Senay Solak

Optimization of R&D project portfolios under endogenous uncertainty

Project portfolio management deals with the dynamic selection of research and development (R&D) projects and determination of resource allocations to these projects over a planning period. Given the uncertainties and resource limitations over the planning period, the objective is to maximize the expected total discounted return or the expectation of some other function for all projects over a long time horizon. We develop a detailed formal description of this problem and the corresponding decision process, and then model it as a multistage stochastic integer program with endogenous uncertainty. Accounting for this endogeneity, we propose an efficient solution approach for the resulting model, which involves the development of a formulation technique that is amenable to scenario decomposition. The proposed solution algorithm also includes an application of the sample average approximation method, where the sample problems are solved through Lagrangian relaxation and a new lower bounding heuristic. The performance of the overall solution procedure is demonstrated using several implementations of the proposed approach.

A mixed integer program for flight-level assignment and speed control for conflict resolution

We consider the air traffic conflict resolution problem and develop an optimization model for generating speed trajectories that minimize the fuel expended to avoid conflicts. The problem is formulated by metering aircraft at potential conflict points. The developed model is a mixed integer linear program that can be solved in near real-time for large number of aircraft.

Near Real-Time Fuel-Optimal En Route Conflict Resolution

In this paper, we consider the air-traffic conflict-resolution problem and develop an optimization model to identify the required heading and speed changes of aircraft to avoid conflict such that fuel costs are minimized. Nonconvex fuel functions in the optimization problem are modeled through tight linear approximations, which enable the formulation of the problem as a mixed-integer linear program. The significance of the developed model is that fuel-optimal conflict-resolution maneuvers can be identified in near real time, even for conflicts involving a large number of aircraft. Computational tests based on realistic air-traffic scenarios demonstrate that conflicts involving up to 15 aircraft can be solved in less than 10 s with an optimality gap of around 0.02%.

The Stop-And-Drop Problem in Nonprofit Food Distribution Networks

In this paper, we introduce the stop-and-drop problem (SDRP), a new variant of location-routing problems, that is mostly applicable to nonprofit food distribution networks. In these distribution problems, there is a central warehouse that contains food items to be delivered to agencies serving the people in need. The food is delivered by trucks to multiple sites in the service area and partner agencies travel to these sites to pick up their food. The tactical decision problem in this setting involves how to jointly select a set of delivery sites, assign agencies to these sites, and schedule routes for the delivery vehicles. The problem is modeled as an integrated mixed-integer program for which we delineate a two-phase sequential solution approach. We also propose two Benders decomposition-based solution procedures, namely a linear programming relaxation based Benders implementation and a logic-based Benders decomposition heuristic. We show through a set of realistic problem instances that given a fixed time limit, these decomposition based methods perform better than both the standard branch-and-bound solution and the two-phase approach. The general problem and the realistic instances used in the computational study are motivated by interactions with food banks in southeastern United States.

A fuel optimal and reduced controller workload optimization model for conflict resolution

Despite the existence of several automated air traffic conflict resolution algorithms, there is a need for formulations that account for air traffic controller workload. This paper presents such an algorithm with controller workload constraints modeled parametrically. To this end, we first develop an integer programming model for general conflict resolution, which emphasizes the minimization of fuel costs, and runs in near real-time. A parametric procedure based on this model is then developed to consider controller workload limitations. Two versions of the parametric approach are described, along with computational results. It is demonstrated that both formulations can be used to capture a broad range of possible controller actions.

A two-stage stochastic optimization model for air traffic conflict resolution under wind uncertainty

This paper considers the air traffic conflict resolution problem in the context of wind uncertainty. Aircraft are assigned changes in airspeed to prevent conflict. The goal is to determine the optimal maneuver to balance deviation costs (e.g., fuel costs) and the probability of conflict. A two-stage recourse model is developed, in which new airspeeds are assigned in the first stage, based on expected costs due to possible corrective actions in the second stage. The second-stage considers the expected costs for any last-minute maneuvers to compensate wind modeling errors. The resulting model is solved in real-time via numerical methods, providing optimal airspeed values for the resolution of a conflict.

Determining Stochastic Airspace Capacity for Air Traffic Flow Management

Deterministic air traffic flow management (TFM) decisions---the state of the art in terms of implementation---often result in unused airspace capacity. This is because the inherent uncertainties in weather predictions make it difficult to determine the number of aircraft that can be safely accommodated in a region of airspace during a given period. On the other hand, stochastic TFM algorithms are not amenable to implementation in practice due to the lack of valid stochastic mappings between weather forecasts and airspace capacity to serve as inputs to these algorithms. To fill this gap, we develop a fast simulation-based methodology to determine the stochastic capacity of a region of airspace using integrated weather-traffic models. The developed methodology consists of combining ensemble weather forecast information with an air traffic control algorithm to generate capacity maps over time. We demonstrate the overall methodology through a novel conflict resolution procedure and a simple weather scenario generation tool, and also discuss the potential use of ensemble weather forecasts. An operational study based on comparisons of the generated capacity distributions with observed impacts of weather events on air traffic is also presented.

Stochastic models for strategic resource allocation in nonprofit foreclosed housing acquisitions

Increased rates of mortgage foreclosures in the U.S. have had devastating social and economic impacts during and after the 2008 financial crisis. As part of the response to this problem, nonprofit organizations such as community development corporations (CDCs) have been trying to mitigate the negative impacts of mortgage foreclosures by acquiring and redeveloping foreclosed properties. We consider the strategic resource allocation decisions for these organizations which involve budget allocations to different neighborhoods under cost and return uncertainty. Based on interactions with a CDC, we develop stochastic integer programming based frameworks for this decision problem, and assess the practical value of the models by using real-world data. Both policy-related and computational analyses are performed, and several insights such as the trade-offs between different objectives, and the efficiency of different solution approaches are presented.

Formulation of Reduced-Taskload Optimization Models for Conflict Resolution

This paper explores methods to include aspects of controller taskload into conflict-resolution programs through a parametric approach. We are motivated by the desire to create conflict-resolution decision-support tools that operate within a human-in-the-loop control architecture by actively accounting for, and moderating, controller taskload. Specifically, we introduce two conflict-resolution programs with the objective of managing controller conflict-resolution taskload, i.e., the number of maneuvers used to separate air traffic. Managing conflict-resolution taskload is accomplished by penalizing aircraft maneuvers through their L1 norm in the cost function or constraining the number of maneuvers directly. Analysis of the programs reveals that both approaches are successful at managing controller conflict-resolution taskload and minimizing fuel burn. Directly constraining conflict-resolution taskload is more successful at minimizing the variation in the number of aircraft maneuvers issued and returning the aircraft to their desired exit point. Penalizing maneuvers through L1 norm costs is more successful at reducing controller conflict-resolution taskload at lower traffic volumes. Ultimately, results demonstrate that the inclusion of such parametric models can successfully regulate controller conflict-resolution taskload.

A Specialized Column Generation Approach for a Vehicle Routing Problem with Demand Allocation

Motivated by logistical operations for a food bank, this paper addresses a class of vehicle routing problems with demand allocation considerations over a network of partner agencies locations and candidate delivery sites. Any delivery tour starts at a central depot operated by the food bank and selected delivery sites are sequentially visited in order to supply goods to a set of partner agencies who travel from their respective locations to their assigned delivery sites. The problem is modelled as a mixed-integer programme with the objective of minimizing a weighted average of the distances travelled by delivery vehicles and partner agencies, and is tackled via two heuristics. First, a relax-and-fix heuristic is presented for the proposed model and is computationally enhanced using two symmetry-defeating strategies. Second, the problem is reformulated as a set partitioning model with side packing constraints that prompts a specialized column generation approach. Computational experience is provided using realistic data instances to demonstrate the usefulness of the proposed heuristics and the importance of integrated solution techniques for this class of problems.