IMPROVING THE ROBUSTNESS OF FLIGHT SCHEDULE BY FLIGHT RE-TIMING AND IMPOSING A NEW CREW BASE

Transcription

1 Jurnal Karya Asli Lorekan Ahli Matematik Vol. 6 No.1 (2013) Page Jurnal Karya Asli Lorekan Ahli Matematik IMPROVING THE ROBUSTNESS OF FLIGHT SCHEDULE BY FLIGHT RE-TIMING AND IMPOSING A NEW CREW BASE Rieske Hadianti 1, Saladin Uttunggadewa 3, Edy Soewono 4 Department of Mathematics, Institut Teknologi Bandung, Bandung, Indonesia 1 hadianti@math.itb.ac.id, 3 s_uttunggadewa@math.itb.ac.id, 4 esoewono@bdg.centrin.net.id Khusnul Novianingsih 2 Department of Mathematics, Universitas Pendidikan Indonesia, Bandung 2 khusnuln@yahoo.com Abstract : The increasing airline passenger demand leads to the increasing of air traffic. This is one factor that can cause the significant increase of flight delays in nowadays airlines operations. Airlines then need to build robustness into their flight schedules, so that the flight schedules are robust (insensitive) to delays. In this paper we study a problem facing by an airline in improving its schedule robustness. The existing schedule robustness is not so high due to some factors, two of them are minimum crew connection times on the schedule and there is only one crew base. We try to improve the schedule robustness by imposing a new crew base and flight re-timing. We analyze the effect of these actions to the schedule robustness, where we use the probability of finding new optimal crew pairings after a number of flight delays happen as the robustness metric. The probability is evaluated through a simulation which consists of (1) generating a number of delays randomly in daily operations, (2) solving the optimization problem for obtaining the optimal crew pairing, in a number of iterations. The simulation results for a real world data show us that imposing a new crew base and flight re-timing can improve the robustness of flight schedule significantly, while the number of additional crew pairings needed is not so significant. Key Words: Robust Airline Schedule, Crew Pairing Optimization, Simulation. 1. Introduction One serious problem faced by airline industries is flight delays. It is reported that nowadays about of flights are delayed, and it can be worse since flight demand is increasing significantly meanwhile airport and runway capacities are not increasing significantly. Flight delays are unavoidable due to weather conditions, limited runway capacities, high air traffic, aircraft technical problems and others, and it can reduce airlines revenues significantly. To minimize the impact of flight delays to airlines revenues, airlines perform some strategic actions, from the planning stage through the operation stage. In the planning stage, airlines can build robust schedules, ones that anticipate the stochastic nature of the operating environment and reduce the influence of disturbances on its operation. Meanwhile in the operation stage, airlines can re-optimize schedule after disruptions occur. This paper studies building robustness into airline schedules. There are some definitions on robust flight schedule, in Chiraphadhanakul & Barnhart[6] we can find three of them. It is written that a robust schedule is 1. a schedule that minimizing expected delays and disruptions, or 2. a schedule that minimizing the impact of delays and disruptions, once a schedule gets disrupted, or 3. a schedule that minimizing expected schedule costs. In [9] it is stated that this type of robust schedule not necessarily optimal in planning, but perform well in operations Jurnal Karya Asli Lorekan Ahli Matematik Published by Pustaka Aman Press Sdn. Bhd.

2 Rieske Hadianti et al. A robust schedule of definition 1 can be built by maximizing schedule slack subject to available resources, for example, by planning aircraft routes with long aircraft connection times; crew pairings with long rest times between duties and long sit times between plane changes. A crew pairing is a sequence of flights, starting and ending at cockpit crew base, where any two consecutive flights are separated by a crew connection time. A robust schedule of definition 2 can be built by maximizing recovery flexibility or by clustering the airline network into isolated sub networks such that the delays and disruptions arising in one sub network are contained within that sub network. Meanwhile a robust schedule of definition 3 can be built by capturing the trade-offs between costs of robustness and recovery cost savings. Some airline robustness measures are then derived from the definitions, for examples: 15-Minute On-Time Arrival Performance, which measures the percentage of flights that arrive at the gate no later than 15 minutes after the scheduled arrival time, Delay Propagation, Passenger Delay, which measures the difference between the planned arrival time and the actual arrival time at a passenger's final destination. Some measures are actually related to each other. That is why up to now there is no single measure used by airlines to measure the robustness of flight schedule. In real world situation, an airline usually uses a measure which is related to the specific problem faced by that airline. In this paper we consider an airline which has a class of domestic fights with a complex flight network and high coverage, but the flight schedule has minimum crew connection times and there is only one crew base. The minimum crew connection times are set under assumption that building slacks into schedule is very expensive. Without any delay or disruption, we can build its optimal crew pairings which consists of one-day crew pairings and most of the pairings are ones with almost maximum flight duty time (FDT). The optimal crew pairings is the minimum set of crew pairings which covers all flights in the schedule, constructed by solving crew pairing problem. Another characteristic of this class of flights is that there are a number of flights which we call as critical flights, in which each flight can be covered by one and only one possible crew pairing. The possible crew pairing is then selected as a member of the optimal crew pairings. Any delay at a flight in the pairing which contains a critical flight and of almost maximum FDT is vulnerable to disruptions since it will cause there is no one-day pairing that covers the flights. The additional costs effected by this creating a multi-day pairing, such as crew overtime cost and crew accommodation cost, are very significant for reducing the airline revenue so that the airline tries to operate this class of flights by running the one-day crew pairings. So from our point of view, the appropriate robustness measure for this airline is the probability of finding the optimal one-day crew pairings, once a schedule gets disrupted, as we proposed in Novianingsih, et. al.[13]. This measure is related to the completion factor, that is the percentage of accomplished flights, the flights that were not cancelled (see Bian, et.al[4]). The probability is evaluated by a simulation which consists of a number of iterations of the following two steps: generation of delayed flights and its delay times and solving crew pairing problem after delays happen. The probability is defined as the fraction of the number of iterations where the new optimal one-day crew pairings found to the number of iterations. The simulation method is used, like in [4], since it captures the stochastic natures of airlines operations, where a delay and disruption can occur to any flight any time. The characteristic of the class of flights we consider makes the robustness of schedule is low. In [13], it is shown that only 5% of flights delayed makes the probability of finding the optimal oneday crew pairings decreases to It is also shown that flight re-timing of a number of flights can improve the robustness, but the improvement is not so significant (only about 0.06). This leads to our hypothesis that the presence of the critical flights is the key factor for low robustness. In this paper we will show, by observing the types of pairings in the optimal crew pairings, that there is a long-chain type of pairing in which any delay caused by a flight in this pairing potentially lead to a condition where we need to extend the pairing to be a multi-days pairing. The need for creating a multi-days pairing is mostly caused by violation of maximum FDT since the original FDT is almost maximum so that the delay time makes a new possible pairing has FDT which is greater than maximum FDT. The presence of critical flights and long-chain pairings bring us to our approach for improving the 67

3 Jurnal KALAM Vol. 6, No. 1, Page robustness of schedule, i.e. by flight re-timing and imposing a new crew base. A new crew base will create a possibility for decomposing long-chain pairings into shorter-chain pairings, which is possible if we also perform flight re-timing to some flights. We perform a large-scale simulation as in [13] to see the impact of flight re-timing and imposing a new crew base to the improvement of the schedule robustness. Our approach in evaluating the robustness of flight schedule is in Chiraphadhanakul, V. and Eggenberg [7] called by qualitative estimation of robustness, since we do not considering any recovery action due to flight delays. We can find a number of papers on improving models, for example by flight retiming(lan[10]) or by slack re-allocation model the robustness of flight schedule. Most of them concern on the schedule evaluation ([6], AhmadBeygi, et.al.[2], Aloulou, et.al[3]). The other approach is by solving the aircraft routing problem and crew pairing problem simultaneously, so that the solution can capture the many dependencies between the aircraft routing process and crew pairing process. As explained above, for the airline we consider in this paper there is no slack in the flight schedule, so that two consecutive flights in a pairing will have a minimum crew connection time. This means there is no possibility for applying slack re-allocation model. Our approach is then can be seen as the combination of flight re-timing (see [10] and Mercier & Soumis[12] ) and creating hub and spoke network. We apply our approach to a real world data, and the simulation results show us that imposing a new crew base and flight re-timing can improve the robustness of flight schedule significantly, meanwhile the number of additional crew pairings is not so significant. This means that the improvement can be achieved with not significant extra crew cost. This paper is written as follows. After introduction, in section 2 we briefly discuss about the optimization problem for obtaining optimal crew pairings and its type for the airline we study. Based on these types, we derive an approach for improving the robustness of flight schedule, which is presented in section 3. In section 4 we discuss the simulation for evaluating the robustness of flight schedule and in chapter 5 we give numerical examples of the improvement for real world data. We end this paper by a conclusion and discussion, which we present in section The Optimal Crew Pairings and Its Types In this section we will briefly discuss the optimization model for obtaining the crew pairings. We will also discuss the types of crew pairings selected, which will bring us to the approach for improving the robustness of flight schedule. Let F is a set of flights. For i F, let dep i and arr i be its departure time and its arrival time, respectively. The flight time of flight i F is defined by ft i = arr i - dep i. A flight duty time (FDT) of pairing consists of flights is given by where is the period of time needed by crew for briefing and reporting before starting a pairing. One-day pairing is feasible if it satisfies: For the minimum period of time needed for an aircraft to be ready for the next flight after arrived at a gate, the maximum total flight time, 68

4 Rieske Hadianti et al. the maximum FDT, where the parameters on the right hand sides of conditions 1 3 above are given in the airlines operation manual. The optimal set of crew pairing can be obtained by first generating P, the set of all possible pairings of F. Once the set P is generated, we then have the crew pairing problem which is given in the following. Crew Pairing Problem Minimize Subject to The parameters equal 1 if flight f is covered by pairing p, and otherwise. The objective function of the crew pairing problem above is the total of crew pairing cost, where the cost of pairing p and d f is the crew cost deadheading at flight f. A deadhead crew at flight is is a crew flies as a passenger, transferred to the destination of flight for serving other flight that starts at the destination of flight or elsewhere. Allowing deadhead in a pairing can make aircraft pairings optimal, so that the total operation cost can be minimized. The first term of the objective function above is the total cost for running all selected pairings and the second term indicates that the number of deadhead will be minimized. The constrains of the optimization problem above ensure that all flights will be covered by the selected pairings. The crew pairing problem is a set covering model, which is a NP-hard problem. To solve the model using the conventional method such as Branch-and-Bound method will be time consuming. We can solve the optimization model efficiently by using a heuristic algorithm, for example one which is based on the random search (see Hadianti, et. al[14]). Without any delay and disruption, the fight schedule can be operated by running the optimal crew pairings. If we consider the pairings as directed graphs where its vertices denote the airports and its edges denote the flight connections, the types of graphs in the optimal crew pairings are given in Figure 1. The pairings of type (a) consist of a number of cycles where the degree of the hub (crew base) is greater than two. The pairings of type (b) consist of a number of cycles where the degree of the hub is two. 69

5 Jurnal KALAM Vol. 6, No. 1, Page Figure 1. Types of pairings. We categorize a crew pairing as a critical pairing if any delay caused by one flight at this pairing potentially lead to a condition where we need to extend the pairing to be multi-days pairing. A critical pairing can be characterized by the presence of a critical flight in it or it is of type (b). It should be noted that a critical flight must be contained in a pairing of (b) that consists of one cycle. Pairings of type (a) are not categorized as critical pairings since it can be easily decomposed into a number of cycles which are feasible to be crew pairings. 3. Improvement Strategies The schedule robustness can be improved by reducing the number of critical pairings. A critical flight that consists of one cycle is little bit difficult to be handled. The presence of this type of pairing in the optimal crew pairings shows that the flight schedule contains critical flights with large flight time. Defining stop-over in an intermediate airport will change this pairing into a long-chain pairing if the intermediate airport is not a crew base. By assuming the intermediate airport is not considered as a new crew base, we then focus on reducing the number of critical long-chain pairings. One approach that can be done for handling these pairings is imposing a new hub (crew base) so that a long-chain pairing that consists of a new crew base can be cut for creating two or more pairings with shorter FDT. One of new pairing created by this cutting process can be regarded as a pairing as itself or can be amalgamated with another pairing, as illustrated in Figure Figure 2. Cutting and amalgamation of pairings A new hub can be selected from a list of airports which have a large degree in the flight network. As in [], we can perform flight re-timing to a number of flights from and to the new hub in order to make the amalgamation processes yield a number of new possible crew pairings.

6 Rieske Hadianti et al. 4 Simulation for Evaluating the Robustness of Flight Schedule The robustness of flight schedule is evaluated through the following simulation, which is also used in [13]. Simulation 1 Input : flight schedule, (the percentage of flights delayed), (number of iterations) Output : RM (flight schedule robustness) Steps : 1. Generate both flight delays and delays duration randomly, 2. Determine the new optimal crew pairings by solving the crew pairing problem, 3. Repeat step 1-2 until a number of iteration (N). 4. Calculate the number of iterations where the new optimal crew pairings found (I), 5. Calculate RM, the robustness of the flight schedule by It should be noted that the robustness of flight schedule is evaluated under an assumption that there is no recovery action due to flight delays, except creating new optimal crew pairings, is taken. 5 Numerical Examples In the following, we consider a real world data which represent flight schedule of an airline which has a class of domestic fights with a complex flight network and high coverage, but the flight schedule has minimum crew connection times and there is only one crew base. The optimal crew pairings consist of 48 one-day crew pairings, two of them are one-cycle crew pairings. There are a quite large number of long-chain crew pairings which consist of an airport, so that we will consider this airport as a new crew base. In [13] its is shown that the existing robustness of flight schedule is low. We consider three schemes for improving the flight schedule robustness, i.e. 1. Flight re-timing to a number of flights from the (old) crew base, 2. Imposing a new crew base and flight re-timing to a number of flights from and to the new crew base, 3. Combination of scheme 1 and scheme 2. By applying Simulation 1, we can compare the robustness of original flight schedule and the robustness of flight schedule after flight re-timing and or imposing a new crew base. The flight schedule robustness for different values of, for each scheme are given in the following table. 71

7 Jurnal KALAM Vol. 6, No. 1, Page Table 1. The robustness of flight schedule for different values of for the case with single crew base and two crew base Single Crew Base Two Crew Bases α=5% α=10% α=16% α=20% α=5% α=10% α=16% α=20% Original From table 1 we can see that scheme 3 is the best scheme compared to the others schemes. Flight re-timing is considered of no cost, so in the following we try to investigate the additional cost incurred by imposing a new crew base. One can think that imposing a new crew base may lead to a condition where we need a large number of additional crew pairings. Since the crew cost is the second largest cost of the airline operation cost, the large number of additional crew pairings will increase the airline operational cost significantly. In the following table we show that imposing a new crew base only increase the number of crew pairings in the optimal crew pairings by one or two. It means that flight re-timing and imposing a new crew base does not need so significant extra crew cost. Table 2. The number of crew pairings selected for different values of for the case with single crew base and two crew bases Single Crew Base Two Crew Bases α=5% α=10% α=5% α=10% α=5% α=10% α=5% α=10% Original Conclusion and Discussion We discuss the improvement of the robustness of flight schedule through flight re-timing and imposing a new crew base. This approach can improve the robustness of flight schedule significantly, meanwhile the number of additional crew pairings is not so significant. Acknowledgments The authors thank PT. Garuda Indonesia Tbk for supporting the authors work with the flight schedules. References 1. Abdelghany, A., Ekollu, G., Narasimhan, R. and Abdelghany, K., A Proactive Crew Recovery Decision Support Tool for Commercial Airline During Irregular Operations, Annals of Operations Research 127(1-4), (2004). 72

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