Scheduling of Time-Shared Jet Aircraft

Motivated by a real application, we consider the following aircraft scheduling problem. At any time, the aircraft are at diierent locations or are serving a customer and new customer requests arrive, each consisting of a departure location, departure time and destination. Additionally, if a customer request consists of more than one trip, there may be an exclusive use of the aircraft between these trips. Our objective is to satisfy these requests (by subcontracting extra aircraft if necessary) at minimum cost under additional constraints of maintenance requirements and previously scheduled trips. We formulate the problem as a 0-1 integer program, show its complexity and nd that many instances of small and medium size problems can be solved by Cplex. For larger problems and for`bad' instances, we provide a very fast heuristic with good performance. A growing number of executives these days believe that having their own aircraft is really the best ight plan, because using commercial airlines for business trips may sometimes be time consuming and unreliable. On the other hand, a private jet is not always aaordable for many companies, especially if they are of small or medium size. Hence, selling shares of aircraft to customers who could otherwise not aaord their own is a rapidly growing industry Customers become partial owners of aircraft, which would provide them with an allotted number of ying hours per year. A partial owner will call the company that manages these aircraft and book a trip by specifying the departure time, departure location, destination and exclusive use information (if a customer request consists of more than one trip, the customer may ask to use the aircraft between these trips). If the customer has enough ying hours left, the company must provide an aircraft to that customer for that trip. Through the sharing of aircraft, customers avoid the high cost of ownership and other associated overheads of establishing a corporate ight department with its own maintenance staa and pilots. There are tax advantages, too, as partial owners are allowed to take a depreciation expense. For the company which sells shares of aircraft, there are two major types of costs: operating costs (fuel, maintenance, etc.) for ying the aircraft and the penalty costs for not being 1