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    Exploration of a Generalized Benders Decomposition Method for Solving Project Scheduling Problems with Resource Constraints
    (SCITEPRESS - Science and Technology Publications, 2025)
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    Pablo Miranda-Gonzalez
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    This research introduces a new Generalized Benders Decomposition-based Algorithm (GBDA) to solve the Multi-Mode Resource-Constrained Project Scheduling Problem (MRCPSP). The MRCPSP is a scheduling problem that besides precedence constraints, includes renewable and non-renewable resource constraints, as well as the selection of execution modes for the project activities. This mode selection determines the resource usage and duration of each activity. The GBDA splits the problem into a Master Problem (MP) and a Sub- Problem (SP) with a relaxation. Both problems are solved alternately, each one incorporating information from the other at each iteration, until a stopping criterion is met. Additionally, at each iteration, a non-relaxed SP is solved to obtain a solution for the original problem, and the best solution from all iterations is reported. The GBDA was tested, with three different stopping criteria, on benchmark instances from a public library and compared against solving the traditional formulation of the problem with an exact Mixed Integer Linear Programming (MILP) method. The GBDA found solutions of good quality in less than half the computing time than the exact method, with one of the stopping criteria. The analysis of the results provides valuable insights for future research.
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    Generalized Benders decomposition-based matheuristics for the multi-mode resource-constrained project scheduling problem
    (Springer Science and Business Media LLC, 2025-03-13)
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    Pablo A. Miranda-Gonzalez
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    The multi-mode resource-constrained project scheduling problem is an NP-hard optimization problem with practical applications in construction, software development, manufacturing, and other industrial and business situations. It involves a set of activities that need to be sequenced while considering precedence and resource constraints as well as different alternative execution modes, which determine each activity’s duration and resource consumption. This research proposes three matheuristic strategies based on a reformulation and partial relaxation of the problem, including a generalized Benders decomposition (GBD)-based algorithm to solve the relaxed problem and three different procedures to find a solution to the original problem. The strategies were tested using benchmark instances of various sizes obtained from published libraries. These strategies showed a significant improvement in speed, achieving up to 92.77% faster performance than the exact method for finding high-quality sub-optimal solutions. This offers a valuable trade-off between computation time and solution quality. Additionally, the GBD-based algorithm generated tighter lower bounds than other existing methods in the literature for a substantial number of the tested instances, all within a very short computing time.
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    Scopus© Citations 5  9  1
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    A Formulation for the Stochastic Multi-Mode Resource-Constrained Project Scheduling Problem Solved with a Multi-Start Iterated Local Search Metaheuristic
    (MDPI, 2023)
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    Pablo A. Miranda-gonzalez
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    <jats:p>This research introduces a stochastic version of the multi-mode resource-constrained project scheduling problem (MRCPSP) and its mathematical model. In addition, an efficient multi-start iterated local search (MS-ILS) algorithm, capable of solving the deterministic MRCPSP, is adapted to deal with the proposed stochastic version of the problem. For its deterministic version, the MRCPSP is an NP-hard optimization problem that has been widely studied. The problem deals with a trade-off between the amount of resources that each project activity requires and its duration. In the case of the proposed stochastic formulation, the execution times of the activities are uncertain. Benchmark instances of projects with 10, 20, 30, and 50 activities from well-known public libraries were adapted to create test instances. The adapted algorithm proved to be capable and efficient for solving the proposed stochastic problem.</jats:p>
      4
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    A Capacitated Vehicle Routing Model for Distribution and Repair with a Service Center
    (MDPI, 2025)
    Irma-delia Rojas-cuevas
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    <jats:p>Background: Distribution systems often face the dual challenge of delivering products to customers and retrieving damaged items for repair, especially when the service center is separate from the depot. An optimized solution to this logistics problem produces benefits in terms of costs, greenhouse gas emissions, and disposal reduction. Methods: This research proposes a Capacitated Vehicle Routing Problem with Service Center (CVRPwSC) model to determine optimal routes involving customers, the depot, and the service center. AMPL-Gurobi was used to solve the model on adapted instances and new instances developed for the CVRPwSC. Additionally, a Variable Neighborhood Search (VNS) algorithm was implemented and compared with AMPL-Gurobi. Results: The model was applied to a real-world case study, achieving a 40% reduction in fuel costs, a reduction from 5 to 3 routes, and a sustainable logistics operations model with potential reductions of greenhouse gas emissions and item disposals. Conclusions: The main contribution of the proposal is a minimum-cost routing model integrating item returns for repair with customer deliveries, while the limitation is the exclusion of scenarios where return items exceed vehicle capacity. Finally, future research will enhance the CVRPwSC model by incorporating additional constraints and decision variables to address such scenarios.</jats:p>
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