12. Fleet Management

12.1 Introduction The fleet management problem, in its simplest form, involves managing fleets of equipment to meet customer requests as they evolve over time. The equipment might be containers which hold freight (ocean containers, truck trailers, boxcars), equipment such as locomotives, truck tractors, taxicabs, or business jets (companies in the fractional jet ownership business may own up to 1,000 jets). The equipment has to serve customers (people or freight) who typically want to move from one location to the next. We make the assumption throughout that a piece of equipment can serve one request at a time. One of the challenges of fleet management is that customer requests arrive randomly over time, often requiring service within a narrow interval. Since it can take from several days to more than a week to move transportation equipment over long distances, it is not possible to wait until a customer request is known before moving the equipment. As a result, it is necessary to move equipment to serve demands before they are known. In actual applications, there are other sources of randomness, such as transit times and equipment failures. Fleet management problems in practice are quite rich, and it is helpful to focus on a particular application to provide a motivating context. In this chapter we use the classic problem of car distribution in railroads. The problem of optimizing the flows of empty freight cars for railroads is typically formulated as a textbook transportation problem. There are supplies of empty cars and customers placing orders for these cars.