What do you mean by mapping? Geodata collected from say GPS / manual entry? Size of the fleet? Type of data stored? Web based or Win/mac client?
SaaS or license model? Who will be the final user? Languages covered? Customization or other specific requirements?

Contact a local software integrator who can do that sort of research for you, but do prepare a price tag, it really makes a difference if you have 300 USD or 30,000 USD for this (if you have 300 or 3,000 you'll have to do the research yourself, this is too small to bother)

Out of topic for this forum...

You haven't really provided enough information for a good answer. Cost might not be an issue, but the solution to your problem depends on what you're trying to accomplish. That solution might be simple or it might be very complex with a very steep learning curve.

If all you want to do is draw a good-looking map, Illustrator works, but if your needs are more along the lines of storing and manipulating hundreds or thousands of different layers of geospacial information in a database, then your solution will be something else.

Do a Google search on GIS systems (geographic information systems). The wikipedia article, for example, will introduce you to the complexities of the whole thing.

We use ERSI's ArcView/ArcGIS for GIS data, but when we need a good-looking map instead of just a data-filled functional map, we open the ArcView shapefiles (a geospatial vector data format) in Illustrator, then work from there. If we need web-based maps, we'll often take the ArcView data and convert it to KML files which can be used in conjunction with Google Maps or Google Earth.