The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfo...
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The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfolio construction is to use assets' ordering information, expressed in the form of preferences over the stocks, instead of the exact expected returns. Due to the fact that the ranking itself is often described with uncertainty, we introduce a generic robust ranking model and apply it to portfolio optimization. In this problem, there are n objects whose ranking is in a discrete uncertainty set. We want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking. This robust ranking problem is a mixedinteger minimax problem and is very difficult to solve in general. To solve this robust ranking problem, we apply the constraint generation method, where constraints are efficiently generated by solving a network flow problem. For empirical tests, we use post-earnings-announcement drifts to obtain ranking uncertainty sets for the stocks in the DJIA index. We demonstrate that our robust portfolios produce smaller risk compared to their non-robust counterparts. (C) 2012 Elsevier B.V. All rights reserved.
Internet is a worldwide network composed of interconnected but independent networks, called Autonomous Systems. Each network owner has to decide which other networks to interconnect with and how to allocate its traffi...
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Internet is a worldwide network composed of interconnected but independent networks, called Autonomous Systems. Each network owner has to decide which other networks to interconnect with and how to allocate its traffic among its providers. The financial flows between Autonomous Systems depend on these decisions and raise the key issue of revenue management. In this paper, we propose some models and exact methods for the joint optimization problem of interconnection policy and traffic allocation for a customer AS. This problem is analyzed in the top-percentile pricing framework for the interconnection agreements, and we assess the solution methods using real-life instances.
We consider the mixed-integer set where and . This set may arise in a relaxation of mixed-integer problems such as lot-sizing problems. We decompose X into a small number of subsets whose convex hull description is tr...
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We consider the mixed-integer set where and . This set may arise in a relaxation of mixed-integer problems such as lot-sizing problems. We decompose X into a small number of subsets whose convex hull description is trivial. The convex hull of X is equal to the closure of the convex hull of the union of those polyhedra. Using a projection theorem from Balas (Discret Appl Math 89:3-44, 1998) we obtain a compact characterization of the facets of the convex hull of X. Then by studying the projection cone we characterize all the facet-defining inequalities of the convex hull of X in the space of the original variables. Each of those inequalities is either a mixed MIR inequality (Gunluk and Pochet in Math Programm 90:429-457, 2001), or it is based on a directed cycle on a special bipartite graph. When a (1) and a (2) are relative prime, the convex hull of X is described by the mixed MIR inequalities.
Protein purification through chromatographic processes has been broadly used in the biopharmaceutical industry over the last decades, but still remains a major bottleneck. In this work, we address the challenge of sel...
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Protein purification through chromatographic processes has been broadly used in the biopharmaceutical industry over the last decades, but still remains a major bottleneck. In this work, we address the challenge of selecting appropriate chromatographic steps, along with product collecting timeline for separating the target protein from the contaminants in a multicomponent mixture. A novel mixedinteger linear programming (MILP) model for purification process synthesis is proposed. The model allows product losses and is tested on three example protein mixtures, containing up to 13 contaminants and selecting from a set of up to 21 candidate steps. The results are compared with previous literature models attempting to solve the same problem and show that the proposed approach offers significant gains in computational efficiency without compromising the quality of the solution. (C) 2012 Elsevier B.V. All rights reserved.
In this paper, we develop a mixed integer programming model for a supplier selection problem in an international context. The main features that characterize the international supplier selection are first identified. ...
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In this paper, we develop a mixed integer programming model for a supplier selection problem in an international context. The main features that characterize the international supplier selection are first identified. We show that when operating in an international context, the supplier selection process should consider the following issues: several buyers' sites;inventory decisions, in particular the safety stocks that are held by buyers to cope with the delivery lead time uncertainty;inventory capacity constraints in buyers' sites;selection of transportation modes, each having a specific delivery frequency and a transportation capacity;and multiple products and multiple time periods. Then, we propose a supplier selection model that takes into account such characteristics and that is suited for the international context. Finally, we solve the model with the commercial optimization software Cplex and we perform computational experiments based on a realistic case study from the automotive industry in order to prove the solvability and the usefulness of the model. Sensitivity analyzes are also performed for a number of model parameters.
Mine planning is really about seeking an optimal solution to three coupled problems, namely: mine block sequencing, ore-waste discrimination by cut-off grades and determination of production rates. The key objective o...
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Mine planning is really about seeking an optimal solution to three coupled problems, namely: mine block sequencing, ore-waste discrimination by cut-off grades and determination of production rates. The key objective of the optimisation model is to maximise net present value (NPV) under the access and capacity constraints. In current practice, mine block sequencing is implemented for pre-defined cut-off grades and production rates determined outside of optimisation process (Model 1). This article takes a further step in improving the optimisation process by enabling ore-waste discrimination and block sequencing to be optimised concurrently through a mixed integer programming (MIP) model for given capacities (Model 2). This optimisation model gives rise to the problem of size in terms of the number of destinations. However, it allows more block configuration in tandem with increases in NPV. To demonstrate the superior attributes of this enhanced model, a case study was implemented using data from a gold mine. The new model generated 5% more NPV. Increasing computer capacity and CPU speed enables mine planners to use Model 2 for solving mine production planning problems efficiently.
For the purpose of production scheduling, open-pit mines are discretized into three-dimensional arrays known as block models. Production scheduling consists of deciding which blocks should be extracted, when they shou...
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For the purpose of production scheduling, open-pit mines are discretized into three-dimensional arrays known as block models. Production scheduling consists of deciding which blocks should be extracted, when they should be extracted, and what to do with the blocks once they are extracted. Blocks that are close to the surface should be extracted first, and capacity constraints limit the production in each time period. Since the 1960s, it has been known that this problem can be cast as an integerprogramming model. However, the large size of some real instances (3-10 million blocks, 15-20 time periods) has made these models impractical for use in real planning applications, thus leading to the use of numerous heuristic methods. In this article we study a well-known integerprogramming formulation of the problem that we refer to as C-PIT. We propose a new decomposition method for solving the linear programming relaxation (LP) of C-PIT when there is a single capacity constraint per time period. This algorithm is based on exploiting the structure of the precedence-constrained knapsack problem and runs in O(mn log n) in which n is the number of blocks and m a function of the precedence relationships in the mine. Our computations show that we can solve, in minutes, the LP relaxation of real-sized mine-planning applications with up to five million blocks and 20 time periods. Combining this with a quick rounding algorithm based on topological sorting, we obtain integer feasible solutions to the more general problem where multiple capacity constraints per time period are considered. Our implementation obtains solutions within 6% of optimality in seconds. A second heuristic step, based on local search, allows us to find solutions within 3% in one hour on all instances considered. For most instances, we obtain solutions within 1-2% of optimality if we let this heuristic run longer. Previous methods have been able to tackle only instances with up to 150,000 blocks and 15 time pe
Light duty plug-in hybrid electric vehicle (PHEV) technology holds a promising future due to its "friendliness" to the environment and potential to reduce dependence on fossil fuels. However, the likely sign...
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Light duty plug-in hybrid electric vehicle (PHEV) technology holds a promising future due to its "friendliness" to the environment and potential to reduce dependence on fossil fuels. However, the likely significant growth of PHEVs will bring new challenges and opportunities for power system infrastructures. This paper studies the impacts of PHEV charging patterns on power system operations and scheduling. The stochastic unit commitment model described in this paper considers coordination of thermal generating units and PHEV charging loads, as well as the penetration of large-scale wind power. The proposed model also addresses ancillary services provided by vehicle-to-grid techniques. Daily electricity demands by various types of PHEVs are estimated on the basis of a PHEV population projection and transportation survey. The stochastic unit commitment model is used to simulate power system scheduling with different charging patterns for PHEVs. The results show that a smart charging pattern can reduce the operating costs of a power system and compensate for the fluctuation in wind power. The proposed model also can serve as a foundation and tool to perform long-term cost-benefit analysis and to assist policy making.
This paper considers the problem of how to determine an optimal fueling schedule and contracting policy with fuel suppliers so as to minimize the total cost of the fueling operation. The problem is formulated as a mix...
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This paper considers the problem of how to determine an optimal fueling schedule and contracting policy with fuel suppliers so as to minimize the total cost of the fueling operation. The problem is formulated as a mixedinteger program and the formulation is enhanced by valid inequalities and domination rules. The enhanced model allows us to obtain near optimal solutions for large scale instances. (C) 2011 Elsevier B.V. All rights reserved.
This paper presents an optimization study of the net present value of a biomass-to-ethanol supply chain in a 9-state region in the Midwestern United States. The study involves formulating and solving a mixedinteger l...
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This paper presents an optimization study of the net present value of a biomass-to-ethanol supply chain in a 9-state region in the Midwestern United States. The study involves formulating and solving a mixedinteger linear programming (MILP) problem. A biochemical technology is assumed for converting five types of agricultural residues into ethanol utilizing dilute acid pretreatment and enzymatic hydrolysis. Optimal locations and capacities of biorefineries are determined simultaneously with biomass harvest and distribution. Sensitivity analysis is performed to elucidate the impact of price uncertainty on the robustness of the supply chain and whether or not the proposed biorefineries will be built or will fail financially after being built. (C) 2011 Elsevier Ltd. All rights reserved.
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