1. Fleet Investment under Market, Regulatory and Technological Uncertainty
Xishu Li, Rob Zuidwijk, René de Koster, Rommert Dekker
Erasmus University Rotterdam
1 Introduction
Fleet investments face uncertainties in demand growth, environmental regulations that lack consistency, and new
technologies that are costly at an early stage of development.
There is often some leeway in the timing, type and amount of investment since one can "learn" and "update" knowledge over
the uncertainties as more information becomes available over time.
Besides exogenous uncertainties, the force of oligopolistic competition cannot be neglected.
Why are enormous investments common during recession in an oligopolistic market (Figure 1)?
Why is it always small firms that are facing bankruptcies (Figure 2)?
The leader firm has the incentive to invest earlier or favor large-scale investments during market depression in order to push the
follower firms to sell less and eventually cause them to go out of business. After reducing competition, the leader can
compensate the loss by earning monopoly-alike profits in the long run.
What factors influence the success of such investment strategies? How should the follower firms respond?
Figure 1 Demand and supply in the containership market Figure 2 Market consolidation
2 Research Questions
Dynamic investment problem where
1) exogenous uncertainties exist,
2) competitive interaction is considered,
3) each firm’s objective is to maximize the expected value of its
own long-term strategy, which is adapted to the evolution of the
state of the world.
What is the optimal fleet capacity investment strategy?
When should one buy new (green) ships and by how many?
Is it better to have many small investments or a few large
ones?
Does a simple description of the coupled dynamics and a
natural ordering of investment decisions exist?
3 Methodology
Markov decision process with a predetermined horizon
State space: market condition
Action space: invest, stay put or disinvest
Transition function:
competitive interaction ⇒ Stackelberg model
exogenous demand uncertainty ⇒ Brownian motion
Reward function: expected net present value
Find the optimal policy (e.g.,stay-put region St) which
prescribes the best action for each state.
Technological uncertainty can be incorporated in
investment cost functions.
Regulatory uncertainty: scenario analysis or model it as
a "surprise" event.
Kt−1,1
Sl,t(Sf,t)
Sf,t(K∗
l,t)
Disinvest 1
Stay put 2 Sf,t(Ka
l,t)
Sf,t(Kb
l,t)
K∗
l,t
Invest 1
Invest 2
Stay put 1
Invest 2
Invest 1
Stay put 2
Disinvest 1
Invest 2
Kl,t−1
Stay put
Stay put
Invest 1
Disinvest 2
Structure of a two-dimensional optimal investment policy
Kt−1,2
Kf,t−1
4 Scientific and Managerial Relevance
We explore the economic theory of dynamic
competitive investment under uncertainty.
We consider real-world features, e.g., multiple types of
investment decisions and an adapted strategy.
Our models allow one to compute the optimal
investment strategy that supports firms in maintaining
profitably while operating sustainably.
The 3rd Erasmus Smart Port Rotterdam/Port Research Centre Poster Session