A Lagrangian Decomposition Algorithm for Robust Green Transportation Location Problem

In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, and consequently, makes the air pollution enhance. In this paper, two green approaches are introduced which demand is the main uncertain parameter in both. These approaches are addressed to provide a trade-off between using available trucks and buying new hybrid trucks for evaluating total costs besides air pollution. Due to growing complexity, a Lagrangian decomposition algorithm is applied to find a tight lower bound for each approach. In this propounded algorithm, the main model is decomposed into master and subproblems to speed up convergence with a tight gap. Finally, the suggested algorithm is compared with commercial solver regarding total cost and computational time. Due to computational results for the proposed approach, the Lagrangian decomposition algorithm is provided a close lower bound in less time against commercial solver.

[1]  Jacques Renaud,et al.  An exact solution approach for multi-objective location-transportation problem for disaster response , 2014, Comput. Oper. Res..

[2]  N. Javadian,et al.  A Bi-objective Stochastic Optimization Model for Humanitarian Relief Chain by Using Evolutionary Algorithms , 2017 .

[3]  Gülay Barbarosoglu,et al.  A two-stage stochastic programming framework for transportation planning in disaster response , 2004, J. Oper. Res. Soc..

[4]  Ignacio E. Grossmann,et al.  Offshore oilfield development planning under uncertainty and fiscal considerations , 2017 .

[5]  Héctor J. Carlo,et al.  Transportation-location problem with unknown number of facilities , 2017, Comput. Ind. Eng..

[6]  Ulku Yetis,et al.  Hazardous waste management system design under population and environmental impact considerations. , 2017, Journal of environmental management.

[7]  Qingsong Wang,et al.  A transportation-location problem model for pedestrian evacuation in chemical industrial parks disasters , 2015 .

[8]  A. Hamidieh,et al.  A Robust Reliable Forward-reverse Supply Chain Network Design Model under Parameter and Disruption Uncertainties , 2017 .

[9]  Pavel Popela,et al.  Two-Stage Stochastic Programming for Transportation Network Design Problem , 2015, MENDEL.

[10]  Teodor Gabriel Crainic,et al.  A Study of Demand Stochasticity in Service Network Design , 2009, Transp. Sci..

[11]  J. Puerto,et al.  A two-stage stochastic transportation problem with fixed handling costs and a priori selection of the distribution channels , 2014 .

[12]  Rafael Caballero,et al.  Solving a bi-objective Transportation Location Routing Problem by metaheuristic algorithms , 2014, Eur. J. Oper. Res..

[13]  Melvyn Sim,et al.  The Price of Robustness , 2004, Oper. Res..

[14]  A. Hamidieh,et al.  A Robust Reliable Closed Loop Supply Chain Network Design under Uncertainty: A Case Study in Equipment Training Centers , 2017 .

[15]  Arthur M. Geoffrion,et al.  Lagrangian Relaxation for Integer Programming , 2010, 50 Years of Integer Programming.

[16]  Allen L. Soyster,et al.  Technical Note - Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming , 1973, Oper. Res..

[17]  Cécile Murat,et al.  Robust location transportation problems under uncertain demands , 2014, Discret. Appl. Math..

[18]  Sarah M. Ryan,et al.  Hybrid robust and stochastic optimization for closed-loop supply chain network design using accelerated Benders decomposition , 2016, Eur. J. Oper. Res..

[19]  Zhen Zhu,et al.  A Lagrangian decomposition approach to computing feasible solutions for quadratic binary programs , 2018, Optim. Lett..

[20]  Arkadi Nemirovski,et al.  Robust solutions of Linear Programming problems contaminated with uncertain data , 2000, Math. Program..

[21]  F. Sibel Salman,et al.  Deployment of field hospitals in mass casualty incidents , 2014, Comput. Ind. Eng..