One of the most challenging tasks in today's food industry is controlling the product quality throughout the food supply chain. In this paper, we integrate food quality in decision-making on ...production and distribution in a food supply chain. We provide a methodology to model food quality degradation in such a way that it can be integrated in a mixed-integer linear programming model used for production and distribution planning. The resulting model is applied in an illustrative case study, and can be used to design and operate food distribution systems, using both food quality and cost criteria.
The golden ticket Fortnow, Lance
2013., 20130327, 2013, 2013-03-27, c2013
eBook
The P-NP problem is the most important open problem in computer science, if not all of mathematics.The Golden Ticketprovides a nontechnical introduction to P-NP, its rich history, and its algorithmic ...implications for everything we do with computers and beyond. In this informative and entertaining book, Lance Fortnow traces how the problem arose during the Cold War on both sides of the Iron Curtain, and gives examples of the problem from a variety of disciplines, including economics, physics, and biology. He explores problems that capture the full difficulty of the P-NP dilemma, from discovering the shortest route through all the rides at Disney World to finding large groups of friends on Facebook. But difficulty also has its advantages. Hard problems allow us to safely conduct electronic commerce and maintain privacy in our online lives.
The Golden Ticketexplores what we truly can and cannot achieve computationally, describing the benefits and unexpected challenges of the P-NP problem.
Fuzzy set theory has been extensively employed in mathematical programming, especially in linear programming problems. As a generalization of fuzzy sets, a hesitant fuzzy set is a very useful tool in ...places where there are some hesitations in determining the membership of an element to a set. There are few studies on hesitant fuzzy linear programming problems; therefore, in this paper, we have studied such problems. For this purpose, at first, the motivation of this paper is explained; then, types of hesitant fuzzy linear programming models are introduced. Since it is not easy to examine all of the hesitant fuzzy models for the linear programming problems in one paper, we have restricted ourselves to symmetric and right-hand-side hesitant fuzzy linear programming problems with the flexible approach and then proposed two new approaches to solve them. Finally, to illustrate the applicability of the proposed approaches, three examples under hesitant fuzzy information are given.
Any simple perturbation in a part of the game whether in the cost function and/or conditions is a big problem because it will require a game re-solution to obtain the perturbed optimal solution. This ...is a waste of time because there are methods required several steps to obtain the optimal solution, then at the end we may find that there is no solution. Therefore, it was necessary to find a method to ensure that the game optimal solution exists in the case of a change in the game data. This is the aim of this paper. We first provided a continuous static game rough treatment with Min-Max solutions, then a parametric study for the processing game and called a parametric rough continuous static game (PRCSG). In a Parametric study, a solution approach is provided based on the parameter existence in the cost function that reflects the perturbation that may occur to it to determine the parameter range in which the optimal solution point keeps in the surely region that is called the stability set of the \(1^{st}\) kind. Also the sets of possible upper and lower stability to which the optimal solution belongs are characterized. Finally, numerical examples are given to clarify the solution algorithm.
Due to increasing penetration of intermittent renewable energy and introduction of demand response programs, uncertainties occur in both supply and demand sides in real time for the current power ...grid system. To address these uncertainties, most ISOs/RTOs perform reliability unit commitment runs after the day-ahead financial market to ensure sufficient generation capacity available in real time to accommodate uncertainties. Two-stage stochastic unit commitment and robust unit commitment formulations have been introduced and studied recently to provide day-ahead unit commitment decisions. However, both approaches have limitations: 1) computational challenges due to the large scenario size for the stochastic optimization approach and 2) conservativeness for the robust optimization approach. In this paper, we propose a novel unified stochastic and robust unit commitment model that takes advantage of both stochastic and robust optimization approaches, that is, this innovative model can achieve a low expected total cost while ensuring the system robustness. By introducing weights for the components for the stochastic and robust parts in the objective function, system operators can adjust the weights based on their preferences. Finally, a Benders' decomposition algorithm is developed to solve the model efficiently. The computational results indicate that this approach provides a more robust and computationally trackable framework as compared with the stochastic optimization approach and a more cost-effective unit commitment decision as compared with the robust optimization approach.
In this article, we present a fault diagnosis approach for discrete event systems using labeled Petri nets. In contrast to the existing works, a new fault class containing all the fault transitions ...is additionally introduced in the diagnosis function, leading to a more informative and precise diagnosis result. An integer linear programming (ILP) problem is built according to an observed word. By specifying different objective functions to the ILP problem, the diagnosis result is obtained without enumerating all observable transition sequences consistent with the observed word, which is more efficient in comparison with the existing ILP-based approaches.
In practice, the operation of high-speed trains is often affected by adverse weather conditions or equipment failures, which result in delays and even cancellations of train services. In this ...article, a novel two-layer hierarchical model predictive control (MPC) model is proposed for on-line high-speed railway delay management and train control for minimizing train delays and cancellations. The upper layer manages the global objectives of the train operation, that is, minimizing the total train delays and providing guidance for the speed control in the lower layer. The objectives of the lower layer are to satisfy the running time requirements given by the upper layer and to save energy at the same time. The optimization problems in both levels of the hierarchical MPC framework are formulated as small-scale mixed integer linear programming problems, which can be solved efficiently by existing solvers. Particularly, the train control problem is solved in a distributed way for each train. Simulation analysis based on the real-life data of the Beijing-Shanghai high-speed railway shows that the proposed hierarchical MPC framework can meet the real-time requirements and reduce train delays effectively when compared with widely accepted strategies, for example, first-scheduled-first-serve and first-come-first-serve. Moreover, the proposed hierarchical MPC framework also provides good robustness performance for different disturbance scenarios.
Microgrids are subsystems of the distribution grid, which comprises generation capacities, storage devices, and controllable loads, operating as a single controllable system either connected or ...isolated from the utility grid. In this paper, we present a study on applying a model predictive control approach to the problem of efficiently optimizing microgrid operations while satisfying a time-varying request and operation constraints. The overall problem is formulated using mixed-integer linear programming (MILP), which can be solved in an efficient way by using commercial solvers without resorting to complex heuristics or decompositions techniques. Then, the MILP formulation leads to significant improvements in solution quality and computational burden. A case study of a microgrid is employed to assess the performance of the online optimization-based control strategy and the simulation results are discussed. The method is applied to an experimental microgrid located in Athens, Greece. The experimental results show the feasibility and the effectiveness of the proposed approach.
This paper presents a mixed-integer linear programming (MILP) reformulation of the thermal unit commitment (UC) problem. The proposed formulation is simultaneously tight and compact. The tighter ...characteristic reduces the search space and the more compact characteristic increases the searching speed with which solvers explore that reduced space. Therefore, as a natural consequence, the proposed formulation significantly reduces the computational burden in comparison with analogous MILP-based UC formulations. We provide computational results comparing the proposed formulation with two others which have been recognized as computationally efficient in the literature. The experiments were carried out on 40 different power system mixes and sizes, running from 28 to 1870 generating units.
Modern power systems are facing increased risk of disasters that can cause extended outages. The presence of remote control switches, distributed generators (DGs), and energy storage systems (ESS) ...provides both challenges and opportunities for developing post-fault service restoration methodologies. Inter-temporal constraints of DGs, ESS, and loads under cold load pickup conditions impose extra complexity on problem formulation and solution. In this paper, a multi-time step service restoration methodology is proposed to optimally generate a sequence of control actions for controllable switches, ESSs, and dispatchable DGs to assist the system operator with decision making. The restoration sequence is determined to minimize the unserved customers by energizing the system step by step without violating operational constraints at each time step. The proposed methodology is formulated as a mixed-integer linear programming model and can adapt to various operation conditions. The proposed method is validated through several case studies that are performed on modified IEEE 13-node and IEEE 123-node test feeders.
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