Frequently, parameters in optimization models are subject to a high level of uncertainty coming from several sources and, as such, assuming them to be deterministic can lead to solutions that are infeasible in practic...
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Frequently, parameters in optimization models are subject to a high level of uncertainty coming from several sources and, as such, assuming them to be deterministic can lead to solutions that are infeasible in practice. Robust optimization is a computationally efficient approach that generates solutions that are feasible for realizations of uncertain parameters near the nominal value. This paper develops a data-driven robust optimization approach for the scheduling of a straight pipeline connecting a single refinery with multiple distribution centers, considering uncertainty in the injection rate. For that, we apply support vector clustering to learn an uncertainty set for the robust version of the deterministic model. We compare the performance of our proposed robust model against one utilizing a standard robust optimization approach and conclude that data-driven robust solutions are less conservative.
Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this c...
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Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the dial-a-ride problem (DARP): Given a set of transportation requests with pickup and delivery locations, passenger numbers, time windows, and maximum ride times, an optimal routing for a fleet of vehicles, including an optimized passenger assignment, needs to be determined. We present tight mixed-integer linear programming (MILP) formulations for the DARP by combining two state-of-the-art models into novel location-augmented-event-based formulations. Strong valid inequalities and lower and upper bounding techniques are derived to further improve the formulations. We then demonstrate the theoretical and computational superiority of the new models: First, the linearprogramming relaxations of the new formulations are stronger than existing location-based approaches. Second, extensive numerical experiments on benchmark instances show that computational times are on average reduced by 53.9% compared to state-of-the-art event-based approaches.
Despite the adverse impacts of occupational fatigue such as accidents and injuries in the manufacturing industry, it has not been systematically examined in the literature on production scheduling. In this paper, we i...
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Despite the adverse impacts of occupational fatigue such as accidents and injuries in the manufacturing industry, it has not been systematically examined in the literature on production scheduling. In this paper, we integrate the classic bio-mathematical fatigue prediction model from the brain science literature into the simple single machine scheduling problem with sequence-dependent setup times. Then, we formulate the problem as a mixed-integer linear programming model and propose an adaptive large neighborhood search heuristic. The effectiveness of the heuristic is numerically validated through real cases. Finally, we argue that considering bio-mathematical fatigue prediction can lead to safer production schedules, notably reducing the fatigue working hours in our real case.
We study mathematical formulations for batch-processing machine scheduling problems (BPMPs), which are the challenging issues in the machine scheduling literature where machines are capable of processing a batch of jo...
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We study mathematical formulations for batch-processing machine scheduling problems (BPMPs), which are the challenging issues in the machine scheduling literature where machines are capable of processing a batch of jobs simultaneously if jobs with non-identical sizes can be packed in a capacitated machine. In this paper, we tackle single- and parallel-machine BPMPs, and other interesting problem variants that aim at minimizing the makespan. We develop novel formulations along with valid inequalities and an algorithm framework that makes use of dual information and bounding techniques to achieve efficiency when instances are intractable. Extensive computational experiments on benchmark instances show that our approaches achieve state-of-the-art results and prove the optimality of intractable instances in the literature.
In this paper, we consider an oilfield planning problem with decisions about where and when to invest in wells and facilities to maximize profit. The model, in the form of a mixed-integerlinear program, includes an o...
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In this paper, we consider an oilfield planning problem with decisions about where and when to invest in wells and facilities to maximize profit. The model, in the form of a mixed-integerlinear program, includes an option to expand capacity for existing facilities, annual budget constraints, well closing decisions, and fixed production profiles once wells are opened. While fixed profiles area novel and important feature, they add another set of time-indexed binary variables that makes the problem difficult to solve. To find solutions, we develop a three-phase sequential algorithm that includes (1) ranking, (2) branching, and (3) refinement. Phases 1 and 2 determine which facilities and wells to open, along with well-facility assignments. Phase 3 ensures feasibility with respect to budget constraints and adjusts construction times and facility capacities to increase profit. We first demonstrate how our algorithm navigates the problem's complex features by applying it to a case study parameterized with realistic production profiles. Then, we perform computational experiments on small instances and show that our algorithm generally achieves the same objective function values as CPLEX but in much less time. Lastly, we solve larger instances using our three-phase algorithm and several variations to demonstrate its scalability and to highlight the roles of specific algorithmic components.
This paper explores a mixed-integer linear programming (MILP) approach to plan the maintenance tasks in an airline. The MILP model finds feasible maintenance plans, by minimizing the costs associated with maintenance ...
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This paper explores a mixed-integer linear programming (MILP) approach to plan the maintenance tasks in an airline. The MILP model finds feasible maintenance plans, by minimizing the costs associated with maintenance activities and costs associated with unavailability. A constructive matheuristic approach is put forward, by solving the maintenance planning problem sequentially. The model and the matheuristic is then applied to a case study from the main Portuguese airline company. The results suggest that the proposed matheuristic approach for maintenance planning in practice, as explored in the case study, finds feasible solutions in a much lower computational time. Moreover, a sensitivity analysis is conducted to assess the impact of hangar's capacity and other input parameters in the maintenance plan. Our approach provides an effective way to support decision-making in maintenance planning for a fleet of aircraft, while complying with several operational, technical, and labour constraints.
The multi-row facility layout problem is a prevalent and significant planning challenge in manufacturing workshops. This problem requires distributing facilities with pairwise transport weights among several rows to a...
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The multi-row facility layout problem is a prevalent and significant planning challenge in manufacturing workshops. This problem requires distributing facilities with pairwise transport weights among several rows to attain a layout with minimal logistics costs. However, the significance of aisles in multi-row facility layout has frequently been overlooked. An efficient aisle structure can result in a smooth transportation path and reduced material-handling costs. This paper contributes to the existing literature by introducing a new multi-row facility layout problem that considers long-straight aisles. First, mathematical formulas for the actual transportation distance between facilities through aisles are defined, and a mixed-integerprogramming model is constructed. Second, a hybrid algorithm based on an intelligent algorithm and a mathematical model is proposed. This method utilizes an improved teaching-learning-based optimization algorithm as a framework for optimizing the discrete facility sequence, and two decoding methods based on linearprogramming are designed to obtain the facility locations and transportation paths. Experimental results demonstrate that the two decoding strategies have their own advantages in terms of solution quality, efficiency, and area utilization. Moreover, improvement strategies for teaching-learning-based optimization algorithms are observed to be effective. Finally, we present two actual workshop examples of multi-row layout designs. The comparison of different algorithms reveals that the proposed algorithm has significant advantages in terms of solution quality and stability.
Microgrids (MGs) are revolutionizing modern power systems by enabling decentralized energy production, renewable energy integration, and enhanced grid resilience. However, the increasing complexity of MGs, particularl...
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Microgrids (MGs) are revolutionizing modern power systems by enabling decentralized energy production, renewable energy integration, and enhanced grid resilience. However, the increasing complexity of MGs, particularly with the integration of Distributed Energy Resources (DERs), poses significant challenges for traditional protection schemes. This study addresses the coordination of Directional Overcurrent Relays (DOCRs) in MGs through a mixed-integer linear programming (MILP) model. The main contribution is a MILP model that optimizes relay settings, including Time Multiplier Settings (TMS) and standard characteristic curves, to minimize tripping times, while ensuring selectivity. Another key contribution of this work is the integration of both IEC and IEEE standard curves, which enhances coordination performance compared to using a single standard. The model was tested on the IEC benchmark microgrid, and the results demonstrated significant improvements in fault-clearing times across various operational modes. By leveraging advanced optimization techniques and diverse characteristic curves, this study contributes to the development of resilient and efficient protection systems for modern microgrids, ensuring reliable operation under varying fault conditions and DER penetration.
Thoroughly assessing future energy systems requires examining both their end states and the paths leading to them. Employing dynamic investment or multi-stage optimization models is crucial for this analysis. However,...
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Thoroughly assessing future energy systems requires examining both their end states and the paths leading to them. Employing dynamic investment or multi-stage optimization models is crucial for this analysis. However, solving these optimization problems becomes increasingly challenging due to their long time horizons - often spanning several decades - and their dynamic nature. While simplifications like aggregations are often used to expedite solving procedures, they introduce higher uncertainty into the results and might lead to suboptimal solutions compared to non-simplified models. Against this background, this paper presents a rigorous optimization method tailored for multi-stage optimization problems in long-term energy system planning. By dividing the solution algorithm into a design and operational optimization step, the proposed method efficiently finds feasible solutions for the non-simplified optimization problem with simultaneous quality proof. Applied to a real-life energy system of a waste treatment plant in Germany, the method significantly outperforms a benchmark solver by reducing the computational time to find the first feasible solution from more than two weeks to less than one hour. Furthermore, it exhibits greater robustness compared to a conventional long-term optimization approach and yields solutions closer to the optimum. Overall, this method offers decision-makers computationally efficient and reliable information for planning investment decisions in energy systems.
In this paper, we propose a novel model that is based on a hybrid paradigm composed of a graph convolution network and an integerprogramming solver. The model utilizes the potential of graph neural networks, which ha...
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In this paper, we propose a novel model that is based on a hybrid paradigm composed of a graph convolution network and an integerprogramming solver. The model utilizes the potential of graph neural networks, which have the ability to capture complex relationships and preferences among nodes. While the graph neural network forms node embeddings that are fed as input into the next layer of the model, the introduced MILP solver works to solve the team formation problem. Finally, our experimental work shows that the outcome of the model is balanced teams.
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