Given a weighted directed graph without positive cycles, we construct a framework to detect all longest paths for pairs of nodes in a network. The interest is to identify all routes with the highest cumulative cost fo...
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Given a weighted directed graph without positive cycles, we construct a framework to detect all longest paths for pairs of nodes in a network. The interest is to identify all routes with the highest cumulative cost for each source-destination pair. The significance and need for this arises in several scheduling contexts, an example of which is called critical chain project management. All longest routes are enumerated and compared for each output to determine a bottleneck path referred to as critical chain. Besides finding longest paths, minimizing duration needs to be considered. This indicates that multiple types of optimization problems coexist in one methodology. We thus aim to contain the longest-paths problem through constraints, for which an optimal solution that minimizes duration can be detected by solving a single optimization problem. The framework is reduced to a constraint satisfaction problem in a mixed-integerlinear-programming context, and the solution can be derived using a general purpose solver. Optimality for the longest-paths problem is proven using the small-m method. Since the developed framework does not require an objective function specification, the methodology can also be incorporated within other optimization based problem contexts.
作者:
Marques, InesCaptivo, M. EugeniaBarros, NaraUniv Lisbon
Ctr Management Studies Inst Super Tecn Ave Rovisco Pais P-1049001 Lisbon Portugal Univ Lisbon
Fac Ciencias Ctr Matemat Aplicacoes Fundamentais & Invest Oper P-1749016 Lisbon Portugal Univ Lisbon
Fac Ciencias Dept Estat & Invest Operac P-1749016 Lisbon Portugal
This paper proposes a new mixed-integer linear programming model to build cyclic master surgery schedules (MSSs) for a case study of a medium-sized Portuguese private hospital. The problem integrates tactical and stra...
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This paper proposes a new mixed-integer linear programming model to build cyclic master surgery schedules (MSSs) for a case study of a medium-sized Portuguese private hospital. The problem integrates tactical and strategical decisions of operating room (OR) planning and scheduling. OR time blocks are assigned to surgical services and to individual surgeons. A target OR time per surgical specialty is not given as it is often the case of other studies in the literature. The model aims to: level the workload at downstream departments (hospitalization units);avoid sharing OR time among different surgical specialties;allocate OR time blocks to the surgical specialty with the highest number of surgeons available;renew the MSS based on recent demand for surgeries. This approach allows the surgical suite to be more efficiently managed, while increasing the sense of fairness among surgeons and facilitating the negotiation for OR time. Moreover, this automated system releases the surgical suite manager to more added value tasks. (C) 2018 Elsevier Ltd. All rights reserved.
mixed-integer linear programming (MILP) methods have been applied widely to optimal design of energy supply systems in consideration of multi-period operation. A hierarchical MILP method has been proposed to solve suc...
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ISBN:
(纸本)9789729959646
mixed-integer linear programming (MILP) methods have been applied widely to optimal design of energy supply systems in consideration of multi-period operation. A hierarchical MILP method has been proposed to solve such optimal design problems efficiently. An original problem has been solved by dividing it into a relaxed optimal design problem at the upper level and optimal operation problems which are independent of one another at the lower level. In addition, some strategies have been proposed to enhance the computation efficiency furthermore. In this paper, a method of reducing model by time aggregation is proposed as a novel strategy to search design candidates efficiently in the relaxed optimal design problem at the upper level. In addition, the previous strategies are modified in accordance with the novel strategy. This method is realized only by clustering periods and averaging energy demands for clustered periods, while it guarantees to derive the optimal solution. Thus, it may decrease the computation time at the upper level. Through a case study on the optimal design of a gas turbine cogeneration system, it is clarified how the model reduction is effective to enhance the computation efficiency in comparison and combination with the modified previous strategies. (C) 2019 Elsevier Ltd. All rights reserved.
Traditionally, power system operations use a static network to deliver power and meet demand optimally. Network topology reconfiguration through transmission switching (TS) has gained significant interest recently to ...
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ISBN:
(纸本)9781728104072
Traditionally, power system operations use a static network to deliver power and meet demand optimally. Network topology reconfiguration through transmission switching (TS) has gained significant interest recently to reduce the operational cost of power system operations. However, implementation of TS also causes large disturbance in the network and as a result the use of corrective transmission switching (CTS) in response to power system contingencies is currently being researched extensively. This paper emphasizes the importance of CTS to accomplish flexible transmission in N-1 security-constrained unit commitment (SCUC) model. An N-1 SCUC mathematical model implementing a dynamic network in the post-contingency scenario is proposed as opposed to current industry practices of static network in shortterm operations. The proposed model is tested and validated on the IEEE 24-bus system. The proposed model results in cost-effective implementation and leads to overall reduced cost, and congestion reduction in the post-contingency scenario.
State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consid...
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State-of-the-art baggage handling systems transport luggage in an automated way using destination coded vehicles (DCVs). These vehicles transport the bags at high speeds on a network of tracks. In this paper we consider the problem of controlling the route of each DCV in the system. In general this results in a nonlinear, nonconvex, mixed-integer optimization problem, usually very expensive in terms of computational effort. Therefore, we present an alternative approach for reducing the complexity of the computations by simplifying and approximating the nonlinear optimization problem by a mixed-integer linear programming (MILP) problem. The advantage is that for MILP problems solvers are available that allow us to efficiently compute the global optimal solution. The solution of the MILP problem can then be used as a good initial starting point for the original nonlinear optimization problem. We use model predictive control (MPC) for solving the route choice problem. To assess the performance of the proposed (nonlinear and MILP) formulations of the MPC optimization problem, we consider a benchmark case study, the results being compared for several scenarios. (C) 2010 Elsevier Ltd. All rights reserved.
This paper from a macroscopic viewpoint develops a real-time train timetable rescheduling approach on a single high-speed railway line in case of a typical large disruption, where the availability of a certain track s...
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ISBN:
(纸本)9781728140940
This paper from a macroscopic viewpoint develops a real-time train timetable rescheduling approach on a single high-speed railway line in case of a typical large disruption, where the availability of a certain track segment is temporarily lost. A multi-objective mixed-integer linear programming model is constructed to minimise the number of cancelled trains and the total delay of trains that incorporates arrival delays and departure delays. A heuristic rolling horizon algorithm is also applied so as to obtain the feasibly near-optimal solution and satisfy the practical demand of the real-time performance. The proposed approach is further tested on a real-world case study and the numerical results show that it yields better feasible solutions and consumes the desired computation time, thereby demonstrating its effectiveness and efficiency.
A closed-loop supply chain is defined as the combination of both forward and reverse supply chains. However, it is in reverse supply chains that environmental issues are emphasized. In this research, a closed-loop sup...
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We consider the design of a charging infrastructure based on fast-charging capacitated stations to enable electric vehicles to carry out long-distance trips. We focus on taking into account the impact of the non-syste...
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ISBN:
(纸本)9781728105215
We consider the design of a charging infrastructure based on fast-charging capacitated stations to enable electric vehicles to carry out long-distance trips. We focus on taking into account the impact of the non-system-optimal drivers' behavior on the station capacity consumption in the modeling of the facility location problem. This leads to the formulation of a bi-level optimization model. In this bi-level program, the upper level represents the station location problem faced by the charging infrastructure provider and the lower level represents the selfish behavior of EV drivers who will seek to use the charging stations opened by the infrastructure provider to carry out their trips with a minimum number of stops. We propose a solution approach based on the reformulation of the bi-level program into a mixed-integerlinear program thanks to the use of the primal-dual optimality conditions of linearprogramming. Our preliminary computational experiments carried out on small instances show the impact on the global system performance of ignoring the selfish drivers' behavior and the potential benefit from using a bi-level programming model.
In this paper, we present alternate integerprogramming formulations for the multi-dimensional assignment problem, which is typically employed for multi-sensor fusion, multi-target tracking (MTT) or data association i...
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ISBN:
(纸本)9780996452786
In this paper, we present alternate integerprogramming formulations for the multi-dimensional assignment problem, which is typically employed for multi-sensor fusion, multi-target tracking (MTT) or data association in general. The first formulation is the Axial Multidimensional Assignment Problem with Decomposable Costs (MDADC). The decomposable costs comes from the fact that there are only pairwise costs between stages or scans of a target tracking problem or corpuses of a data association context. The difficulty with this formulation is the large number of transitivity or triangularity constraints that ensure if entity A is associated to entity B and entity B is associated with entity C, then it must also be that entity A is associated to entity C. The second formulation uses both pairs and triplets of observations, which offer more accurate representation for kinematic tracking of targets. This formulation avoids the large number of transitivity constraints but significantly increases the number of variables due to triples. Solution to large-scale problems has alluded researchers and practitioners alike. We present solution methods based on Lagrangian Relaxation and massively parallel algorithms that are implemented on Graphics Processing Units (GPUs). We test the problem formulations and solution algorithms on MTT problems. The triples formulation tends to be more accurate for tracking measures and the MDADC solver can solve much larger problems in reasonable computational time.
By splitting unit commitment into a coupling problem and individual unit commitment subproblems, Lagrangian relaxation is very effective in decreasing the solving time of large scale problems. Consequently, unit commi...
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ISBN:
(纸本)9781728112572
By splitting unit commitment into a coupling problem and individual unit commitment subproblems, Lagrangian relaxation is very effective in decreasing the solving time of large scale problems. Consequently, unit commitment subproblems should be solved equally fast. If they have been originally formulated in mixed-integer linear programming, performance advantages can be expected by replacing it with dynamic programming. However, it has not been reported whether a one-to-one reformulation is feasible. We suggest approaches to choose states for dynamic programming that replicate equal solutions as well as measures to reduce memory requirements. Results of the two subproblem models differ only fractionally and for explicable reasons. Subproblem computation time has been reduced by up to 100 times at modest memory requirements.
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