Abstract The paper presents the problem of searching for the right amount of time needed to wait for a passenger who is late for boarding a plane. This problem, although practically ignored by airline and handling agents' operational manuals, is common and very important for flight punctuality, and thus for both passenger satisfaction and the financial performance of air transport companies. The discrete Dynamic Programming task for finding the minimum amount of time wasted on waiting for a late passenger, depending on the moment in time in which the passenger arrives, is formally defined in this paper. The task is solved based on sample data. Dependence of the results on the average period of time needed to find the luggage of a passenger who did not arrive for boarding is examined. The paper also presents the preliminary results of the impact of the random variable describing the arrival time of the last passenger on the moment when the decision to stop waiting should be made. The function, which allows to determine the expected value of that lost time, was specified for different moments of the end of waiting by taking into account the random characteristics of the arrival of the last passenger. The obtained results show that in each of the analyzed cases there is a global minimum of that function. The moment for which the minimum occurs can be considered as the optimal (in terms of time wasted on waiting) moment to stop waiting for the late passenger.

Highlights • Waiting for a late passenger problem was studied. • Mathematical model of this situation was developed. • Dynamical Programming allows to determine the reasonable waiting time. • The maximum waiting time was calculated for five different cases. • Probability distribution of the arrival of the last passenger was taken into account.