A mixed-integer linear programming model to optimize the vertical alignment considering blocks and side-slopes in road construction

In the vertical alignment phase of road design, one minimizes the cost of moving material between different sections of the road while maintaining safety and building code constraints. Existing vertical alignment models consider neither the side-slopes of the road nor the natural blocks like rivers, mountains, etc., in the construction area. The calculated cost without the side-slopes can have significant errors (more than 20 percent), and the earthwork schedule without considering the blocks is unrealistic. In this study, we present a novel mixed integer linear programming model for the vertical alignment problem that considers both of these issues. The numerical results show that the approximation of the side-slopes can generate solutions within an acceptable error margin specified by the user without increasing the time complexity significantly.

[1]  Shrikant M. Nandgaonkar.  Earthwork Transportation Allocations: Operations Research , 1981 .

[2]  Erhan Kozan,et al.  A disjunctive graph model and framework for constructing new train schedules , 2010, Eur. J. Oper. Res..

[3]  Shahadat Hossain,et al.  Models and strategies for efficiently determining an optimal vertical alignment of roads , 2014, Comput. Oper. Res..

[4]  Erhan Kozan,et al.  An integrated approach for earthwork allocation, sequencing and routing , 2014, Eur. J. Oper. Res..

[5]  Said M. Easa,et al.  EARTHWORK ALLOCATIONS WITH NONCONSTANT UNIT COSTS , 1987 .

[6]  M. Trypia.  MINIMIZING 'CUT AND FILL' COSTS IN ROADMAKING , 1979 .

[7]  Kok Lay Teo,et al.  Control parametrization: A unified approach to optimal control problems with general constraints , 1988, Autom..

[8]  Ricardo García-Ródenas,et al.  A continuous bi-level model for the expansion of highway networks , 2014, Comput. Oper. Res..

[9]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[10]  Ahmad A. Moreb,et al.  A Linear Programming Model Combining Land Levelling and Transportation Problems , 1994 .

[11]  A. Burak Göktepe,et al.  Optimization of vertical alignment of highways utilizing discrete dynamic programming and weighted ground line , 2009 .

[12]  A. A. Moreb,et al.  Quadratic representation for roadway profile that minimizes earthwork cost , 2004 .

[13]  Jeff R. Wright,et al.  Civil And Environmental Systems Engineering , 1996 .

[14]  S. Easa.  Earthwork Allocations with Linear Unit Costs , 1988 .

[15]  T. F. FwA,et al.  HIGHWAY VERTICAL ALIGNMENT ANALYSIS BY DYNAMIC PROGRAMMING , 1989 .

[16]  Ek Peng Chew,et al.  Discrete and continuous models for computation of optimal vertical highway alignment , 1988 .

[17]  Ahmad A. Moreb,et al.  Linear programming model for finding optimal roadway grades that minimize earthwork cost , 1996 .

[18]  Paul Schonfeld,et al.  Intelligent Road Design , 2006 .

[19]  Valentin R. Koch,et al.  A note on: Spline technique for modeling roadway profile to minimize earthwork cost , 2010 .

[20]  Jian-chuan Cheng,et al.  Accuracy Comparison of Roadway Earthwork Computation between 3D and 2D Methods , 2013 .

[21]  Nicholas J. Garber,et al.  Traffic and Highway Engineering , 1988 .

[22]  Said M. Easa,et al.  Selection of roadway grades that minimize earthwork cost using linear programming , 1988 .

[23]  Warren Hare,et al.  Models and algorithms to improve earthwork operations in road design using mixed integer linear programming , 2011, Eur. J. Oper. Res..

[24]  Johannes Bisschop,et al.  AIMMS - Optimization Modeling , 2006 .

[25]  Yuchun Pan,et al.  Accuracy Analysis Of Earthwork Calculation Based On Triangulated Irregular Network (Tin) , 2011, Intell. Autom. Soft Comput..

[26]  A. A. Moreb.  Spline technique for modeling roadway profile to minimize earthwork cost , 2009 .

[27]  Manoj K. Jha,et al.  Highway Alignment Optimization Using Cost-Benefit Analysis Under User Equilibrium , 2011, Int. J. Oper. Res. Inf. Syst..

[28]  Md. Faisal Rahman,et al.  Optimizing the vertical alignment under earthwork block removal constraints in road construction , 2012 .

[29]  Selim Altun,et al.  DYNAMIC OPTIMIZATION ALGORITHM FOR VERTICAL ALIGNMENT OF HIGHWAYS , 2005 .

[30]  Selim Altun,et al.  Method for optimal vertical alignment of highways , 2009 .