A Benders Based Rolling Horizon Algorithm for a Dynamic Facility Location Problem

This study presents a well-known capacitated dynamic facility location problem (DFLP) that satisfies the customer demand at a minimum cost by determining the time period for opening, closing, or retaining an existing facility in a given location. To solve this challenging NP-hard problem, this paper develops a unique hybrid solution algorithm that combines a rolling horizon algorithm with an accelerated Benders decomposition algorithm. Extensive computational experiments are performed on benchmark test instances to evaluate the hybrid algorithm’s efficiency and robustness in solving the DFLP problem. Computational results indicate that the hybrid Benders based rolling horizon algorithm consistently offers high quality feasible solutions in a much shorter computational time period than the stand-alone rolling horizon and accelerated Benders decomposition algorithms in the experimental range

Hybrid Set Covering and Dynamic Modular Covering Location Problem: Application to an Emergency Humanitarian Logistics Problem

This paper presents an extension of the covering location problem as a hybrid covering model that utilizes the set covering and maximal covering location problems. The developed model is a multi-period model that considers strategic and tactical planning decisions. Hybrid covering location problem (HCLP) determines the location of the capacitated facilities by using dynamic set covering location problem as strategic decisions and assigns the constructive units of facilities and allocates the demand points by using dynamic modular capacitated maximal covering location problem as tactical decisions. One of the applications of the proposed model is locating first aid centers in humanitarian logistic services that have been addressed by studying a threat case study in Japan. In addition to validating the developed model, it has been compared to other possible combined problems, and several randomly generated examples have been solved. The results of the case study and model validation tests approve that the main hybrid developed model (HCLP) is capable of providing better coverage percentage compared to conventional covering models and other hybrid variants

Modular Supply Network Optimization of Renewable Ammonia and Methanol Co-production

To reduce the use of fossil fuels and other carbonaceous fuels, renewable energy sources such as solar, wind, geothermal energy have been suggested to be promising alternative energy that guarantee sustainable and clean environment. However, the availability of renewable energy has been limited due to its dependence on weather and geographical location. This challenge is intended to be solved by the utilization of the renewable energy in the production of chemical energy carriers. Hydrogen has been proposed as a potential renewable energy carrier, however, its chemical instability and high liquefaction energy makes researchers seek for other alternative energy carriers. Ammonia and methanol can serve as promising alternative energy carriers due to their chemical stability at room temperature, low liquefaction energy, high energy value. The co-production of these high energy dense energy carriers offers economic and environmental advantages since their synthesis involve the direct utilization of CO2 and common unit operations. This problem report aims to review the optimization of the co-production of methanol and ammonia from renewable energy. Form this review, research challenges and opportunities are identified in the following areas: (i) optimization of methanol and ammonia co-production under renewable and demand uncertainty, (ii) impacts of the modular exponent on the feasibility of co-production of ammonia and methanol, and (iii) development of modern computational tools for systems-based analysis

General Bounds for Incremental Maximization

We propose a theoretical framework to capture incremental solutions to cardinality constrained maximization problems. The defining characteristic of our framework is that the cardinality/support of the solution is bounded by a value $k\in\mathbb{N}$ that grows over time, and we allow the solution to be extended one element at a time. We investigate the best-possible competitive ratio of such an incremental solution, i.e., the worst ratio over all $k$ between the incremental solution after $k$ steps and an optimum solution of cardinality $k$. We define a large class of problems that contains many important cardinality constrained maximization problems like maximum matching, knapsack, and packing/covering problems. We provide a general $2.618$-competitive incremental algorithm for this class of problems, and show that no algorithm can have competitive ratio below $2.18$ in general. In the second part of the paper, we focus on the inherently incremental greedy algorithm that increases the objective value as much as possible in each step. This algorithm is known to be $1.58$-competitive for submodular objective functions, but it has unbounded competitive ratio for the class of incremental problems mentioned above. We define a relaxed submodularity condition for the objective function, capturing problems like maximum (weighted) ($b$-)matching and a variant of the maximum flow problem. We show that the greedy algorithm has competitive ratio (exactly) $2.313$ for the class of problems that satisfy this relaxed submodularity condition. Note that our upper bounds on the competitive ratios translate to approximation ratios for the underlying cardinality constrained problems.Comment: fixed typo

Runway exit designs for capacity improvement demonstrations. Phase 2: Computer model development

The development is described of a computer simulation/optimization model to: (1) estimate the optimal locations of existing and proposed runway turnoffs; and (2) estimate the geometric design requirements associated with newly developed high speed turnoffs. The model described, named REDIM 2.0, represents a stand alone application to be used by airport planners, designers, and researchers alike to estimate optimal turnoff locations. The main procedures are described in detail which are implemented in the software package and possible applications are illustrated when using 6 major runway scenarios. The main output of the computer program is the estimation of the weighted average runway occupancy time for a user defined aircraft population. Also, the location and geometric characteristics of each turnoff are provided to the user