Constructing an Optimal Fleet for a Transportation Schedule

I. Gertsbach and Yu. Gurevich
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I. Gertsbach: Ben Gurion University of the Negev, Beer Sheva, Israel
Yu. Gurevich: Ben Gurion University of the Negev, Beer Sheva, Israel

Transportation Science, 1977, vol. 11, issue 1, 20-36

Abstract: A schedule is a set of passages; a passage is a 4-tuple p = ( p 1, p 2, p 3, p 4) where p 1, p 2 denote departure and arrival terminals, p 3, p 4 departure and arrival times. A fleet is a partition of the schedule into chains; each chain is a finite or infinite sequence of passages p 1 , p 2 , ... having the property p n 2 = p n +1 1 and p n 4 (le) p n +1 3. The fleet-size is the minimal possible dimension (i.e., the number of chains) of the fleets. The deficit function d ( t , a ) for a terminal a is the difference between the number of departures and arrivals occurring at a during the interval [0, t ]. It is proved that the fleet-aim is equal to (sum) a max t (ge)0 d ( t , a ). A general method for constructing all optimal fleets is described. A special case of periodic schedules is studied and it is proved that a periodic schedule can be decomposed into an optimal periodic fleet. Applications of the deficit function technique to practical scheduling when passages have tolerances for departure times are discussed.

Date: 1977
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