Optimal CH-47 and C-130 Workload Balance

The Air Force can save thousands of dollars by reducing the number of blade hours on the CH-47 through finding an optimal mixture of CH-47s and C-130s to conduct current operations in Afghanistan and Iraq. Ultimately these savings will relieve maintenance operations for the CH-47 and lengthen the lifespan of the CH-47 airframe. Moreover, incorporating C-130s into the operations will reduce cargo transit time from supply depots. This study looks at the involvement of the C-130 in CH-47 airlift operations to reduce CH-47 usage and increase supply efficiency. The research focus is narrowed to current airlift operations in Afghanistan and Iraq in the CENTCOM theater of operation. A mathematical representation of current CH-47 operations augmented with C-130s is the foundation of this research. Particularly, these operations in CENTCOM\u27s area of operations are formulated as linear transportation problems using network mathematics. The uniqueness this research offers entails modified scenarios of the transportation problem solved as an optimization model. AMC requires additional constraints to be augmented with the basic transportation linear model that pushes this application in new areas. In addition, the uncommon layout of supply depots to the specified receiving airfields in Afghanistan and Iraq provide an altogether new kind of transportation problem

DEMAND-RESPONSIVE AIRSPACE SECTORIZATION AND AIR TRAFFIC CONTROLLER STAFFING

This dissertation optimizes the problem of designing sector boundaries and assigning air traffic controllers to sectors while considering demand variation over time. For long-term planning purposes, an optimization problem of clean-sheet sectorization is defined to generate a set of sector boundaries that accommodates traffic variation across the planning horizon while minimizing staffing. The resulting boundaries should best accommodate traffic over space and time and be the most efficient in terms of controller shifts. Two integer program formulations are proposed to address the defined problem, and their equivalency is proven. The performance of both formulations is examined with randomly generated numerical examples. Then, a real-world application confirms that the proposed model can save 10%-16% controller-hours, depending on the degree of demand variation over time, in comparison with the sectorization model with a strategy that does not take demand variation into account. Due to the size of realistic sectorization problems, a heuristic based on mathematical programming is developed for a large-scale neighborhood search and implemented in a parallel computing framework in order to obtain quality solutions within time limits. The impact of neighborhood definition and initial solution on heuristic performance has been examined. Numerical results show that the heuristic and the proposed neighborhood selection schemes can find significant improvements beyond the best solutions that are found exclusively from the Mixed Integer Program solver's global search. For operational purposes, under given sector boundaries, an optimization model is proposed to create an operational plan for dynamically combining or splitting sectors and determining controller staffing. In particular, the relation between traffic condition and the staffing decisions is no longer treated as a deterministic, step-wise function but a probabilistic, nonlinear one. Ordinal regression analysis is applied to estimate a set of sector-specific models for predicting sector staffing decisions. The statistical results are then incorporated into the proposed sector combination model. With realistic traffic and staffing data, the proposed model demonstrates the potential saving in controller staffing achievable by optimizing the combination schemes, depending on how freely sectors can combine and split. To address concerns about workload increases resulting from frequent changes of sector combinations, the proposed model is then expanded to a time-dependent one by including a minimum duration of a sector combination scheme. Numerical examples suggest there is a strong tradeoff between combination stability and controller staffing

OPTIMIZATION MODELS AND METHODOLOGIES TO SUPPORT EMERGENCY PREPAREDNESS AND POST-DISASTER RESPONSE

This dissertation addresses three important optimization problems arising during the phases of pre-disaster emergency preparedness and post-disaster response in time-dependent, stochastic and dynamic environments. The first problem studied is the building evacuation problem with shared information (BEPSI), which seeks a set of evacuation routes and the assignment of evacuees to these routes with the minimum total evacuation time. The BEPSI incorporates the constraints of shared information in providing on-line instructions to evacuees and ensures that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. A mixed-integer linear program is formulated for the BEPSI and an exact technique based on Benders decomposition is proposed for its solution. Numerical experiments conducted on a mid-sized real-world example demonstrate the effectiveness of the proposed algorithm. The second problem addressed is the network resilience problem (NRP), involving an indicator of network resilience proposed to quantify the ability of a network to recover from randomly arising disruptions resulting from a disaster event. A stochastic, mixed integer program is proposed for quantifying network resilience and identifying the optimal post-event course of action to take. A solution technique based on concepts of Benders decomposition, column generation and Monte Carlo simulation is proposed. Experiments were conducted to illustrate the resilience concept and procedure for its measurement, and to assess the role of network topology in its magnitude. The last problem addressed is the urban search and rescue team deployment problem (USAR-TDP). The USAR-TDP seeks an optimal deployment of USAR teams to disaster sites, including the order of site visits, with the ultimate goal of maximizing the expected number of saved lives over the search and rescue period. A multistage stochastic program is proposed to capture problem uncertainty and dynamics. The solution technique involves the solution of a sequence of interrelated two-stage stochastic programs with recourse. A column generation-based technique is proposed for the solution of each problem instance arising as the start of each decision epoch over a time horizon. Numerical experiments conducted on an example of the 2010 Haiti earthquake are presented to illustrate the effectiveness of the proposed approach

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Modeling and Analysis of Multicommodity Network Flows via Goal Programming

In this research we focused on the mobility system modeled by the AMC mobility planner\u27s calculator (AMPCALC). We developed AMPCALC as a user-friendly tool and allow the user to easily carry out strategic airlift, air refueling and aeromedical evacuation calculations that are covered in Air Force Pamphlet 10-1403. In this study, Excel software and its macro language, Visual Basic for Application, are our two main tools. In the methodology of the thesis we examined fundamental aspects of the mobility system in AMPCALC. We discussed formulation logic of the mobility cycle. We presented ramp use optimization and tanker optimization processes. We also conducted verification and validation of AMPCALC. Sensitivity analysis of the model includes a response surface study. To be able to investigate the main effects and interaction effects of the input factors on closure time, we performed a 26 factorial design. No linear relations are observed, but some relations between inputs and closure time are observed