**Appendix D**

#### *Appendix D.1 Data Related to Economic Cost*

An ordinary 3800 TEU container ship, which usually navigates on the open water, should cost 60 million, the equity is 30%, and the interest rate is 3% with a 20-year loan [65]. Therefore, we can obtain the ordinary capital cost by Equation (23): 10,200 USD/day.

On the NSR, an IB-classed 3800 TEU container ship may have extra building cost due to the principal structure and strength, propulsion system, hull form, etc. [59]. Literature related to extra building cost can be seen in Table A6. From Table A6, the range of the extra building cost for IB-classed vessel is from 5% to 35%.

Suppose *C* is a new ship price, *eq* is the equity, *r* is the interest rate and *i* is the term of loan.


**Table A6.** Extra building cost for a commercial ice-classed vessel.

1 According to approximate equivalence of ice class classification systems made by [44], PC6 is equal to 1AS and PC7 is equal to 1A.

The fuel consumption of an ordinary 3800 TEU vessel under the designed speed can be derived based on Table A5: 97.98 ton/day. The current fuel price can be obtained by Bunker Index (www.bunkerindex.com): 450 USD/ton.

It is relatively well-documented in the literature that the fuel consumption of an ice-classed vessel will be more than an ordinary vessel with the same size due to extra weight, bow shape, hull appendages, which increases the frictional resistance [66]. Data related to extra fuel consumption can be seen in Table A7.


**Table A7.** Extra fuel consumption rate for a commercial ice-class ship.

The crew cost for a 3800 TEU ordinary vessel is 2740 USD/day [57]. Data related to extra crew cost can be found in Table A8.

**Table A8.** Extra crew cost for a 3800 TEU IB-classed vessel.


The Maintenance cost of a 3800 TEU ordinary vessel is 1644 USD/day [57]. On the NSR, the IB-classed vessel needs to undergo more challenging operation conditions, which will put extra cost on vessel and equipment (see Table A9).

**Table A9.** Extra maintenance cost for a 3800 TEU IB-classed vessel.


The maintenance cost of a 3800 TEU ordinary vessel is 1644 USD/day [57]. Data related to the extra insurance fee of the IB-classed vessel can be seen in Table A10.


**Table A10.** Extra insurance cost for a 3800 TEU IB-classed vessel.

Ice breaking and ice pilot remain necessary for safe navigation for an IB-classed vessel [71]. The ice-breaking cost of an IB-classed vessel is 356250 USD/trip [62].

#### *Appendix D.2 The Calculation of Economic Cost Based on HFS*

The economic cost of an IB-classed 3800 TEU vessel can be derived as follows: 

$$\begin{array}{l} \text{Cost}\_{EC\\_NSR} = \left(1 + E\_{crapital}\right) \times \text{Cost}\_{capital} + \left(1 + E\_{fuel}\right) \times \text{Cost}\_{fuel} \\ \qquad + \left(1 + E\_{crew}\right) \times \text{Cost}\_{crew} + \left(1 + E\_{mintenance}\right) \times \text{Cost}\_{mintenance} \\ \qquad + \left(1 + E\_{insurance}\right) \times \text{Cost}\_{insurance} + \text{Cost}\_{ilecbreak} \end{array} \tag{A1}$$

where, the value of each kind of extra cost on the NSR can be determined by 1000 times random sampling from the information mentioned above by Monte Carlo methods using the software of Matlab (Table A11).

**Table A11.** Parameters related to the economic cost of an IB-classed 3800 TEU vessel.


From Equations (22)–(27), the economic cost of an IB-classed 3800 TEU vessel for each grid can be obtained as follows: 

$$\rm{EC}\_{i} = \left(20,028 + 55,555 \times \sqrt[3]{\frac{v\_{i}}{24}}\right) \times \frac{S\_{i}}{24v\_{i}}\tag{A2}$$

Specially, the icebreaking fee for each route on the NSR is the same (356,250 USD), so it can be omitted when used as a criterion of route optimization. *h*i3 is the normalization of EC*i*.
