Replacement optimization of ageing infrastructure under differential inflation

Figures & data

Table 1. Overview of classic and advanced replacement techniques.

Classic replacement techniques	Underlying assumptions	Limitations
EAC comparison when traditional NPV replacement scenarios have unequal lives	Assumes that the EAC’s of different replacement scenarios are comparable which means an underlying repeatability assumption of the combined cash flows of the defender and challenger.	Cannot handle differential inflation, technology change, multiple different successive challengers.
Economic service life comparison	Repeatability assumption of the challenger’s life cycle cash flows.	Cannot handle differential inflation, technology change, multiple different successive challengers.
Marginal analysis	Repeatability assumption of the challenger’s life cycle cash flows. Gradually increasing operating marginal expenditures of the defender.	Cannot handle differential inflation, technology change, multiple different successive challengers. Cannot handle fluctuating operational marginal expenditures of a defender caused by e.g. major overhauls.
Capitalised equivalent approach	Repeatability assumption of the challenger’s life cycle cash flows.	Cannot handle differential inflation, technology change, multiple different successive challengers.
Advanced replacement techniques
Case-specific DP or LP modelling	No mathematical assumptions. Can handle non-repeatable cash flows caused by whatever reason.	Complex and time consuming in its application.

Figure 1. Typical engineering PPI and CPI developments in the Netherlands during 2000–2018.

Table 2. Long-term differential inflation rates and their impact on discounting.

	1	2	3	4	5	6	7	8	9
Total inflation	2.6%	1.9%	3.1%	2.8%	1.7%	2.3%	2.5%	2.3%	1.9%
General inflation	1.8%	1.8%	1.8%	1.8%	1.8%	1.8%	1.8%	1.8%	1.8%
Differential inflation	0.7%	0.0%	1.3%	1.0%	−0.2%	0.5%	0.7%	0.4%	0.1%
Real discount rate A	5.0%	5.0%	5.0%	5.0%	5.0%	5.0%	5.0%	5.0%	5.0%
Net discount rate A	4.2%	5.0%	3.7%	4.0%	5.2%	4.5%	4.3%	4.5%	4.9%
Deviation for A	15.2%	0.7%	26.9%	20.6%	−3.4%	10.6%	14.2%	9.3%	1.5%
Real discount rate B	3.0%	3.0%	3.0%	3.0%	3.0%	3.0%	3.0%	3.0%	3.0%
Net discount rate B	2.3%	3.0%	1.7%	2.0%	3.2%	2.5%	2.3%	2.5%	2.9%
Deviation for B	24.8%	1.1%	44.0%	33.7%	−5.5%	17.4%	23.3%	15.3%	2.5%

1. Civil engineering construction (weighted average).

2. Road construction; brick paving.

3. Road construction; asphalt paving.

4. Railways and underground railways.

5. Bridges and tunnels.

6. Construction of pipelines.

7. Construction for water projects.

8. Site preparation works.

9. Electrical installation works.

Figure 2. Cash flows of a perpetuity of investment $I_0$ with interval $N,$ starting at time $T$ and subject to differential inflation.

Figure 3. Cash flows of a perpetuity of an annuity starting at year $t=T+1$ and subject to differential inflation $d.$

Figure 4. Cash flows of a perpetuity of an annuity starting at year $t=T+1$ and subject to ageing.

Figure 5. Cash flows of a perpetuity of an annuity starting at year $t=T+1$ and subject to differential inflation and ageing.

Table 3. Data for defender – challenger analysis under differential inflation and ageing.

	Start year first cycle (year)	Interval $n\mathrm{ }$(year)	Ageing $g\mathrm{ }$(%/year)	Differential inflation $d\mathrm{ }$(%/year)	Costs in price level year 0^a (€)
Defender
Renovation	0	–	–	–	€ 3,000,000
O&M	1	1	0.50%	0.85%	€ 26,250
Major overhauls steel	10	20	–	0.96%	€ 1,500,000
Major overhauls concrete	20	20	–	0.80%	€ 425,000
Major overhauls asphalt	10	10	–	1.44%	€ 62,500
Challenger
Investment	0	100	–	0.12%	€ 8,300,000
O&M	1	1	0.20%	0.85%	€ 7,500
Major overhauls steel	20	20	–	0.96%	€ 178,750
Major overhauls concrete	20	20	–	0.80%	€ 175,000
Major overhauls asphalt	10	10	–	1.44%	€ 62,500

^aCosts begin at start year of a cycle and repeat with interval $n.$

Figure 6. Present values for keep-replace scenarios subject to differential inflation and ageing.

Table 4. Comparison of the differential inflation adjusted capitalized equivalent approach with a DP-solution for the challenger’s replacement chain starting at T = 30 years.

	Differential inflation adjusted capitalized equivalent approach	DP-approach
Primary feature	Challenger’s replacement chain with fixed life N	Challenger’s replacement chain optimised for economic lives N*(t)
Calculation horizon	Infinite	Approximation of infinity by 300 years
Result: economic lives of successive challengers	Cyclic: 100 years	Optimised economic lives by applying a shortest path algorithm, for case study calculated at 100 – 100 – 70 years.
Result: present value	$P_C{\left[0,\mathrm{\infty }\right]}_{T=30}=\mathrm{€}\mathrm{ }2,203,435\mathrm{ }$(see Table B1 or B3)	$P_C{\left[0,300\right]}_{T=30}=\mathrm{€}\mathrm{ }2,203,424$

Data availability statement

The PPI data that support the findings of this study are openly available in CBS Statline at https://opendata.cbs.nl/statline/#/CBS/en/dataset/81139eng/table?ts=1527152344968

The CPI data that support the findings of this study are openly available in CBS Statline at https://opendata.cbs.nl/statline/#/CBS/en/dataset/83131ENG/table?ts=1542629902989