Modelling and computation of optimal multiple investment timing in multi-stage capacity expansion infrastructure projects

Jinghuan Li; Shuhua Zhang; Yu Li

doi:10.3934/jimo.2020154

Article Contents

2022, Volume 18, Issue 1: 297-314. Doi: 10.3934/jimo.2020154

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Modelling and computation of optimal multiple investment timing in multi-stage capacity expansion infrastructure projects

1.
Department of Mathematics, Tianjin University of Commerce, Tianjin 300134, China
2.
Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China

^* Corresponding author: Jinghuan Li
^* Corresponding author: Jinghuan Li

Received: December 31, 2019

Revised: July 31, 2020

Early access: October 2020

Published: January 2022

This project was supported by the Scientific Research Plan of Tianjin Municipal Education Commission (2017SK076)

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Abstract

So far, the optimal investment timing to maximize the total profit of multi-stage capacity expansion infrastructure projects is not clear. In the case of uncertain demands, the optimal multiple stopping time theory is adopted to model the optimal decision-making of investment timing for multi-stage expansion infrastructure projects in a finite time horizon. In this context, the first-stage of the project involves a dedicated asset investment for later expansion, and the capacity of the project at each stage is constrained, which makes the cash flow of the project exhibit the characteristic of bull call spread. The upwind finite difference method and multi-least squares Monte Carlo simulation are combined to solve the project value and determine the optimal exercise boundaries at all stages described by a sequence of demand thresholds. A multi-stage power plant project is taken as an example to validate the model. Through the example, the optimal investment strategies and the value of the multi-stage project are provided; the effects of the dedicated asset and capacity constraint are illustrated. This study novelly reveals the effect of the capacity constraints on the project value using the bull call spread theory.

Keywords:

Multi-stage infrastructure projects,
investment timing,
limited capacity,
optimal multiple stopping time,
finite difference,
multi-least squares Monte Carlo simulation.

Mathematics Subject Classification: Primary: 49J20, 65C05, 65M06.

Citation:

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Figure 1. The operation load of the $ i $-th stage project

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Figure 2. The comparisons between multi-stage and single period investments

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Figure 3. The distribution of investment times from one million sample path

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Figure 4. The optimal exercise boundaries for the i-th investment

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Figure 5. The influences of the dedicated asset ratio

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Figure 6. The net revenue of the i-th stage project for different demand levels

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Figure 7. The impacts of the demand volatility on the project value

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Table 1. Default parameters used in the calculations

Parameter	Symbol	Value	Unit
Investment period	$ T $	10	Year
Planned investment times	$ N $	3	time
Construction period	$ \nu $	1.5	Year
Refraction time	$ \delta $	2	Year
Capacity of i-th stage	$ m_{i} $	$ 6\times10^{4} $	MW$ \cdot $h/year
Unit price	$ p $	$ 5\times10^{-4} $	million CNY/MW$ \cdot $h
Unit operational cost	$ c $	$ 4\times10^{-5} $	million CNY/MW$ \cdot $h
Construction cost parameter	$ \lambda $	$ 1\times10^{-2} $	million CNY/MW$ \cdot $h
Construction cost parameter	$ \beta $	0.9
Drift	$ \alpha $	6%
Volatility rate	$ \sigma $	15%
Discount rate	$ r $	8%
Dedicated asset ratio	$ \eta $	0.1

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