5.2 Evaluation of the Test Results
5.2.2 Testing the Effect of a Kite Propulsion System
The test runs also show that the installation of a kite propulsion system has only a small effect on the objective function value. The difference in the objective function values between a test set with the same type of ships is given in the last column of Table 5.4. The percentage expresses the objective function value for test sets where ships have an alternative kite propulsion system installed divided by the objective function value of the same types of ships without a kite propulsion system (in percent -100%). Except for two couples of the test sets with 16 harbours, all other test sets show only a small difference when using or not using an alternative kite propulsion system. The
Table 5.4: Evaluating the effect of an alternative kite propulsion system Available number of a given type of ship:
Test set NumberofHarbours Rafaela RafaelawS Alicante AlicantewS Moliere MolierewS Hamburg HamburgwS Laetitia LaetitiawS BuenosAires BuenosAireswS Objective functionvalue Difference inobjective functionvalue
3sSnS 10 5 4 4 16,026,400
3.30%
3sSwS 10 5 4 4 16,572,800
3lSnS 10 4 4 3 14,640,600
2.39%
3lSwS 10 4 4 4 14,998,700
6SnS 10 3 4 4 3 3 2 15,100,900
2.69%
6SwS 10 2 3 3 4 2 3 15,517,800
3sSnS 16 7 6 7 47,385,200
11.67%
3sSwS 16 7 7 7 53,644,800
3lSnS 16 5 5 6 56,229,800
15.12%
3lSwS 16 6 8 6 66,242,800
6SnS 16 8 7 7 6 4 4 63,718,200
1.15%
6SwS 16 8 5 6 7 6 4 64,461,800
3sSnS 23 7 11 11 58,316,200
2.56%
3sSwS 23 8 11 10 59,848,300
3lSnS 23 11 10 11 70,955,200
3.31%
3lSwS 23 11 11 10 73,386,000
6SnS 23 10 11 9 9 8 8 93,760,100
3.45%
6SwS 23 9 11 9 11 7 8 97,107,200
3sSnS 33 10 10 9 73,850,000
1.78%
3sSwS 33 10 8 10 75,187,600
3lSnS 33 17 17 20 101,618,000
0.44%
3lSwS 33 16 18 12 102,068,000
6SnS 33 7 8 5 12 11 7 119,137,000
0.51%
6SwS 33 6 8 5 13 10 8 119,748,000
two couples of the test sets with 16 harbours are 3sSnS, 3sSwS and 3lSnS, 3lSwS. For these two the objective function value of ships travelling with an alternative kite propulsion system is 11.67% and 15.12% higher then their counterparts travelling without a kite propulsion system. The reason for this might be that weather and ocean currents conditions may have a greater
influence on trips between these 16 harbours around the Antlantic Ocean than on trips conencting harbours of other regions. As an example, the difference in objective function value of 3.3% between the three small ships and 16 Harbours of the Atlantic Ocean, travelling either with or without an alternative kite propulsion, corresponds to an absolut difference of 546,400$
per week. Dividing this amount by 13, the total number of ships needed when using a kite propulsion, results in 42,031$ savings per week and installed kite system. If all kite related fixed and variable weekly costs exceed this amount, investing into a kite propulsion system is not profitable. It has to be kept in mind that a part or all of those differences in objective function values may result from using a heuristic solution approach, which does not guarantee finding an overall optimal solution.
Figure 5.2: Harbour visiting sequence of ships of type ’Rafaela’ (white line) ’Alicante’ (grey line) and ’Moliere’ (black line) and their corre- sponding schedules (see tables at harbours; Arr = arrival time; Dep
= departure time)( c2011 Google). To view this figure in colour please refer to: www.springer-gabler.de/Buch/978-3-658-00698-3/
A-Liner-Shipping-Network-Design.html.
Figure 5.2 shows a solution for the 3 smaller ships of type ’Rafaela’,
’Alicante’ and ’Molier’ and harbours of the Gulf of Mexico. All three types of ships are in use. The black line indicates the round trip ship of type
’Moliere’ is travelling on, the grey line represents the round trip of ship of type ’Alicante’ and the white line corresponds to ship of type ’Rafaela’. The width of the lines indicates the speed at which a ship is travelling between two consecutive harbours. The smallest width corresponds to a speed of 14kn, the medium width to 18kn and the widest to 23kn. For example ships of type Moliere (black line) travelling at 14kn from New Orleans to Altamira, ships of type Alicante travelling at 18kn from Mobile to Houston and ships of type ’Rafaela’ travelling at 23kn from Fort de France to Puerto Limon.
With 5 ships of each type all available cargo can be transported between the harbours. The complete parameter setting of this underlying test set is (10, 3sSnS, 01, 650, 4.9, 0.5, 20, 5, 20) with an objective function value of 14,246,900$. Also given in the figure are the times when a ship will arrive in the next harbour. These times are presented in tables on the map located near the harbour. Harbour Puerto Moin located at the easterly entrance of the Panama Canal functions as starting and ending harbour of the round trips, which is the harbour with index 1. The departure time is set to 0 and the arrival time equals to 812 hours for ships of type ’Moliere’ and 822 hours for ships of type ’Rafaela’. Only ships of type ’Alicante’ start and end at harbour Puerto Limon in Costa Rica, which has index 2. The total round trip duration indicates that for a weekly visiting frequency 5 ships are needed to maintain the round trip. After 840 hours the ships start again for their next round trip. The differences in arrival and departure times at the harbours is used for loading or unloading activities. Longer harbour visits include times that can be used for maintenance or repair work or to catch up on possible delays. This additional stopover time might also be distributed among all harbours or adjusted manually by an operator according to unforeseen events or based on his operational experience.