An equilibrium network design model with a social cost function for multimodal networks

Abstract

In this paper, we present a comprehensive investment planning model and its solution approach. The model takes a bilevel programming form and allows a variety of effects of the investments incorporated. The model is characterized by its ability to address the total social costs occurring in transportation networks and to estimate the equilibrium link volumes in multimodal networks. Two solution algorithms were proposed. Both algorithms handle the discrete optimization problem by exploiting the strings of binary digits of integer variables. In an illustrative example, we performed network design analyses for three scenarios in which 25, 50, and 75% of the total required capital is available. By applying the two solution algorithms to the example problem, the optimal network alternative for each scenario was found. If a cost/benefit analysis is coupled with the proposed model, the optimal investments and the optimal network configuration will be determined simultaneously.

Appendix

1.1 Data File for the example

a. Existing Network Data

# of nodes			9
Highway Data		# of links			12
from		To		distance		FF speed		capacity
	1		2		70		100		4000
	1		4		50		100		2000
	2		3		70		100		2000
	2		5		50		100		4000
	3		6		50		100		2000
	4		5		80		100		2000
	4		7		100		100		2000
	5		6		80		100		2000
	5		8		50		100		4000
	6		9		100		100		2000
	7		8		70		100		2000
	8		9		70		100		4000
Rail Data		# of links			4
from		To		distance		FF speed		capacity
	1		2		70		80		999999
	2		5		50		80		999999
	5		8		50		80		999999
	8		9		70		80		999999

b. OD Demand Data

O/D Data		# of O/D			12
from		To		Demand
	1		3		3000
	1		7		3000
	1		9		4000
	3		1		3000
	3		7		2500
	3		9		2500
	7		1		3000
	7		3		2500
	7		9		3000
	9		1		4000
	9		3		2500
	9		7		3000

c. Candidate Link Data

Candidate		Data	9					Total Invest			1060
Highway		# of links			4
from		To		distance		FF speed		capacity		investments
	1		5		100		100		2000		100
	5		9		150		100		2000		150
	3		5		100		100		2000		100
	5		7		150		100		2000		150
Rail		# of links			4
	1		5		100		80		999999		110
	5		9		150		80		999999		170
	3		5		100		80		999999		110
	5		7		150		80		999999		170