Port capacity investment size and timing under uncertainty and congestion

ABSTRACT

Well-planned port capacity investments are required to accommodate growing maritime trade, especially in developing countries. Such investments prove to be expensive, irreversible and subject to uncertainty. Under these conditions, the application of real options is better suited than the traditionally used NPV approach, given that specific port and market characteristics are taken into account. In this paper, we consider the investment in a new container port. The port is operated by one single actor who also owns the port and absence of competing ports in the neighbourhood is assumed. Two decisions have to be made: the size of the port and when to build it. Our real options model evaluating the option of flexible size and timing of the investment is based on a geometric Brownian motion. This approach has the advantage of analysing the impact of economic growth and uncertainty independently. Additionally, port users differ in aversion to congestion. Our model allows examining this impact on the optimal port investment. This paper shows that ports with more waiting-time averse customers are better off when investment is delayed to install a larger port. This result holds in both privately owned, profit-maximising ports and government-owned, social welfare-maximising ports.

KEYWORDS:

• Port capacity investment
• congestion
• uncertainty
• flexible investment size
• flexible timing
• real options

Acknowledgments

This research was funded by a PhD grant from Research Foundation Flanders (FWO). The authors would like to thank Siri Pettersen Strandenes, Anming Zhang, Trevor Heaver and the participants of various conferences for their valuable help in improving the realism of the port model.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Hence, a higher threshold value corresponds to investing later.

2. Without this convergence, discounted future cash flows would grow infinitely, resulting in eternal postponement of the investment.

3. As expected and required, $\mathrm{\partial }{q}^{opt}/\mathrm{\partial }X>0$ in $R_2$. A higher $X$ leads to a higher potential demand. Economic theory states that, if available capacity allows, optimal realised throughput $q^{opt}$ increases when demand shifts upwards and the supply curve has a positive inclination.

4. If $R_3$ does not exist, the final two conditions can be omitted, and $G_{2,1}$ and $G_{3,2}$ both equal zero.

5. The RO rule leads to postponing the investment to $X_T=37.63$, as opposed to $X_T=22.49$ under NPV.