During a medical emergency in the USA, critical medical supplies such as medications, vaccines, gloves, masks and ventilators, are delivered to one location within each state. The state and local governments are respo...
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During a medical emergency in the USA, critical medical supplies such as medications, vaccines, gloves, masks and ventilators, are delivered to one location within each state. The state and local governments are responsible for delivering the supplies from this location, called the receiving, staging and storage (RSS) site to the points of dispense (PODs). The supplies can be sent from the RSS to PODs directly or via regional distribution nodes (RDNs). We develop two mixed-integer programming models for this emergency logistics network (ELN) problem. These two models are simplified to obtain equivalent models that lead to the same results, but with fewer constraints. The equivalent models are much less complex and have lower computational memory and time requirements. We optimise the required number and locations of RSSs and RDNs needed to satisfy the demands at the PODs within the required time windows. Experiments are conducted to illustrate how the proposed models can be applied to a real life problem.
There are four key aspects for water use in hydraulic fracturing, including source water acquisition, wastewater production, reuse and recycle, and subsequent transportation, storage, and disposal. Water use life cycl...
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There are four key aspects for water use in hydraulic fracturing, including source water acquisition, wastewater production, reuse and recycle, and subsequent transportation, storage, and disposal. Water use life cycle is optimized for wellpads through a discrete-time two-stage stochastic mixed-integer linear programming model under uncertain availability of water. The objective is to minimize expected transportation, treatment, storage, and disposal cost while accounting for the revenue from gas production. Assuming freshwater sources, river withdrawal data, location of wellpads, and treatment facilities are given, the goal is to determine an optimal fracturing schedule in coordination with water transportation, and its treatment and reuse. The proposed models consider a long-time horizon and multiple scenarios from historical data. Two examples representative of the Marcellus Shale play are presented to illustrate the effectiveness of the formulation, and to identify optimization opportunities that can improve both the environmental impact and economical use of water. (c) 2014 American Institute of Chemical Engineers AIChE J, 60: 3490-3501, 2014
A two-class classification problem is considered where the objects to be classified are bags of instances in d-space. The classification rule is defined in terms of an open d-ball. A bag is labeled positive if it meet...
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A two-class classification problem is considered where the objects to be classified are bags of instances in d-space. The classification rule is defined in terms of an open d-ball. A bag is labeled positive if it meets the ball and labeled negative otherwise. Determining the center and radius of the ball is modeled as a SVM-like margin optimization problem. Necessary optimality conditions are derived leading to a polynomial algorithm in fixed dimension. A VNS type heuristic is developed and experimentally tested. The methodology is extended to classification by several balls and to more than two classes. (C) 2013 Elsevier Ltd. All rights reserved.
This paper presents an optimization model for the design of global supply chains where the emphasis is made on transfer pricing for both tangible and intangible elements. We adopt the profit split transfer pricing met...
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This paper presents an optimization model for the design of global supply chains where the emphasis is made on transfer pricing for both tangible and intangible elements. We adopt the profit split transfer pricing method which is dictated by OECD guidelines and may be accepted by fiscal authorities. The proposed model is particularly suited for the offshoring context. In addition to transfer pricing, the model integrates several relevant decisions such as the location of tangible and intangible activities. Intangible activities refer to R&D and supplier management. Experimental analyses are conducted in order to prove the feasibility and the solvability of the model and to show the impacts of transfer pricing on supply chain decisions and profits. (C) 2014 Elsevier Ltd. All rights reserved.
We derive linear inequality characterizations for sets of the form conv{(x, q) is an element of R-d x R : q >= Q(x), x is an element of R-d - int(P)}, where Q is convex and differentiable and P subset of R-d. We sh...
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We derive linear inequality characterizations for sets of the form conv{(x, q) is an element of R-d x R : q >= Q(x), x is an element of R-d - int(P)}, where Q is convex and differentiable and P subset of R-d. We show that in several cases our characterization leads to polynomial-time separation algorithms that operate in the original space of variables, in particular when Q is a positive-definite quadratic and P is a polyhedron or an ellipsoid.
This study optimizes the structure and size of a district heating network. The optimization task is formulated as a mixed-integer problem on a graph of possible pipe locations. Both structure (where to build pipes) an...
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This study optimizes the structure and size of a district heating network. The optimization task is formulated as a mixed-integer problem on a graph of possible pipe locations. Both structure (where to build pipes) and size (pipe capacities) are decision variables in a mathematical description of the optimization problem. The validity of its results are then tested on a case study in Munich, using a published district heating extension plan as reference. The district heating model employs an idealized graph of the street network to represent potential sites for pipes. This street graph is derived from publicly available data, which is also the main source for estimating the heat demand of buildings. Heat demand of individual buildings is aggregated along streets;heat supply, in turn, is possible at pre-defined source locations. The structural optimization relies on a concave investment cost function which represents the diameter-independent part of pipeline investment costs. The case study results finally show a good correspondence between the overall structure of the optimized network and the real expansion plan of a district heating network.
Hospitals typically lack effective enterprise level strategic planning of bed and care resources, contributing to bed census levels that are statistically "out of control." This system dysfunction manifests ...
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Hospitals typically lack effective enterprise level strategic planning of bed and care resources, contributing to bed census levels that are statistically "out of control." This system dysfunction manifests itself in bed block, surgical cancelation, ambulance diversions, and operational chaos. This is the classic hospital admission scheduling and control (HASC) problem, which has been addressed in its entirety only through inexact simulation-based search heuristics. This paper develops new analytical models of controlled hospital census that can, for the first time, be incorporated into a mixed-integer programming model to optimally solve the strategic planning/scheduling portion of the HASC. Our new solution method coordinates elective admissions with other hospital subsystems to reduce system congestion. We formulate a new Poisson-arrival-location model (PALM) based on an innovative stochastic location process that we developed and call the patient temporal resource needs model. We further extend the PALM approach to the class of deterministic controlled-arrival-location models (d-CALM) and develop linearizing approximations to stochastic blocking metrics. This work provides the theoretical foundations for an efficient scheduled admissions planning system as well as a practical decision support methodology to stabilize hospital census.
This paper addresses the static aircraft sequencing problem over a mixed-mode single runway (or closely interacting parallel runways), which commonly constitutes a critical bottleneck at airports. In contrast with dis...
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This paper addresses the static aircraft sequencing problem over a mixed-mode single runway (or closely interacting parallel runways), which commonly constitutes a critical bottleneck at airports. In contrast with disjunctive formulations, our modeling approach takes advantage of the underlying structure of an asymmetric traveling salesman problem with time-windows. This enables the development of efficient preprocessing and probing procedures, and motivates the derivation of several classes of valid inequalities along with partial convex hull representations to enhance problem solvability via tighter reformulations. The lifted model is further embedded within the framework of two proposed heuristics that are compared against the traditional first-come first-served (FCFS) heuristic with landing priority: an optimized FCFS policy (OFCFS) and a threshold-based suboptimized heuristic (TSH) with an a priori fixing of the relative order of aircraft that are sufficiently time-separated. Computational results using real data based on Doha International Airport (DOH) as well as simulated instances are reported to demonstrate the efficacy of the proposed exact and heuristic solution methods. In particular, for the DOH instances, heuristics OFCFS and TSH achieved an attractive runway utilization (4.3% and 5.0% makespan reduction, respectively, over the base FCFS policy with landing priority), while exhibiting limited aircraft position deviations (0.45 and 0.49 deviations on average, respectively, from the base FCFS positions with landing priority, with similar results being obtained for the simulated instances). The superiority of the proposed optimization models over previous disjunctive formulations is also demonstrated for challenging problem instances, resulting in over 50% CPU savings for the larger instances in our test-bed.
One of the essential components of a branch-and-bound based mixedinteger linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the ...
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One of the essential components of a branch-and-bound based mixedinteger linear programming (MIP) solver is the branching rule. Strong branching is a method used by many state-of-the-art branching rules to select the variable to branch on. It precomputes the dual bounds of potential child nodes by solving auxiliary linear programs and thereby helps to take good branching decisions that lead to a small search tree. In this paper, we describe how these dual bound predictions can be improved by including domain propagation into strong branching. Domain propagation is a technique that MIP solvers usually apply at every node of the branch-and-bound tree to tighten the local domains of variables. Computational experiments on standard MIP instances indicate that our improved strong branching method significantly improves the quality of the predictions and causes almost no additional effort. For a full strong branching rule, we are able to obtain substantial reductions of the branch-and-bound tree size as well as the solving time. Moreover, the state-of-the-art hybrid branching rule can be improved this way as well.
In order to derive continuity and stability of two-stage stochastic programs with mixed-integer recourse when all coefficients in the second-stage problem are random, we first investigate the quantitative continuity o...
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In order to derive continuity and stability of two-stage stochastic programs with mixed-integer recourse when all coefficients in the second-stage problem are random, we first investigate the quantitative continuity of the objective function of the corresponding continuous recourse problem with random recourse matrices. Then by extending derived results to the mixed-integer recourse case, the perturbation estimate and the piece-wise lower semi-continuity of the objective function are proved. Under the framework of weak convergence for probability measure, the epi-continuity and joint continuity of the objective function are established. All these results help us to prove a qualitative stability result. The obtained results extend current results to the mixed-integer recourse with random recourse matrices which have finitely many atoms.
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