Persistent calls come from within the graduate medical education community and from external sources for regulating the resident duty hours in order to meet the obligations about the quality of resident education, the...
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Persistent calls come from within the graduate medical education community and from external sources for regulating the resident duty hours in order to meet the obligations about the quality of resident education, the well-being of residents themselves, and the quality of patient care services. The report of the Accreditation Council for Graduate Medical Education (ACGME) proposes common program requirements for resident hours. In this paper, we first develop a mixed-integer programming model for scheduling residents' duty hours considering the on-call night, day-off, rest period, and total work-hour ACGME regulations as well as the demand coverage requirements of the residency program. Subsequently, we propose a column generation model that consists of a master problem and an auxiliary problem. The master problem finds a configuration of individual schedules that minimizes the sum of deviations from the desired service levels for the day and night periods. The formulation of this problem is possible by representing the feasible schedules using column variables, whereas the auxiliary problem finds the whole set of feasible schedules using constraint programming. The proposed approach has been tested on a series of problems using real data obtained from a hospital. The results indicate that high-quality schedules can be obtained within a few seconds. (C) 2010 Elsevier Ltd. All rights reserved.
The fixed-charge transportation problem is a fixed-charge network flow problem on a bipartite graph. This problem appears as a subproblem in many hard transportation problems, and has also strong links with the challe...
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ISBN:
(纸本)9783642208072
The fixed-charge transportation problem is a fixed-charge network flow problem on a bipartite graph. This problem appears as a subproblem in many hard transportation problems, and has also strong links with the challenging big-bucket multi-item lot-sizing problem. We provide a polyhedral analysis of the polynomially solvable special case in which the associated bipartite graph is a path. We describe a new class of inequalities that we call "path-modular" inequalities. We give two distinct proofs of their validity. The first one is direct and crucially relies on sub-and super-modularity of an associated set function, thereby providing an interesting link with flow-cover type inequalities. The second proof is by projecting a tight extended formulation, therefore also showing that these inequalities suffice to describe the convex hull of the feasible solutions to this problem. We finally show how to solve the separation problem associated to the path-modular inequalities in O(n(3)) time.
This paper considers a stochastic p-hub center problem, in which travel time is characterized by discrete random vector. The objective of the problem is to minimize the efficient time point of total travel time. For P...
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ISBN:
(纸本)9783642210891
This paper considers a stochastic p-hub center problem, in which travel time is characterized by discrete random vector. The objective of the problem is to minimize the efficient time point of total travel time. For Poisson travel time, the problem is equivalent to a deterministic programming problem by finding the quantiles of the related probability distribution functions. For general discrete distributed travel time, the proposed problem is equivalent to a deterministic mixed-integer linear programming problem. So, we can employ conventional optimization algorithms such as branch-and-bound method to solve the deterministic programming problem. Finally, one numerical example is presented to demonstrate the validity of the proposed model and the effectiveness of the solution method.
With increasing wind farm integrations, unit commitment (UC) is more difficult to solve because of the intermittent and random nature of wind power outputs. A robust optimization model for UC is built to deal with the...
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ISBN:
(纸本)9781457710018
With increasing wind farm integrations, unit commitment (UC) is more difficult to solve because of the intermittent and random nature of wind power outputs. A robust optimization model for UC is built to deal with the errors on wind power predictions. The robust optimization method is based on scenario analysis, while the probability of each selected scenario is derived mathematically. In the proposed UC formulation, spinning reserve requirement is specially considered to support possible wind power change between any two successive periods. Network security constraints are considered by DC power flow equations and the whole UC formulation is a mixed-integer programming problem. Case studies on the IEEE 30-bus system demonstrate the effectiveness of the proposed method. The influences of wind power on UC results and network security are also discussed.
This paper uses artificial intelligent algorithms for reconfiguration of the distribution network. The problem is formulated as an optimization problem where the objective function to be minimized is the power losses,...
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ISBN:
(纸本)9789898425843
This paper uses artificial intelligent algorithms for reconfiguration of the distribution network. The problem is formulated as an optimization problem where the objective function to be minimized is the power losses, and the constraints are nodal voltage magnitude limits, branch current limits, Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL) and the network radiality condition. While the state (on-off) of the tie switch is considered as control or independent variable, the nodal voltage magnitude, branch current are considered as state or dependent variables. These state variables are continuous whilst the switch state is an integer (binary) variable. The problem being a mixed-integer programming one because of the state of switch (on=closed=1 or off=open=0), a Binary Particle Swarm Optimization (BPSO) and Neural Network are used separately to solve this problem. The effectiveness of proposed method is demonstrated through an example.
We consider the automated guided vehicle (AGV) dispatching problem in container terminals where vehicles are allowed to carry more than one container at a time. The main focus of the study is on dual-load AGVs, which ...
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We consider the automated guided vehicle (AGV) dispatching problem in container terminals where vehicles are allowed to carry more than one container at a time. The main focus of the study is on dual-load AGVs, which may carry either two 20-ft containers or one 40/45-ft container. We propose a new mathematical formulation for the corresponding optimisation problem under a rolling horizon approach;the proposed model is a simplification over existing formulations. The performance of the model is evaluated against different scenarios with respect to minimising a defined dispatching 'cost'. Our computational results are based on a number of scenarios for container terminals, with various layout configurations and levels of workload, and show that the model can generally be solved quickly providing good quality solutions.
This paper addresses the problem of storage assignment in a warehouse characterized by multi-command picking and served by milkrun logistics. In such a logistic system, vehicles circulate between the warehouse and the...
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This paper addresses the problem of storage assignment in a warehouse characterized by multi-command picking and served by milkrun logistics. In such a logistic system, vehicles circulate between the warehouse and the production facilities of the plant according to a pre-defined schedule, often with multiple cycles (routes) serving different departments. We assume that a request probability can be assigned to each item and each cycle, which leads to a special case of the correlated storage assignment problem. A MIP model is proposed for finding a class-based storage policy that minimizes the order cycle time, the average picking effort, or a linear combination of these two criteria. Computational experiments show that our approach can achieve an up to 36-38% improvement in either criterion compared to the classical COI-based strategy. (C) 2010 Elsevier B.V. All rights reserved.
This article reviews the use of the software program Ip_solve version 5.5 for solving mixed-integer automated test assembly (ATA) problems. The program is freely available under Lesser General Public License 2 (LGPL2)...
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This article reviews the use of the software program Ip_solve version 5.5 for solving mixed-integer automated test assembly (ATA) problems. The program is freely available under Lesser General Public License 2 (LGPL2). It can be called from the statistical language R using the IpSolveAPI interface. Three empirical problems are presented to demonstrate how to use the program and interface to (a) simultaneously assemble multiple test forms with absolute targets for their test information functions, (b) assemble shadow tests for computerized adaptive testing, and (c) assemble multistage tests using relative targets for their test information functions, all subject to various quantitative and categorical constraints. The results of this study indicate that it is now possible for researchers and testing organizations to implement ATA for small to moderately sized test assembly problems using free software.
In this paper, a real maintenance workforce-constrained scheduling problem is formulated as a bi-objective mixed-integer programming model with the aim of simultaneously minimizing the workforce requirements and maxim...
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In this paper, a real maintenance workforce-constrained scheduling problem is formulated as a bi-objective mixed-integer programming model with the aim of simultaneously minimizing the workforce requirements and maximizing the equipment availability. The skilled workforce is provided by internal and external resources using regular time, overtime and contracting. The equipment availability is measured by the downtime required for preventive maintenance (scheduled) and failure repair (unscheduled) jobs. We also encounter imminent or potential failures whose priorities depend on the severity of the failure on the system (secondary failure). The total weighted flow time is used as a scheduling criterion to measure the equipment availability;the weight of each job directly depends on the expected downtime resulting from the associated failure. The proposed model is verified using two comprehensive numerical examples and some sensitivity analyses. We conclude by discussing the results. Journal of the Operational Research Society (2011) 62, 1005-1018. doi: 10.1057/jors.2010.51 Published online 9 June 2010
A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with two equations, two free integer variables, and nonnegative continuous variables. Recently, Andersen et al. and Cornuejols and...
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A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with two equations, two free integer variables, and nonnegative continuous variables. Recently, Andersen et al. and Cornuejols and Margot showed that the facet-defining inequalities of this set are either split cuts or intersection cuts obtained from lattice-free triangles and quadrilaterals. From an example given by Cook et al. it is known that one particular class of facet-defining triangle inequality does not have finite split rank. In this paper we show that all other facet-defining triangle and quadrilateral inequalities have finite split rank.
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