A SIMULATION MODEL FOR THE ASSESSMENT OF THE NORTHERN SEA ROUTE TROUGHPUT
5. COMPUTATIONAL EXPERIMENTS
5.3. Data generation
Navigation period. Officially, the normal navigation period lasts from the mid of July till the mid of November (Northern Sea Route Information Office, 2015a). In the experiments we consider the navigation period from the beginning of July till the end of November.
Icebreaker speed. Icebreaker speed is defined as a parameter with the triangular probability distribution for each zone of the NSR and for easy, moderate and severe ice conditions. The minimum, maximum and mode values of probability distributions are generated based on the information derived from Liu and Kronbak (2010).
Requested transit order start dates. The fractions of transit orders for each month of the navigation period are established in relation to the transit statistics of the Suez Canal (Suez Canal Authority, 2015).
Vessel's ice class. The parameters for the ice class discrete probability distribution are modelled based on the NSR transit statistics for 2013 (Northern Sea Route Administration, 2015a).
Ice conditions. Ice condition types are generated from the triangular probability distribution.
The values for the minimum, maximum and mode of the ice concentration values for each month and each zone are generated based on the on information available from the Arctic and Antarctic Research Institute (2015).
Maximum delay time. As outlined in Section 3.2, the customers’ decision concerning the cancellation of an order is based on the limit on the maximum delay of the actual transit start from the requested transit start. The limit is set to 15 days based on the difference in sailing times from Kirkenes, Norway, to Lianyungang, China, via the Suez Canal and via the NSR (Bergo, 2014).
Distances and waypoints. We consider the shortest possible route between Kara Gate and Bering Strait. The waypoints correspond to the borders of the NSR zones defined by the NSRA (Northern Sea Route Information Office, 2015e), eight in total. Distances between waypoints are calculated based on the waypoints' coordinates.
Convoy size. The size of convoy is generated from the triangular probability distribution with minimum, maximum and mode values generated based on the information on convoy formation provided by (Šarlaj, 2015).
5.4. Results
The fractions of satisfied transit orders for all developed scenarios are presented in Figure 5.1.
Contrary to the expected results, no constant declining trend is observed. Instead, the fraction of orders satisfied for all icebreaker scenarios increases initially at a higher rate. For example, it grows from 60% to 90% for the cases with 5 and 6 icebreakers when the number of orders increases from 70 to 210 respectively. The trend in fraction of orders satisfied continues with a gentle decline (by 5% to 10% for each subsequent increase in total orders) for the number of orders exceeding 210 per navigation period. It can be explained by the following phenomena.
With the small number of orders, the time intervals between the requested transit start days are relatively large. During convoy generation, the planned convoy start date may deviate significantly from the requested start dates of orders assigned to the convoy. This results in about 40% of orders being cancelled due to the exceeded limit on maximal delay.
12 Figure 5.1 Fractions of satisfied transit orders
Figure 5.2 Average delay time from the requested transit start date
With the initial growth in the total number of orders (<210), the fraction of orders cancelled due to exceeded limit on maximal delay is reduced. This happens due to smaller deviations between the planned convoy starts and the requested transit starts of orders in the convoy. At the same time, the fraction of orders cancelled due to the deviation between the actual convoy start dates and the requested transit start dates is low due to sufficient icebreaker capacity and almost no waiting for available icebreaker. With the further increase in the total number of orders (>210), a smaller fraction of orders is satisfied due to more order cancellations explained by large deviations between the actual and the requested transit starts caused by more convoys and longer waiting time for an available icebreaker.
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The dependence of the average transit delay time from the requested transit start date on the total number of orders and the number of icebreakers is visualised in Figure 5.2. The total transit order delay time is the sum of two possible delays: first, the delay from the planned convoy start to the requested transit start and, second, the delay from the actual convoy start compared to the planned convoy start. The planned convoy start is determined by the last transit order assigned to the convoy. With the small total number of orders and large time intervals between the requested start dates of transit orders assigned to convoys, the delays from the planned convoy start dates to the requested transit starts are relatively large. On the contrary, the delays from the actual until the planned convoys' start dates are insignificant due to sufficient icebreaker capacity. The average order delay time for the scenario with 70 orders and 3 available icebreakers is 10 days and is reduced to 7.5 days when the number of icebreakers is increased to 6. With the initial increase in the total number of transit orders (up to 210 in total) and shorter time intervals between the requested transit start days, the delays between the planned convoy starts and the requested transit starts in the convoys will reduce substantially. While the deviations between the actual and the planned convoy start dates may only grow slowly, resulting in the smaller total order delays and the average delays. With the continued increase in the total number of orders (>210), the total order delays start to increase due to a significant increase in the delays from the actual to the planned convoy starts thereby outweighing the reduction in delays from the planned and the requested starts. The average order delays for the largest number of orders converge to the maximal delay limit.
6. CONCLUSIONS AND FURTHER RESEARCH
This paper addresses the analysis of the NSR throughput under icebreaker support. The objective of the research is to define the main factors influencing the route's throughput (ice conditions, vessels ice class and speed, navigation rules for icebreaker support, number of icebreakers in operation, order processing logic, convoy formation, etc.), and to model the transit of vessels via the NSR. Discrete-event simulation is used as a methodology for the throughput assessment due to the stochastic components of the transit process.
The NSR has not yet been used at large scale therefore the historical transit data is not representative. The model of the transit process is developed based on the information obtained from the transit data and expert assessments obtained from open sources. It is tested on the simulated data taking the transits of the past few years as a starting point. Results of experiments on generated data show that the initial increase in the total number of orders leads to a substantial increase in the fraction of orders satisfied and average delay time reduction. Further increase in the total number of the transit orders changes the trend to the opposite. Obtained results confirm the expectations that the increase in the number of icebreakers in operation leads to a higher fraction of satisfied orders and shorter delay times.
The developed simulation model may have a value for the shippers and transport providers operating in the Arctic, and for the NSR Administration since it allows for the assessment of the average delay time from the requested transit start date and the NSR throughput for increased flows of vessels via the NSR and the various icebreaker fleet sizes. However, more advanced weather conditions and vessel speed modelling could be incorporated, and further investigation of the decision making logic related to convoy formation and order processing should be accounted for in further research.
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