Table 3 Energy intensity M&C by objective reduction from 2021 to 2030 (10,000 tons of standard coal/100 million yuan, base period was 2011).

From: Management and control decision of energy intensity in logistics industry under the background of dual carbon strategy in China

Year

Exponential model(M1)

\(y_{t} = y_{0} e^{at}\), a = ln(0.73)/9

\(y_{t} = y_{0} \lambda^{t}\),\(\lambda = 0.73^{1/9}\)

Difference model(M2)

\(y_{t} = (1{ - }\phi )^{{\text{t}}} (y_{0} - \mathop y\limits^{ \wedge } ) + \mathop y\limits^{ \wedge }\), \(\mathop y\limits^{ \wedge }\) = 0.7*\(y_{0}\),\(\phi = 1 - 0.1^{1/9}\)

Linear model(M3)

\(y_{t} = y_{0} + bt\)

b = −0.27*\(y_{0}\)/9;

Period overall objective

2021

1.795576

1.795576

1.795576

reduce 27%

2022

1.733874

1.673978

1.741709

2023

1.674292

1.579829

1.687842

2024

1.616757

1.506933

1.633974

2025

1.56120

1.450492

1.580107

2026

1.507551

1.406792

1.526240

2027

1.455746

1.372957

1.472372

2028

1.405722

1.346759

1.418505

2029

1.357416

1.326476

1.364638

2030

1.310771

1.310771

1.310771

  1. Note: The two exponential models export the same results. In the difference model, the long-term desire value is set as 70% (\(\mathop y\limits^{ \wedge }\) = 0.7*\(y_{0}\)), which is smaller than an overall objective 73% (reduce 27%). After \(\mathop y\limits^{ \wedge }\) is set, \(y_{t} = 0.73y_{0}\), \(\phi\) can be calculate as \(\phi = 1 - 0.1^{1/9}\). In the linear model, \(y_{t} = (1 - 0.73)y_{0}\), \(b = -0.27*y_{0}/9\).
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