We study the mixed-integer knapsack polyhedron, that is, the convex hull of the mixed-integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet-defining inequalities of t...
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We study the mixed-integer knapsack polyhedron, that is, the convex hull of the mixed-integer set defined by an arbitrary linear inequality and the bounds on the variables. We describe facet-defining inequalities of this polyhedron that can be obtained through sequential lifting of inequalities containing a single integer variable. These inequalities strengthen and/or generalize known inequalities for several special cases. We report computational results on using the inequalities as cutting planes for mixed-integer programming.
In this paper routing adaptation methodologies are investigated, which utilize conventional routing protocols such as OSPF in combination with MPLS. While having the majority of traffic routed along optimized shortest...
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ISBN:
(纸本)0780378024
In this paper routing adaptation methodologies are investigated, which utilize conventional routing protocols such as OSPF in combination with MPLS. While having the majority of traffic routed along optimized shortest paths, MPSL is only partly introduced to complement the adaptation process. We present a novel algorithm based on simulated annealing to optimize link metrics in OSPF networks. The algorithm takes into account the original routing configuration and allows tradeoff considerations between routing optimality and adaptation impact. For the setup of complementary MPLS paths, two mixed-integer programming models are proposed. It can be shown that already a relatively small number of MPLS paths is sufficient to greatly improve a network's quality of service.
In many countries civil engineers play a fundamental role in the processes through which the location and capacities of public facilities like medical centers, schools, sanitary landfills, libraries, swimming-pool, et...
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In many countries civil engineers play a fundamental role in the processes through which the location and capacities of public facilities like medical centers, schools, sanitary landfills, libraries, swimming-pool, etc., are decided. This paper describes a study aimed at evaluating the aptitude of general methods of mixed-integer programming (MIP) for solving public facility planning problems using PCs. The application of these methods is quite easy today, even for people with limited optimization and computing skills, thanks to the good, friendly MIP packages now available. The evaluation was performed on a collection of basic problems types involving both minimum-cost and maximum-accessibility objectives. The main, general conclusion of the study was that, at present, problems with up to 100 centers and 100 sites, like most real-world problems are, can be solved rather efficiently on many occasions.
Earthmoving is the process of moving and processing soil from one location to another to alter an existing land surface into a desired configuration. Highways, dams, and airports are typical examples of heavy earthmov...
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Earthmoving is the process of moving and processing soil from one location to another to alter an existing land surface into a desired configuration. Highways, dams, and airports are typical examples of heavy earthmoving projects. Over the years, construction managers have devised methods to determine the quantities of material to be moved from one place to another. Various types of soil (soft earth, sand, hard clay, ... etc.) create different levels of difficulty of the problem. The earthmoving problem has traditionally been solved using mass diagram or variety of operational research techniques. However, existing models do not present realistic solution for the problem. Multiple soil types are usually found in cut areas and specific types of soil are required in fill sections. Some soil types in cut areas are not suitable for use in fill sections and must be disposed-off. In this paper a new mathematical programming model is developed to find-out the optimum allocation of earthmoving materials. In developing the proposed model, different soil types are considered as well as variations of unit cost with earth quantities moved. Suggested borrow pits and/or disposal sites are introduced to minimize the overall earthmoving cost. The proposed model is entirely formulated using the programming capabilities of VB6 while LINDO is used to solve the formulated model. An example project is presented to show how the model can be implemented. A case study project is analyzed using the developed model and a sensitivity analysis is then performed.
To satisfy public demands for environmental values, forest companies are facing the prospect of a reduction in wood supply and increases in costs. Some Canadian provincial governments have proposed intensifying silvic...
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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 optimizat...
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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.
Based on research on the polyhedral structure of lot-sizing models over the last 20 years, we claim that there is a nontrivial fraction of practical lot-sizing problems that can now be solved by nonspecialists just by...
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Based on research on the polyhedral structure of lot-sizing models over the last 20 years, we claim that there is a nontrivial fraction of practical lot-sizing problems that can now be solved by nonspecialists just by taking an appropriate a priori reformulation of the problem, and then feeding the resulting formulation into a commercial mixed-integer programming solver. This claim uses the fact that many multi-item problems decompose naturally into a set of single-item problems with linking constraints, and that there is now a large body of knowledge about single-item problems. To put this knowledge to use, we propose a classification of lot-sizing problems (in large part single-item) and then indicate in a set of tables, what is known about a particular problem class and how useful it might be. Specifically, we indicate for each class (i) whether a tight extended. formulation is known, and its size;(ii) whether one or more families of valid inequalities are known defining the convex hull of solutions, and the complexity of the corresponding separation algorithms;and (iii) the complexity of the corresponding optimization algorithms (which would be useful if a column generation or Lagrangian relaxation approach was envisaged). Three distinct multi-item lot-sizing instances are then presented to demonstrate the approach, and comparative computational results are presented. Finally, we also use the classification to point out what appear to be some of the important open questions and challenges.
The available-to-promise (ATP) function is becoming increasingly important in supply chain management since it directly links production resources with customer orders. In this paper, a mixedintegerprogramming (MIP)...
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The available-to-promise (ATP) function is becoming increasingly important in supply chain management since it directly links production resources with customer orders. In this paper, a mixedintegerprogramming (MIP) ATP model is presented. This model can provide an order-promising and -fulfillment solution for a batch of orders that arrive within a predefined batching interval. A variety of constraints, such as raw material availability, production capacity, material compatibility, and customer preferences, are considered. Simulation experiments using the model investigate the sensitivity of supply chain performance to changes in certain parameters, such as batching interval size and customer order flexibility.
In order to assess the economic and ecological effects of inter-company energy supply concepts, an optimising model integrating investment and longterm production planning has been developed. The model represents the ...
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In order to assess the economic and ecological effects of inter-company energy supply concepts, an optimising model integrating investment and longterm production planning has been developed. The model represents the energy production of companies on a very disaggregated level taking into account different resources, energy carriers and production processes. This model has been applied to five industrial companies to analyse the economic and ecological implications resulting from investments in inter-company energy supply concepts. Existing technologies as well as possible investment options have been assessed by a techno-economic analysis taking into account company specific circumstances. In addition;the new German combined heat and power law has been modelled in detail, because the supplementary payments legally established in this law may effect energy go supply concepts in a considerable way. Computational results show the installation of a combined cycle power plant adapted to the specific conditions of the case at hand would be the most promising. option to fulfil the future energy demand of the companies involved.
This paper addresses the resident scheduling problem (RSP) at hospitals concerned with prescribing work-nights for residents while considering departmental staffing and skill requirements as well as residents' pre...
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This paper addresses the resident scheduling problem (RSP) at hospitals concerned with prescribing work-nights for residents while considering departmental staffing and skill requirements as well as residents' preferences. Three scenarios that represent most situations and account for various departmental requirements and needs are described. Although similar scheduling problems are considered in the literature, no analysis exists that adequately deals with the specific nature of this problem. The problem is modeled as a mixed-integer program and heuristic solution procedures are developed for the different identified scheduling scenarios. These procedures exploit the inherent network structure of the problem which is an important feature that enhances problem solvability. For the sake of comparison, the problem is also solved exactly via the CPLEX-MIP (version 6.0) package. The contribution of this work is important since many hospitals are still utilizing manual techniques in preparing their own schedules, expending considerable effort and time and yet contending with limited scheduling flexibility.
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