Abstract
This paper describes a robust optimization approach for a network design problem explicitly incorporating traffic dynamics and demand uncertainty. In particular, we consider a cell transmission model based network design problem of the linear programming type and use box uncertainty sets to characterize the demand uncertainty. The major contribution of this paper is to formulate such a robust network design problem as a tractable linear programming model and demonstrate the model robustness by comparing its solution performance with the nominal solution from the corresponding deterministic model. The results of the numerical experiments justify the modeling advantage of the robust optimization approach and provide useful managerial insights for enacting capacity expansion policies under demand uncertainty.
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Notes
Costs in general do not vary linearly with respect to the transportation facility capacity or size. Typically, scale economies or diseconomies exist. Abdulaal and LeBlanc (1979) discussed the cases of linear relationship, scale economies and scale diseconomies in the context of transportation network design problems. If the average investment cost per unit of capacity is declining, then scale economies exist. Empirical data are needed to establish the economies of scale for road construction. This paper assumes a linear relationship between the investment cost and the capacity, for the reasons of simplicity and the requirement of the linear model. The linear case can be regarded as an approximation to the case of scale economies in an expected capacity-increasing range.
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Acknowledgment
This work was partially supported by the grant awards CMMI-0824640 and CMMI-0900040 from the National Science Foundation.
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Chung, B.D., Yao, T., Xie, C. et al. Robust Optimization Model for a Dynamic Network Design Problem Under Demand Uncertainty. Netw Spat Econ 11, 371–389 (2011). https://doi.org/10.1007/s11067-010-9147-2
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DOI: https://doi.org/10.1007/s11067-010-9147-2