, it should be men-tioned that for the sake of reducing the load on our server, this application provides only a demo, where the number of input locations is maximized by 10. IT development is planned in the near future in our department, when this restriction can be removed. Thus, the real project was optimized by an oine genetic algorithm written in MATLAB. In the following section, we will demonstrate the optimization of the industrial problem, however, only representative locations are shown (which are really close to the real situation).
3http://193.6.44.35/gmaps/
First of all, user has to dene a map with the Google Maps service. In this example, it contains 30 locations. After that, the rst step is the information retrieval from this map, like the longitude and latitude information. The result of this step is an Excel spreadsheet, which serves as the input for the next step, which is the determination of the distance matrix. A portion of the resulted distance table is shown in Table 2.5. It contains 30 locations (with the depot). The task is to determine the optimal routes for these locations with the following constraints: maximum number of salesmen is 5 ; maximum travelling distance of each salesman is 450 km.
Kilometers Gyõr Ják Kõszeg
Gyõr 0 117.14 96.54
Ják 117.14 0 34.59
Kõszeg 96.58 34.8 0
Table 2.5. Part of the industrial problem's distance table - kilometers.
After distance matrix determination the algorithm computes the solution with the new representation. The GA ran with population size 320 and it did 200 iterations.
Figure 2.19. Results of the Visualiser component for 30 locations with at most 5 salesmen and at most 450 km tour length per salesman.
It resulted that 4 salesman is enough to satisfy the constraints. With the visualizer component we can visualize the results, as it is shown in Fig. 2.19.
The visualizer component also capable to compute the costs for each routes considering the per kilometer cost, the hourly wage of the drivers and the packing sta (including time windows). The length of the resulted routes in our example are 261 km, 422 km, 333 km and 384 km respectively, i.e.
they satisfy the constraints, thus the algorithm provided a feasible solution of the problem. The algorithm necessitates the input data as XLS tables and provides the resulted route system as an Excel table also. The optimization can be performed for the traveling times as well, where time windows have to be considered for each mechanics (usually 5-7 minutes). The number of mechanics for each bases is provided by the company, as well as the length of time windows.
As far as we know, these automated, web-based solution is unique, the information retrieval from a Google Maps map, the distance matrix
determi-nation and the automated optimization process are all novel tools, as well as the applied algorithm behind the scenes or the visualizer components, which can draw the resulted routes one after the other.
2.5 Conclusions
Since the travel for material of mobile mechanics is a non-productive task, a novel approach presented in this paper for the optimization of serving loca-tions to reduce the activities related to material handling. A modied mTSP with additional constraints was introduced and solved by a novel approach.
The complexity of the motivating problem implied the introduction of a novel genetic algorithm using novel crossover operators for multi-chromosome indi-vidual representation, where a separate chromosome is assigned to all sales-men. The approach presented here is innovative in the reproduction of indi-viduals, in the handling of the constraints, and it gives a whole methodology and a novel complete framework to solve an NP-hard problem, the mTSPTW.
Beside the proposed methodology the paper presented the developed tool uti-lizes Google Maps to visualize the supply structure and collect raw data used for optimization. The new dynamic approach resulted signicant reduction of activities regarding material handling for the mobile teams by extending of serving locations from 20 to 100.
The application of the novel tool containing the optimization process and the web-based framework in a real industrial problem's solution justied the necessity of the research. E.ON Hungária Zrt. already applied the pro-posed tool. Preliminary economic calculations and experiences show that the implementation resulted signicant savings while the quality of service also improved.