Keywords

1 Introduction

In the dynamic and complex world of aviation, the effective scheduling of flight crews and aircraft is a critical aspect that directly impacts operational efficiency, passenger satisfaction, and airline profitability. The intricate interplay between crew members, their qualifications, aircraft availability, and the ever-changing nature of air travel demands sophisticated optimization techniques to navigate the challenges posed by irregular operations. This study explores the application of Simulated Annealing (SA)—a powerful metaheuristic algorithm—to optimize integrated flight-crew-aircraft scheduling in the face of such disruptions, aiming to achieve effective solutions that mitigate the impact of unforeseen events and maintain operational resilience. Irregular operations, including weather disturbances, air traffic congestion, mechanical issues, and crew unavailability, can cause disruptions to airline schedules, leading to delays, cancellations, and missed connections. These disturbances not only result in increased costs for airlines but also have a profound impact on customer satisfaction. As a result, airlines strive to minimize the adverse effects of irregular operations by developing robust scheduling solutions that allow for rapid adaptations and optimal resource allocation.

SA, a metaheuristic optimization technique inspired by the annealing process in metallurgy, has proven to be a valuable tool in addressing complex scheduling problems. SA has gained popularity in various domains for its ability to find near-optimal solutions in large solution spaces, even in the presence of highly nonlinear and non-convex objective functions. By simulating the gradual cooling and reorganization of atoms in a solid, this algorithm emulates the search for an optimal configuration through iterative adjustments and stochastic transitions, allowing for the exploration of a wide range of solutions. In the context of integrated flight-crew-aircraft scheduling, SA can effectively handle the complexities arising from the need to align crew qualifications, contractual regulations, and aircraft availability. By considering a multitude of constraints, such as crew rest requirements, duty time limitations, and aircraft maintenance needs, SA provides a robust framework to optimize the allocation of flight crews to aircraft in the face of irregular operations. Furthermore, this technique can account for various factors, such as minimizing delays and cancellations, maximizing crew utilization, and ensuring efficient resource utilization, all while maintaining compliance with regulatory standards.

This study delves into the intricacies of integrating SA with flight-crew-aircraft scheduling, highlighting its potential in mitigating the disruptive impact of irregular operations. By harnessing the power of this optimization method, airlines can enhance their operational performance, reduce costs, and improve customer satisfaction by efficiently managing the allocation of crews and aircraft during challenging circumstances. Through a comprehensive exploration of the SA approach, we aim to provide valuable insights and practical guidelines for aviation professionals seeking effective solutions in the complex realm of integrated flight-crew-aircraft scheduling.

2 Literature Review

There are many studies in the literature that propose SA method for different airline scheduling problems. These problems are sometimes considered individually and sometimes in an integrated manner. The following Table 1 indicates just the studies, which are mainly considered to implement SA for the integrated airline scheduling problem, in the literature.

Table 1. The considered studies to use SA for the ıntegrated airline scheduling problem
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The inception of the mathematical model was sparked by a study conducted by Stojkovıć and Soumis [5, 6], aiming to present an optimization framework addressing the challenge of concurrent operational flight and crew scheduling. Subsequently, the comprehensive integrated flight crew scheduling model was formulated with a primary focus on aircraft scheduling considerations. Therefore, the studies [1, 2, 7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28] focusing on aircraft scheduling (fleet assignment and/or aircraft routing) problems with integrating flight and/or crew scheduling problems in the literature are considered to suggest an optimization model for the integrated flight-aircraft-crew scheduling problem. To develop the optimization problem about only the crew scheduling perspective, the latest studies [29,30,31,32,33,34,35,36,37] in the literature are considered.

3 Methodology

In this study, the formidable task of optimizing integrated flight-crew-aircraft scheduling in the challenging context of irregular operations was approached with a powerful tool—SA, implemented using the R programming language. R’s versatility in handling data and conducting complex optimization procedures played a pivotal role in our research. By leveraging R, we were able to develop and execute an efficient SA algorithm, enabling us to tackle the intricate scheduling problem faced by the aviation industry. The flexibility and ease of use of R allowed us to adapt our code to the specific needs of this demanding domain, ensuring that our solutions were not only effective but also tailored to the unique constraints of the airline industry. Through this study, R has demonstrated its significance as a valuable resource in the quest for more resilient and cost-effective integrated flight operations. The steps involved in the SA algorithm can be summarized as below:

  • Initialize: Start with an initial solution. This solution can be generated randomly or based on some heuristics.

  • Set Parameters: Define parameters like initial temperature and cooling rate. These parameters control the annealing schedule.

  • Define a Stopping Criterion: Decide when to stop the algorithm. This could be a maximum number of iterations, a specific temperature threshold, or other criteria related to the problem.

  • Main Loop:

  • Repeat the following steps until the stopping criterion is met.

  • Generate a Neighbor Solution: Create a neighboring solution by making a small change to the current solution. The nature of this change depends on the problem, but it should be based on some probabilistic criteria.

  • Calculate Cost: Compute the cost or objective function value of the new solution and the current solution.

  • Evaluate Acceptance: Determine whether to accept the neighbor solution. Typically, if the neighbor solution has a lower cost, it’s accepted. However, it may also be accepted with some probability if it has a higher cost, based on a probabilistic criterion (Metropolis criterion).

  • Update Current Solution: If the neighbor solution is accepted, set it as the new current solution.

  • Update Best Solution: If the current solution is better than the best solution found so far, update the best solution.

  • Cooling: Reduce the temperature according to the cooling rate. This reduces the likelihood of accepting worse solutions as the algorithm progresses.

  • Output: Once the stopping criterion is met, or after a predefined number of iterations, output the best solution found during the search.

A new mathematical model, which is constructed by using Mixed Integer Non-linear Programming (MINLP) in this study includes the following objectives:

  • Minimizing the total flight-crew assignment cost,

  • Minimizing the total penalty cost of using flights that have long connection/waiting time (in-active time),

  • Minimizing the total flight delay cost and

  • Minimizing the total aircraft assignment cost. The aircraft assignment cost includes two main cost items: the total operating cost and the total passenger spill cost.

The considered constraints are related to:

  • Flight coverage constraints

  • Flight precedence constraints

  • Task assignment constraints

  • Network flow balance constraints

  • Unit flow constraints

  • Constraints for the requirement for nonlinear compatibility between flow and time variables.

  • Time windows constraints

The small-sized problem of the AnadoluJet airline company is considered in this study. The integrated problem modelled by using MINLP was solved by SA algorithm in the R programming language. The suggested code in R programming language in this study is as the following. The required packages to run the code and the explanations of each line (considered parameters, decision variables, objective function, SA steps, etc.) are shown below.

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The following Fig. 1 gathered by R code shows the best solutions over iterations.

Fig. 1.
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The best solutions over iterations

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After applying the SA algorithm using the R programming language to solve the complex integrated flight-crew-aircraft scheduling problem, which is often modelled as a MINLP problem, we have observed the remarkable utility of this approach in delivering highly efficient solutions. The combination of SA adaptability and the computational capabilities of R proved to be a formidable force in addressing the intricate scheduling challenges posed by the aviation industry. The algorithm, driven by R, successfully navigated the complex solution space, yielding solutions that not only met operational constraints but also demonstrated cost-effectiveness and adaptability in the face of irregular operations. This underscores the power of SA as a practical and effective tool in optimizing integrated flight-crew-aircraft scheduling, contributing to more streamlined and resilient operations in the aviation sector.

4 Conclusions

In the fast-paced and dynamic world of aviation, optimizing integrated flight-crew-aircraft scheduling is a paramount challenge. The intricate web of variables, from crew availability to aircraft maintenance, becomes even more complex when irregular operations disrupt the well-laid plans. In our exploration of this complex problem, we turned to the powerful optimization technique known as SA to find effective solutions that can withstand the turbulence of unexpected disruptions.

SA emerges as a potent ally in the intricate realm of integrated flight-crew-aircraft scheduling, especially when confronted with the turbulence of irregular operations. Its capacity to swiftly adapt to changing circumstances, explore diverse solutions, and minimize costs positions it as a valuable tool for the aviation industry. As airlines continue to grapple with the ever-evolving challenges of scheduling, SA offers a path towards more efficient, resilient, and cost-effective operations, ultimately ensuring smoother journeys for both airlines and passengers in the face of unexpected disruptions. It is aimed that the applied methodology can be source of inspiration for the decision makers working on the integrated airline scheduling problems.