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Pavement rehabilitation scheduling and toll pricing under different regulatory regimes

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Abstract

This paper addresses the highway pavement rehabilitation scheduling and toll pricing issues over a planning horizon. In the highway system concerned, two types of agents are considered, namely highway operator and road users. Two models, which account for different highway regulatory regimes (i.e. public and private), are proposed. In the public regulatory model, the government aims to maximize total discounted social welfare of the transportation system over the planning horizon by determining the optimal pavement rehabilitation schedule and toll level. In the private regulatory regime, a profit-driven private operator seeks to optimize the pavement rehabilitation schedule and toll level to maximize its own discounted net profit over the planning horizon. The proposed models treat the interactions between the highway operator and the road users in the system as a bi-level hierarchical problem in which the upper level is a multi-period pavement rehabilitation scheduling and toll pricing problem, while the lower level is a multi-period route choice equilibrium problem. A heuristic solution algorithm that combines a greedy approach and a sensitivity analysis based approach is developed to solve the proposed bi-level multi-period optimization models. An illustrative example is used to show the applications of the proposed models. The findings show that the highway regulatory regime, pavement deterioration parameter and the roughness-induced vehicle operating cost can significantly affect the pavement rehabilitation schedules and the toll level as well as the performance of transportation system in terms of total life-cycle travel demand, net profit and social welfare.

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Abbreviations

N :

Set of all nodes in the network

A :

Set of all links in the network

W :

Set of all origin–destination (OD) pairs in the network

R w :

Set of all routes between OD pair w ∈ W

T :

Set of discrete time periods

Λ(·):

Total discounted net profit over the planning horizon

Θ(·):

Total discounted social welfare over the planning horizon

M a (·):

Highway operator’s cost function

ρ a (τ):

Tolls on link a in period τ

φ a (τ):

Rehabilitation intensity of link a in period τ

u a (τ):

Travel disutility on link a in period τ

u rw (τ):

Travel disutility on route r between OD pair w in period τ

t a (τ):

Travel time on link a in period τ

c a (τ):

Vehicle operating cost on link a in period τ

v a (τ):

Flow on link a in period τ

K a (τ):

Capacity of link a in period τ

\( D_{w}^{ - 1} ( \cdot ) \) :

Inverse of the elastic demand function

f rw (τ):

Flow on route r between OD pair w in period τ

η w (τ):

Minimum travel disutility between OD pair w in period τ

q w (τ):

Actual travel demand between OD pair w in period τ

Q w (τ):

Potential travel demand between OD pair w in period τ

ψ w (τ):

Consumer surplus between OD pair w in period τ

δ ar :

Indicator variable equals 1 if route r traverses link a and 0 otherwise

s a (τ):

Pavement roughness of link a in period τ

s a (τ −):

Pavement roughness of link a before rehabilitation activity

s a (τ +):

Pavement roughness of link a after rehabilitation activity

R a (·):

Threshold of rehabilitation effectiveness on link a

F(·):

Pavement deterioration process function

G(·):

Pavement rehabilitation effectiveness function

ρ max(τ):

Upper bound of tolls in period τ

β :

Travellers’ value of time

c a0, c a1 :

Fixed operating cost and variable operating cost/veh km due to a marginal increase in the pavement roughness, respectively

L a :

Length of link a

t a0 :

Free-flow travel time on link a

B(τ):

Budget in period τ

h :

Average annual growth rate of potential travel demand

m a0, m a1 :

Parameters in rehabilitation cost function

g 1, g 2, g 3 :

Parameters in rehabilitation effectiveness function

λ :

Marginal pavement roughness increase per unit of traffic load

σ :

Length of discrete time period (e.g. 1 year)

ξ :

Interest rate

μ :

Parameter for reflecting the relationship between capacity and roughness

θ :

Parameter that reflects demand sensitivity to travel disutility by OD pair

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Acknowledgments

We are grateful to anonymous referees for their helpful comments and suggestions on an earlier version of the paper. The work described in this paper was jointly supported by grants from the National Natural Science Foundation of China (71222107), the Doctoral Fund of Ministry of Education of China (20120142110044), the Fok Ying Tung Education Foundation (132015), and the Center for Modern Information Management Research at the Huazhong University of Science and Technology.

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  1. School of Management, Huazhong University of Science and Technology, Wuhan, 430074, China

    Zhi-Chun Li & Dian Sheng

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  1. Zhi-Chun Li
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  2. Dian Sheng
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Correspondence to Zhi-Chun Li.

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Li, ZC., Sheng, D. Pavement rehabilitation scheduling and toll pricing under different regulatory regimes. Ann Oper Res 217, 337–355 (2014). https://doi.org/10.1007/s10479-014-1557-y

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