Congested airports benefit from parallel-point merge systems (P-PMSs) for efficient arrival route control. However, the decline in air traffic due to COVID-19 has curtailed its optimal utilisation, especially with the reduced need for long sequencing legs. As air traffic is poised to rebound, the evident volatility seen during and post COVID-19, as well as the daily fluctuations between peak and off-peak hours, underscore the importance of the dynamic utilisation of sequencing legs in P-PMSs. EUROCONTROL proposes various leg configurations to manage fluctuating traffics, ensuring both efficiency and safety. First, we proposed two additional leg configurations for the Istanbul Airport, offering continuous descent with the engines operating at idle thrust during leg flights; partially overlapped and fully dissociated. While they offer an alternative for controllers during low to medium traffic scenarios, current long and fully overlapped parallel legs may be used in high traffic due to the volatility of traffic density throughout a day. Therefore, we suggest an approach that provides dynamic utilisation of these configurations. We first modeled and analysed the configurations for various traffic numbers and scenarios. Then, we introduced a new stochastic matheuristic model that considers the configuration changes throughout the day and provides feasible and robust sequences applicable to all configurations by combining the benefits of mathematical models with the adaptability and speed of heuristic methods. Several test problems were evaluated using the terminal manoeuvering area structure of Istanbul Airport as a case study. The results indicate that by changing configurations, an average of 35 kg in fuel savings per aircraft can be achieved. The results also show that the proposed approach outperforms traditional stochastic mathematical models and the first-come first-serve (FCFS) strategy, ensuring efficient air traffic management in terms of fuel and delay with robust sequencing by eliminating the need for re-sequencing during configuration changes.

This study presents a stochastic mixed-integer linear programming model for the aircraft sequencing and scheduling problem. The proposed model aims to minimise the average fuel consumption per aircraft in the Terminal Manoeuvring Area while considering uncertain flight durations for each flight. The tabu search algorithm was selected to solve the problem. The stochastic solution and deterministic solution results were compared to show the benefits of the stochastic solution. The average sample approximation technique was applied to this problem, and enhancement rates of the average fuel consumption per aircraft were 8.78% and 9.11% comparing the deterministic approach

Aircraft sequencing and scheduling within terminal airspaces has become more complicated due to increased air traffic demand and airspace complexity. A stochastic mixed-integer linear programming model is proposed to handle aircraft sequencing and scheduling problems using the simulated annealing algorithm. The proposed model allows for proper aircraft sequencing considering wind direction uncertainties, which are critical in the decision-making process. The proposed model aims to minimise total aircraft delay for a runway airport serving mixed operations. To test the stochastic model, an appropriate number of scenarios were generated for different air traffic demand rates. The results indicate that the stochastic model reduces the total aircraft delay considerably when compared with the deterministic approach.

We propose a stochastic programming model as a solution for optimizing the problem of locating and allocating medical supplies used in disaster management. To prepare for natural disasters, we developed a stochastic optimization approach to select the storage location of medical supplies and determine their inventory levels and to allocate each type of medical supply. Our model also captures disaster elaborations and possible effects of disasters by using a new classification for major earthquake scenarios. We present a case study for our model for the preparedness phase. As a case study, we applied our model to earthquake planning in Adana, Turkey. The experimental evaluations showed that the model is robust and effective. (Disaster Med Public Health Preparedness. 2017;11:747–755)

This paper analyzes the effects of uncertain soil loss in farm planning models. A disaggregated approach was used because of an interest in examining the impact of probabilistic soil loss constraints on farm level decisionmaking. A stochastic programming model was used to consider different levels of probability of soil loss. Traditional methods of analysis are shown to consistently overestimate net returns.

In this paper we study asymptotic consistency of law invariant convex risk measures and the corresponding risk averse stochastic programming problems for independent, identically distributed data. Under mild regularity conditions, we prove a law of large numbers and epiconvergence of the corresponding statistical estimators. This can be applied in a straightforward way to establish convergence with probability 1 of sample-based estimators of risk averse stochastic programming problems.

Motivated by the observationthat the gain-loss criterion, while offering economically meaningful prices of contingent claims,is sensitive to the reference measure governing the underlying stock price process (a situationreferred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure. Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem ofasset pricing under ambiguity of measure, and illustrate its use.

Vector autoregressive processes of the first order are considered which are non-negative and optimize a linear objective function. These processes may be used in stochastic linear programming with a dynamic structure. By using Tweedie's results from the theory of Markov chains, conditions for geometric rates of convergence to stationarity (i.e. so-called geometric ergodicity) and for existence and geometric convergence of moments of these processes are obtained.