Browsing by Subject "Conic integer programming"
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Item Open Access Aircraft rescheduling with cruise speed control(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014-05-23) Aktürk, M. S.; Atamtürk, A.; Gürel, S.Airline operations are subject to frequent disruptions typically due to unexpected aircraft maintenance requirements and undesirable weather conditions. Recovery from a disruption often involves propagating delays in downstream flights and increasing cruise stage speed when possible in an effort to contain the delays. However, there is a critical trade-off between fuel consumption (and its adverse impact on air quality and greenhouse gas emissions) and cruise speed. Here we consider delays caused by such disruptions and propose a flight rescheduling model that includes adjusting cruise stage speed on a set of affected and unaffected flights as well as swapping aircraft optimally. To the best of our knowledge, this is the first study in which the cruise speed is explicitly included as a decision variable into an airline recovery optimization model along with the environmental constraints and costs. The proposed model allows one to investigate the trade-off between flight delays and the cost of recovery. We show that the optimization approach leads to significant cost savings compared to the popular recovery method delay propagation. Flight time controllability, nonlinear delay, fuel burn and CO2 emission cost functions, and binary aircraft swapping decisions complicate the aircraft recovery problem significantly. In order to mitigate the computational difficulty we utilize the recent advances in conic mixed integer programming and propose a strengthened formulation so that the nonlinear mixed integer recovery optimization model can be solved efficiently. Our computational tests on realistic cases indicate that the proposed model may be used by operations controllers to manage disruptions in real time in an optimal manner instead of relying on ad-hoc heuristic approaches.Item Open Access Assortment planning under non-linear cost structures(Bilkent University, 2019-04) Shams, FarzadWe first consider the assortment optimization problem with fixed product costs under the Mixtures of Multinomials (MMNL) Model. The problem is NP-hard even under the Multinomial Logit Model and the existing literature focuses on developing heuristics and bounds. We develop a conic integer programming formulation for the problem and valid inequalities to strengthen the formulation. We show that this approach can be used to solve instances that are very large { sizes beyond which it would be very difficult to accurately estimate parameters of the choice model { in a short amount of time, eliminating the need to develop and implement specialized algorithms for the problem. We also study the assortment planning problem where the inventory and replenishment costs are considered using the Economic Order Quantity model and the customers' choice is governed by the MMNL model. We show that the problem is NP-hard and propose a conic integer program for this problem. Our numerical experiments show that moderately sized instances can be solved in reasonable times and McCormick inequalities are effective in tightening the formulation.Item Open Access A Conic Integer Programming Approach to Constrained Assortment Optimization under the Mixed Multinomial Logit Model(Institute for Operations Research and the Management Sciences (INFORMS), 2017-08-12) Şen, Alper; Atamtürk, Alper; Kaminsky, P.We consider the constrained assortment optimization problem under the mixed multinomial logit model. Even moderately sized instances of this problem are challenging to solve directly using standard mixed-integer linear optimization formulations. This has motivated recent research exploring customized optimization strategies and approximation techniques. In contrast, we develop a novel conic quadratic mixed-integer formulation. This new formulation, together with McCormick inequalities exploiting the capacity constraints, enables the solution of large instances using commercial optimization software.Item Open Access Multi-location assortment optimization under capacity constraints(Bilkent University, 2016-08) Bebitoğlu, BaşakWe study the assortment optimization problem in an online setting where a retailer determines the set of products to carry in each of its distribution centers under a capacity constraint so as to maximize its expected profit (revenue minus the shipping costs). It is assumed that each distribution center is primarily responsible for a geographical location whose customers' choice is governed by a separate multinomial logit model. A distribution center can satisfy a demand of a region that it is not primarily responsible for, but this incurs an additional shipping cost for the retail company. We consider two variants of this problem. In the first variant, customers have access to the entire assortment in all locations but in the second variant, the online retail company can select which product to show to each region. Under each variant, we first assume that there is a constant shipping cost for all products between any two location. In the second case, we allow the shipping costs to differ based on the origin and destination. We develop conic quadratic mixed integer programming formulations and suggest a family of valid inequalities to strengthen these formulations. Numerical experiments show that our conic approach, combined with valid inequalities over-perform the mixed integer linear programming formulation and enables us to solve large instances optimally. Finally, we study the effect of various factors such as no-purchase preference, capacity constraint and shipping cost on company's profitability and assortment selection.Item Open Access Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times(Elsevier, 2018) Şafak, Ö.; Çavuş, Ö.; Aktürk, SelimWe propose a three-stage stochastic programming model which determines flight timing, fleeting and routing decisions while considering the randomness of demand and non-cruise times. Our model differs from the existing two-stage stochastic models by considering not only flight timing and potential passenger demand, but also expected operational expenses, such as fuel burn and carbon emission costs. We include aircraft cruise speed decisions to compensate for non-cruise time variability so as to satisfy the time requirements of the passenger connections. We handle nonlinear functions of fuel and emission costs associated with cruise speed adjustments by utilizing mixed integer second order cone programming. Because the three-stage stochastic model leads to a large decision tree and can be very time-consuming to solve optimally, we suggest a scenario group-wise decomposition algorithm to obtain lower and upper bounds for the optimal value of the proposed model. The lower and upper bounds are obtained by solving a number of group subproblems, which are similar to proposed multi-stage stochastic model defined over a reduced number of scenarios. We suggest a cutting plane algorithm, along with improvements, to efficiently solve each group subproblem. In the numerical experiments, we provide a significant cost savings over two-stage stochastic programming and deterministic approaches.