Mathematical Modeling of Earthwork Optimization Problems

European Journal of Operational Research

Planning techniques for large scale earthworks have been considered in this article. To improve these activities a "block theoretic" approach was developed that provides an integrated solution consisting of an allocation of cuts to fills and a sequence of cuts and fills over time. It considers the constantly changing terrain by computing haulage routes dynamically. Consequently more realistic haulage costs are used in the decision making process. A digraph is utilised to describe the terrain surface which has been partitioned into uniform grids. It reflects the true state of the terrain, and is altered after each cut and fill. A shortest path algorithm is successively applied to calculate the cost of each haul, and these costs are summed over the entire sequence, to provide a total cost of haulage. To solve this integrated optimisation problem a variety of solution techniques were applied, including constructive algorithms, meta-heuristics and parallel programming. The extensive numerical investigations have successfully shown the applicability of our approach to real sized earthwork problems.

Engineering Optimization, 2014

Earthwork planning has been considered in this article and a generic block partitioning and modelling approach has been devised to provide strategic plans of various levels of detail. Conceptually this approach is more accurate and comprehensive than others, for instance those that are section based. In response to environmental concerns the metric for decision making was fuel consumption and emissions. Haulage distance and gradient are also included as they are important components of these metrics. Advantageously the fuel consumption metric is generic and captures the physical difficulties of travelling over inclines of different gradients, that is consistent across all hauling vehicles. For validation, the proposed models and techniques have been applied to a real world road project. The numerical investigations have demonstrated that the models can be solved with relatively little CPU time. The proposed block models also result in solutions of superior quality, i.e. they have reduced fuel consumption and cost. Furthermore the plans differ considerably from those based solely upon a distance based metric thus demonstrating a need for industry to reflect upon their current practices.

This paper presents a MILP model which identifies the optimal cut-fill pairs and their sequence with minimum total earthwork cost. The proposed model is of value to earthwork managers because it identifies the most favorable EAP by accounting for the rock-earth type of each and every rock-earth, the series of rock-earths occupying each and every cut and fill pits, and the moving directions (i.e., the order of cut-fill rock-earth pairs), expeditiously. A test case confirms the usability and validity of the model.

2013

In this paper we construct earthwork allocation plans for a linear infrastructure road project. Fuel consumption metrics and an innovative block partitioning and modelling approach are applied to reduce costs. 2D and 3D variants of the problem were compared to see what effect, if any, occurs on solution quality. 3D variants were also considered to see what additional complexities and difficulties occur. The numerical investigation shows a significant improvement and a reduction in fuel consumption as theorised. The proposed solutions differ considerably from plans that were constructed for a distance based metric as commonly used in other approaches. Under certain conditions, 3D problem instances can be solved optimally as 2D problems.

Journal of Construction Engineering and Management, 2013

This paper summarizes a mathematical model that relates the geometric and geotechnical features of a road construction site with the allocation of materials, searching for a minimum construction cost. This paper proposes a linear programming model to optimize excavation and paving services. With this model, it is possible to evaluate site alternatives with different soil strata and different degrees of compaction. The borrow pit materials are allocated in the most economical way, and it is possible to incorporate more inputs like materials mix. Software was used to solve the model, and a spreadsheet application was used as an interface for data input. The proposed model demonstrated possible cost savings in earthwork planning. It is expected that earthwork and paving optimization with linear programming will reduce road construction costs considerably.

Journal of Engineering, Project, and Production Management, 2020

The purpose of this paper is to present an optimization model for planning the distribution of materials in earthmoving operations, considering possible interferences between cut-and-fill sections such as rivers, vegetation, topographical features, or expropriations. The earth allocation problem incorporating interferences was modeled as a linear programming problem, aiming to minimize the total earthmoving cost while considering the constraints related to volume balance, construction project duration, and time for the release of traffic. The proposed linear programming model was run by an integrated system, using Excel for data analysis and IBM CPLEX as the optimizer. The mathematical model was evaluated by a sensitivity analysis and validated by a real-world project of a dam access road in the state of Ceará, Brazil. The unit costs and productivity rates used in the fictional example and in the real-world application followed the referential cost system created by Ceará’s Secretar...

TRANSPORTES, 2020

Planejar as atividades de distribuição de materiais em obras de terraplenagem pode representar um ganho na obra como um todo. Uma das formas de fazer isso é minimizar a distância total percorrida pelos veículos, por exemplo caminhões na movimentação de terra entre as zonas de corte e aterro. Há muitos estudos e trabalhos que focam a otimização da distribuição de materiais entre zonas de corte e aterro, porém poucos aplicaram em projetos reais com a consideração de múltiplos equipamentos, além de não terem feito uma análise baseada na distância entre estacas. Este artigo tem como objetivo desenvolver um modelo de Programação Inteira que minimize a distância percorrida pelos caminhões basculantes em atividades de distribuição de materiais na terraplenagem. O modelo elaborado com princípios da Programação Linear Inteira foi baseado no problema de roteamento, cujo objetivo é minimizar o caminho percorrido. O modelo foi aplicado em dois estudo de casos cujos resultados destacam ganhos s...

Transportation Research Part A: General, 1988

Roadway grades are normally established to satisfy the geometric specifications of the road. Once the grades are established, the earthwork allocations that minimize the cost are determined. This paper presents a model that links these two activities. The model selects the roadway grades that minimize the cost of earthwork and satisfy the geometric specifications. The geometric specifications pertain to the elements of the vertical alignment, elevation of grade line at specified stations, horizontal and vertical alignment relations, and type of vertical curve. The model enumerates all technically feasible grades and solves the linear programming problem to minimize earthwork allocation cost for those grade alternatives that satisfy borrow pit and landfill capacity constraints. The model incorporates important earthwork details and guarantees obtaining the global minimum earthwork cost. Application of the model is illustrated bv a numerical examole and model extensions to accommodate other design and construction aspects are presented.

Journal of Construction Engineering and Management, 2015

In highway construction, earthworks refer to the tasks of excavation, transportation, spreading and compaction of geomaterial (e.g. soil, rockfill and soil-rockfill mixture). Whereas relying heavily on machinery and repetitive processes, these tasks are highly susceptible to optimization. In this context Artificial Intelligent techniques, such as Data Mining and modern optimization can be applied for earthworks. A survey of these applications shows that they focus on the optimization of specific objectives and/or construction phases being possible to identify the capabilities and limitations of the analyzed techniques. Thus, according to the pinpointed drawbacks of these techniques, this paper describes a novel intelligent earthwork optimization system, capable of integrating DM, modern optimization and GIS technologies in order to optimize the earthwork processes throughout all phases of design and construction work. This integration system allows significant savings in time, cost and gas emissions contributing for a more sustainable construction.

E3S Web of Conferences

Earthwork cost is one of the major cost items (approximately 25% of the construction costs) in road construction projects. The amount of earthwork volumes therefore earthwork cost, mostly depends on the geometry of the road vertical alignment. We can conclude that an optimized vertical alignment has a profound impact on earthwork costs. In this research paper, we solve the task connected to the minimization of earthwork cost by optimizing vertical alignment by the development of linear optimization model with different categories of unknown variables including vertical offsets between road and surface in different points as well as extremum points’ numbers. Proposed linear optimization model is supposed to be implemented with application of simplex method as the component of complex branch and bound approach. The developed model has been implemented on the basis of practical example. After the optimization of vertical alignment, earthwork volumes have been calculated in the road des...