April  2009, 5(2): 275-283. doi: 10.3934/jimo.2009.5.275

Spline technique for modeling roadway profile to minimize earthwork cost

1. 

Department of Industrial Engineering, King Abdul Aziz University, Saudi Arabia, P.O. Box 80204, Jeddah, 21589, Saudi Arabia

Received  April 2007 Revised  March 2009 Published  April 2009

Roadway design usually involves decisions regarding the grade selection as the first stage; consequently, it is followed by another stage to solve the resulting earthwork allocation problem. Researchers have resorted to linear programming to solve the earthwork allocation problem using piecewise linear segments to model the road profile. Non linear functions were used to resolve the issue of sharp connectivity points present at the piecewise linear models. However, scaling problem may arise in the computational phase.
   In this paper, a one-dimensional (univariate) spline (piecewise polynomials) is used to fit the road profile and solve both the roadway grade selection and the earthwork allocation problem in a single linear programming problem. The mathematical model is purely linear in nature, regardless of the type of spline function used; and it guarantees global optimality. This approach has resolved the scaling problem while preserving the flexibility and smoothness of the road (no sharp connectivity points). The proposed model has exceeded all previous models in terms of efficiency and savings in cost. For illustration, three cases are considered.
Citation: Ahmad A. Moreb. Spline technique for modeling roadway profile to minimize earthwork cost. Journal of Industrial & Management Optimization, 2009, 5 (2) : 275-283. doi: 10.3934/jimo.2009.5.275
[1]

Valentin R. Koch, Yves Lucet. A note on: Spline technique for modeling roadway profile to minimize earthwork cost. Journal of Industrial & Management Optimization, 2010, 6 (2) : 393-400. doi: 10.3934/jimo.2010.6.393

[2]

David Kinderlehrer, Adrian Tudorascu. Transport via mass transportation. Discrete & Continuous Dynamical Systems - B, 2006, 6 (2) : 311-338. doi: 10.3934/dcdsb.2006.6.311

[3]

Qinglan Xia, Shaofeng Xu. On the ramified optimal allocation problem. Networks & Heterogeneous Media, 2013, 8 (2) : 591-624. doi: 10.3934/nhm.2013.8.591

[4]

G.S. Liu, J.Z. Zhang. Decision making of transportation plan, a bilevel transportation problem approach. Journal of Industrial & Management Optimization, 2005, 1 (3) : 305-314. doi: 10.3934/jimo.2005.1.305

[5]

Lorenzo Brasco, Filippo Santambrogio. An equivalent path functional formulation of branched transportation problems. Discrete & Continuous Dynamical Systems - A, 2011, 29 (3) : 845-871. doi: 10.3934/dcds.2011.29.845

[6]

Gershon Wolansky. Limit theorems for optimal mass transportation and applications to networks. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 365-374. doi: 10.3934/dcds.2011.30.365

[7]

Jun Pei, Panos M. Pardalos, Xinbao Liu, Wenjuan Fan, Shanlin Yang, Ling Wang. Coordination of production and transportation in supply chain scheduling. Journal of Industrial & Management Optimization, 2015, 11 (2) : 399-419. doi: 10.3934/jimo.2015.11.399

[8]

Ş. İlker Birbil, Kerem Bülbül, J. B. G. Frenk, H. M. Mulder. On EOQ cost models with arbitrary purchase and transportation costs. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1211-1245. doi: 10.3934/jimo.2015.11.1211

[9]

Qiying Hu, Wuyi Yue. Optimal control for resource allocation in discrete event systems. Journal of Industrial & Management Optimization, 2006, 2 (1) : 63-80. doi: 10.3934/jimo.2006.2.63

[10]

Joss Sánchez-Pérez. On the linearity property for allocation problems and bankruptcy problems. Journal of Dynamics & Games, 2018, 5 (1) : 9-20. doi: 10.3934/jdg.2018002

[11]

Irina Kareva, Faina Berezovkaya, Georgy Karev. Mixed strategies and natural selection in resource allocation. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1561-1586. doi: 10.3934/mbe.2013.10.1561

[12]

Sedighe Asghariniya, Hamed Zhiani Rezai, Saeid Mehrabian. Resource allocation: A common set of weights model. Numerical Algebra, Control & Optimization, 2020, 10 (3) : 257-273. doi: 10.3934/naco.2020001

[13]

Massimiliano Caramia, Giovanni Storchi. Evaluating the effects of parking price and location in multi-modal transportation networks. Networks & Heterogeneous Media, 2006, 1 (3) : 441-465. doi: 10.3934/nhm.2006.1.441

[14]

A. Daducci, A. Marigonda, G. Orlandi, R. Posenato. Neuronal Fiber--tracking via optimal mass transportation. Communications on Pure & Applied Analysis, 2012, 11 (5) : 2157-2177. doi: 10.3934/cpaa.2012.11.2157

[15]

Paulina Ávila-Torres, Fernando López-Irarragorri, Rafael Caballero, Yasmín Ríos-Solís. The multimodal and multiperiod urban transportation integrated timetable construction problem with demand uncertainty. Journal of Industrial & Management Optimization, 2018, 14 (2) : 447-472. doi: 10.3934/jimo.2017055

[16]

Eva Barrena, Alicia De-Los-Santos, Gilbert Laporte, Juan A. Mesa. Transferability of collective transportation line networks from a topological and passenger demand perspective. Networks & Heterogeneous Media, 2015, 10 (1) : 1-16. doi: 10.3934/nhm.2015.10.1

[17]

Gbeminiyi John Oyewole, Olufemi Adetunji. Solving the facility location and fixed charge solid transportation problem. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020034

[18]

Bong Joo Kim, Gang Uk Hwang, Yeon Hwa Chung. Traffic modelling and bandwidth allocation algorithm for video telephony service traffic. Journal of Industrial & Management Optimization, 2009, 5 (3) : 541-552. doi: 10.3934/jimo.2009.5.541

[19]

Ali Gharouni, Lin Wang. Modeling the spread of bed bug infestation and optimal resource allocation for disinfestation. Mathematical Biosciences & Engineering, 2016, 13 (5) : 969-980. doi: 10.3934/mbe.2016025

[20]

Ashkan Ayough, Farbod Farhadi, Mostafa Zandieh, Parisa Rastkhadiv. Genetic algorithm for obstacle location-allocation problems with customer priorities. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020044

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (56)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]