Research on the Recovery of Irregular Flights under Uncertain Conditions

This paper mainly studies the problem of irregular flights recovery under uncertain conditions. Based on the analysis of the uncertain factors affecting the flight, taking the total delay time and the total cost of flight delay as the objective function, and considering the constraints of flight plan and passenger journey, an uncertain objective programming model is constructed. Finally, taking OVS airport temporarily closed due to bad weather as an example, the results show that better quality optimization scheme can be obtained by integrating passenger recovery with narrow sense flight recovery stage and im-plementing integrated recovery.


Introduction
At present, China's air transport industry is in a period of rapid development, and the market demand is growing. Airlines strive for greater profits by making compact flight plans and reducing costs. However, in the implementation of flight plan, it is often affected by many emergencies and deviates from the original plan, resulting in irregular flights, such as bad weather, major geological disasters, military exercises, accidents, aircraft failures, etc. [1]. When the flight is delayed or cancelled, it is necessary to re-plan and resume the passenger journey according to the passenger destination and existing flight resources, so that the disturbed flights can quickly return to normal. The problem of irregular flight recovery not only has complex objective function and many constraints, but also requires high timeliness of calculation [2]. With the current technical conditions, it is still unable to solve the problem of large-scale irregular flights recov-integrates aircraft path recovery and passenger recovery, and abstracts the objectives and constraints involved in these two recovery problems as objective functions and constraints. The meanings of the parameters involved in the model are shown in Table 1.

Objective Function Analysis
The objective function of the irregular flights recovery problem includes the total time of passenger delay and the total cost of flight delay.
where f a T is the total delay time for flight a to execute flight f, 1  , respectively, k represents the k-th time unit, with 5 minutes as one time unit. According to the relevant regulations of the Civil Aviation Administration, the flight cancellation time can be converted into a delay of 8 hours. Therefore, the total time of passenger delay is • The total cost of flights delay. The total cost of flight delay includes direct cost and indirect cost. Direct costs include the cost of airline compensation and aircraft in the air and ground holding and canceled flights. The cost of airline compensation. The Civil Aviation Administration's compensation standard for flight delays stipulates: if the flight is delayed due to the airline's own reasons, the delay is between 4 hours and 8 hours, the passenger will be compensated not less than 200 ¥; the flight will be cancelled if the delay exceeds 8 hours, and each passenger will be compensated Not less than 400 ¥. On the basis of the compensation standard, the airline makes compensation in combination with the actual delay. The passenger compensation cost can be calculated by Equation (3). ( ), 96 If the plane a executes the flight f, it takes off at the time unit k of the delay, then the value is 1, The number of gates available at airport p during The number of aircrafts of model l which required to be parked at airport p after the restoration The set of inbound flights parking at airport p at moment t

PG
The set of the itinerary route of the disturbed passenger (departure airport to arrival airport) The set of outbound flights parking at airport p at moment t

( ) F l
The flight set of aircraft type l cannot be allocated, The set of airports closed due to inclement weather The set of alternative itineraries for disturbed passengers, pg PG ∈ , On the same day, flight f finally lands at airport p, If the flight f stops at the airport p within the spe- If the flight f is on route r of the disturbed passengers, the value is 1, otherwise it is 0, If aircraft a belongs to type l, it is 1, otherwise it is The number of passengers on flight f on route r The aircraft belongs to type l is assigned to flight f, The number of passengers whose flight route is on r and the departure and arrival airport is pg , (200,300), (400, 600)   . The cost of aircraft air/ground holding. The recovery of irregular flights is mainly to study how to reasonably reschedule the flight plan. Therefore, the cost is mainly the cost of aircraft ground waiting, including the cost of aircraft parking at the airport and the cost of aircraft depreciation, which can be calculated by Equation (4).
where f a CW is the ground holding cost of the delay or cancellation of flight f implemented by aircraft a; β is the fee charged for every minute of aircraft a stopping at the airport; ν is the depreciation cost per minute of aircraft a.
The cost of cancelling flights. It is calculated as in Equation (5).  ( ( ) ( )) , 60 96 where f a CI is the indirect cost of aircraft a due to the cancellation or delay of flight f. Therefore, the total cost of flights delay can be calculated by Equation (7).

Constraints Analysis
• Flights schedule constraints.
Flights coverage constraint. Each flight is executed by one aircraft, or the flight is cancelled. The constraint is described as Equation (8).
Aircraft flow balance constraint. After the completion of the recovery, the number and types of aircraft parked at each airport meet the requirements of the plan. The constraint is described as Equation (9).
Parking space constraint. The airport must have enough parking spaces to ensure that flights take off and land normally. The constraint is described as Equation (10).
VIP flights important precedence constraint. Minimize delays on important flights. The constraint is described as Equation (11). , , , , . g Airport closure constraint. The airport was closed due to bad weather and the aircraft could not be taken off or landed during this period. The constraint is described as Equation (12). .
Aircraft type matching constraint. Different aircraft types are not allowed to be exchanged. The constraint is described as Equation (13).
Airplane seats constraint. The seats of the aircraft allocated to a certain flight should meet the needs of passengers. The constraint is described as Equation (14).
Passenger number constraints. Ensure that the new flight plan will not cause overbooking. The constraint is described as Equation (15). .
Passengers itinerary constraints. Ensure that the passenger itinerary in the new plan is consistent with the original plan. The constraint is described as Equation (16).
Therefore, the uncertain multi-objective planning model for the recovery of irregular flights is shown as Equation (18). ( ) g The inverse binary learning fireworks algorithm is used to solve the model (19). Figure 1 shows the length of each flight delay in the new flight plan. Similarly, the length of the vertical line indicates the duration of the flight delay. The longer the vertical line, the longer the delay time of the corresponding flight, and vice versa, the shorter; the "*" point indicates that the corresponding flight is not delayed.
It can be seen from Figure 1 and Figure 2 that 116 of the 172 flights were delayed and no flights were cancelled. The total delay was 2360 time units, or 11,800 minutes, and the total delay of passengers was 207,606 time units, or 1,038,030 minutes; the passengers were required to be compensated for flights delayed for more than 4 hours. 0, the total delay cost is 1,976,900 ¥. If no measures are taken for irregular flights, that is, all affected flights are postponed for 3 hours, the flight will be delayed for a total of 20,880 minutes, and passengers will be delayed for 1,593,180 minutes, and the total cost of delay will be 3,435,600 ¥. Considering passenger constraints, the newly formulated flight plan reduces flight delays by 9080 minutes, passenger delays by 555,150 minutes, and delay

Conclusion
Based on the analysis of the uncertain factors and basic models that affect the recovery of abnormal flights, this paper constructs an uncertain flight recovery model, and uses the binary learning firework algorithm to solve the problem, which provides a solution for abnormal flight recovery under uncertain condi- tions. An example for demonstration and verification was proposed, the results show that integrating the two-stage flight recovery into one model for research can obtain a better quality solution. The next step will be to study the integrated