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On the analysis of last-mile relief delivery on a tree network: Application to the 2015 Nepal earthquake

JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2021年第4期72卷 727-743页

作者： Khare, Abhinav Batta, Rajan Kang, Jee Eun Univ Buffalo Buffalo NY USA

The last mile delivery in humanitarian relief supply often happens on a tree or an almost-tree network allowing split deliveries. We present a relief delivery model incorporating a tree network for last mile delivery. We developed a mixed integer programming (MIP) formulation with the goal of minimizing the unsatisfied demand of the population. For better computational performance, we reformulated the MIP exploiting the tree network structure and found that this gave an order of magnitude reduction in computational time. To further improve computational efficiency, we developed a heuristic solution method based on a decomposition scheme applied to the tree network formulation. This led to the Capacitated Vehicle Routing Problem on trees with split deliveries, for which we derived a closed-form solution. This decomposition scheme resulted in a further order of magnitude reduction in computation time. To demonstrate the application of our approach we applied our model to the humanitarian logistics relief operation encountered in the 2015 Nepal earthquake.

关键词： Tree graphs split delivery last mile delivery mixed-integer programming

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Resilience through multicast - An optimization model for multi-hop wireless sensor networks

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AD HOC NETWORKS 2020年 107卷 102239-102239页

作者： Ostrowski, Bartlomiej Pioro, Michal Tomaszewski, Artur Fitzgerald, Emma Warsaw Univ Technol Inst Telecommun Warsaw Poland Lund Univ Dept Elect & Informat Technol Lund Sweden

In this paper we study resilience of TDMA-based wireless sensor networks to node failures. We investigate exploiting mutlicast routing for providing redundancy in the number of gateways used by data streams, so as to protect them against gateway failures. To do this, we develop an optimization model aiming at packet traffic throughput maximization composed of three mixed-integer programming problem formulations and corresponding solution algorithms. The first formulation assumes predefined multicast routing trees and fixed gateway locations, and optimizes the TDMA frame composition. The second one adds routing trees optimization, while the third formulation additionally includes optimization of gateway locations. We present a numerical study illustrating effectiveness of our model, including efficiency of the solution algorithms. Our results show that substantial gains in traffic throughput can be obtained by including routing trees optimization and optimal gateways selection, especially for high levels of redundancy. (c) 2020 Elsevier B.V. All rights reserved.

关键词： Wirelesssensornetworks Resilience Traffic throughput Multicast mixed-integer programming IoT

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Tank allocation problems in maritime bulk shipping

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COMPUTERS & OPERATIONS RESEARCH 2009年第11期36卷 3051-3060页

作者： Hvattum, Lars Magnus Fagerholt, Kjetil Armentano, Vinicius Amaral Norwegian Univ Sci & Technol Dept Ind Econ & Technol Management N-7034 Trondheim Norway Norwegian Marine Technol Res Inst MARINTEK Trondheim Norway Univ Estadual Campinas Fac Engn Eletr & Comp Campinas Brazil

In real world maritime routing problems, many restrictions and regulations influence the daily operations. The effects of several of these restrictions have not yet been studied in depth from an operations research perspective. This paper introduces the problem of allocating bulk cargoes to tanks in maritime shipping. A model and several variations are presented, and it is shown that the main problem consists of a number of complicating constraints. The problem studied is crucial when determining whether a given route is feasible for a given ship, and computational experiments are performed to assess the difficulty of solving realistically sized instances. The proposed formulation is hoped to provide a suitable starting point for research on stowage problems in maritime bulk shipping. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Maritime transportation Route feasibility Stowage mixed-integer programming

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Combination of Nonlinear and Linear Optimization of Transient Gas Networks

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INFORMS JOURNAL ON COMPUTING 2011年第4期23卷 605-617页

作者： Domschke, Pia Geissler, Bjorn Kolb, Oliver Lang, Jens Martin, Alexander Morsi, Antonio Tech Univ Darmstadt Dept Math Ctr Smart Interfaces D-64289 Darmstadt Germany Univ Erlangen Nurnberg Dept Math D-91058 Erlangen Germany Tech Univ Darmstadt Grad Sch Computat Engn D-64289 Darmstadt Germany

In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed-integer nonlinear program. This is solved by means of a combination of (i) a novel mixed-integer linear programming approach based on piecewise linearization and (ii) a classical sequential quadratic program applied for given combinatorial constraints. Numerical experiments show that better approximations to the optimal control problem can be obtained by using solutions of the sequential quadratic programming algorithm to improve the mixed-integer linear program. Moreover, iteratively applying these two techniques improves the results even further.

关键词： gas networks optimal control mixed-integer programming nonlinear programming sequential quadratic programming

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Polyhedral Results and Branch-and-Cut for the Resource Loading Problem

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INFORMS JOURNAL ON COMPUTING 2021年第1期33卷 105-119页

作者： Song, Guopeng Kis, Tamas Leus, Roel Katholieke Univ Leuven Fac Econ & Business ORSTAT B-3000 Leuven Belgium Natl Univ Def Technol Coll Syst Engn Changsha 410073 Peoples R China Inst Comp Sci & Control H-1111 Budapest Hungary

We study the resource loading problem, which arises in tactical capacity planning. In this problem, one has to plan the intensity of execution of a set of orders to minimize a cost function that penalizes the resource use above given capacity limits and the completion of the orders after their due dates. Our main contributions include a novel mixed-integer linear-programming (MIP)-based formulation, the investigation of the polyhedra associated with the feasible intensity assignments of individual orders, and a comparison of our branch-and-cut algorithm based on the novel formulation and the related polyhedral results with other MIP formulations. The computational results demonstrate the superiority of our approach. In our formulation and in one of the proofs, we use fundamental results of Egon Balas on disjunctive programming.

关键词： capacity planning mixed-integer programming facets branch-and-cut

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A solution method for treatment scheduling in rehabilitation hospitals with real-life requirements

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2019年第4期30卷 367-386页

作者： Xiao, Liyang Dridi, Mahjoub El Hassani, Amir Hajjam Lin, Wanlong Fei, Hongying Univ Bourgogne Franche Comte Nanomed Lab UTBM F-90010 Belfort France Shanghai 3 Rehabil Hosp 100 JiaoCheng Rd Shanghai Peoples R China Shanghai Univ Sch Management 99 ShangDa Rd Shanghai Peoples R China

In this study, we aim to minimize the total waiting time between successive treatments for inpatients in rehabilitation hospitals (departments) during a working day. Firstly, the daily treatment scheduling problem is formulated as a mixed-integer linear programming model, taking into consideration real-life requirements, and is solved by Gurobi, a commercial solver. Then, an improved cuckoo search algorithm is developed to obtain good quality solutions quickly for large-sized problems. Our methods are demonstrated with data collected from a medium-sized rehabilitation hospital in China. The numerical results indicate that the improved cuckoo search algorithm outperforms the real schedules applied in the targeted hospital with regard to the total waiting time of inpatients. Gurobi can construct schedules without waits for all the tested dataset though its efficiency is quite low. Three sets of numerical experiments are executed to compare the improved cuckoo search algorithm with Gurobi in terms of solution quality, effectiveness and capability to solve large instances.

关键词： health management treatment scheduling mixed-integer programming cuckoo search

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A Mathematical Modelling and Optimization Approach for a Maritime Facility Location Transshipment Problem

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INFORMATICA 2018年第4期29卷 609-632页

作者： Al-Yakoob, Salem M. Sherali, Hanif D. Kuwait Univ Dept Math Coll Sci POB 5969 Safat 13060 Kuwait Virginia Tech Grado Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA

This paper presents an optimization based mathematical modelling approach for a single source single destination crude oil facility location transshipment problem. We began by formulating a mixed-integer nonlinear programming model and use a rolling horizon heuristic to find an optimal location for a storage facility within a restricted continuous region. We next design a hybrid two-stage algorithm that combines judicious facility locations resulting from the proposed model into a previously developed column generation approach. The results indicate that improved overall operational costs can be achieved by strategically determining cost-effective locations of the transshipment facility.

关键词： mixed-integer programming vessel scheduling transportation inventory

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A polyhedral study of the cardinality constrained knapsack problem

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MATHEMATICAL programming 2003年第3期96卷 439-467页

作者： de Farias, IR Nemhauser, GL CORE B-1348 Louvain Belgium Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

A cardinality constrained knapsack problem is a continuous knapsack problem in which no more than a specified number of nonnegative variables are allowed to be positive. This structure occurs, for example, in areas such as finance, location, and scheduling. Traditionally, cardinality constraints are modeled by introducing auxiliary 0-1 variables and additional constraints that relate the continuous and the 0-1 variables. We use an alternative approach, in which we keep in the model only the continuous variables, and we enforce the cardinality constraint through a specialized branching scheme and the use of strong inequalities valid for the convex hull of the feasible set in the space of the continuous variables. To derive the valid inequalities, we extend the concepts of cover and cover inequality, commonly used in 0-1 programming, to this class of problems, and we show how cover inequalities can be lifted to derive facet-defining inequalities. We present three families of non-trivial facet-defining inequalities that are lifted cover inequalities. Finally, we report computational results that demonstrate the effectiveness of lifted cover inequalities and the superiority of the approach of not introducing auxiliary 0-1 variables over the traditional MIP approach for this class of problems.

关键词： mixed-integer programming knapsack problem cardinality constrained programming branch-and-cut

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A distributionally robust optimization approach for stochastic elective surgery scheduling with limited intensive care unit capacity

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第3期290卷 901-913页

作者： Shehadeh, Karmel S. Padman, Rema Lehigh Univ Dept Ind & Syst Engn Bethlehem PA 18015 USA Carnegie Mellon Univ Heinz Coll Informat Syst & Publ Policy Pittsburgh PA USA

In this paper, we study the decision process of assigning elective surgery patients to available surgical blocks in multiple operating rooms (OR) under random surgery durations, random postoperative length-of-stay in the intensive care unit (ICU), and limited capacity of ICU. The probability distributions of random parameters are assumed to be ambiguous, and only the mean values and ranges are known. We propose a distributionally robust elective surgery scheduling (DRESS) model that seeks optimal surgery scheduling decisions to minimize the cost of performing and postponing surgeries and the worst-case expected costs associated with overtime and idle time of ORs and lack of ICU capacity (which causes premature discharges or transfers). We evaluate the worst-case over a family of distributions characterized by the known mean values and ranges of random parameters. We leverage the separability of DRESS formulation in deriving an exact mixed-integer nonlinear programming reformulation. We linearize and derive a family of symmetry breaking inequalities to improve the solvability of the reformulation using an adapted column-and-constraint generation algorithm. Finally, we conduct extensive numerical experiments that demonstrate the superior performance of our DR approach as compared to the stochastic programming approach, and provide insights into DRESS. (C) 2020 Elsevier B.V. All rights reserved.

关键词： OR in Health Services Surgery Scheduling Downstream Resource Constraint Distributionally Robust Optimization Column-and-Constraint Generation mixed-integer programming

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A modification of Benders' decomposition algorithm for discrete subproblems: An approach for stochastic programs with integer recourse

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JOURNAL OF GLOBAL OPTIMIZATION 2002年第1-4期22卷 319-342页

作者： Sherali, HD Fraticelli, BMP Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn 0118 Blacksburg VA 24061 USA

In this paper, we modify Benders' decomposition method by using concepts from the Reformulation-Linearization Technique (RLT) and lift-and-project cuts in order to develop an approch for solving discrete optimization problems that yield integral subproblems, such as those that arise in the case of two-stage stochastic programs with integer recourse. We first demonstrate that if a particular convex hull representation of the problem's constrained region is available when binariness is enforced on only the second-stage (or recourse) variables, then the regular Benders' algorithm is applicable. The proposed procedure is based on sequentially generating a suitable partial description of this convex hull representation as needed in the process of deriving valid Benders' cuts. The key idea is to solve the subproblems using an RLT or lift-and-project cutting plane scheme, but to generate and store the cuts as functions of the first-stage variables. Hence, we are able to re-use these cutting planes from one subproblem solution to the next simply by updating the values of the first-stage decisions. The proposed Benders' cuts also recognize these RLT or lift-and-project cuts as functions of the first-stage variables, and are hence shown to be globally valid, thereby leading to an overall finitely convergent solution procedure. Some illustrative examples are provided to elucidate the proposed approach. The focus of this paper is on developing such a finitely convergent Benders' approach for problems having 0-1 mixed-integer subproblems as in the aforementioned context of two-stage stochastic programs with integer recourse. A second part of this paper will deal with related computational experiments.

关键词： stochastic programming mixed-integer programming Benders' decomposition Reformulation-Linearization Technique (RLT) lift-and-project cuts

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