Analysis of Determination of Sea Toll Routes in Eastern Indonesia (KTI) Using Dynamic Programming

: The sea highway program is part of the fourth pillar, namely the pillars of the maritime economy, infrastructure and increasing welfare, one of the seven pillars of Indonesia's Maritime Policy (KKI). The aim of the Sea Highway Program is to grow the maritime economy by turning the sea into a production and marketi ng center between the Indonesian territory and the islands and surrounding areas. This study aims to analyze the decision of maritime highway routes in Eastern Indonesia Region (KTI) in order to provide the best route with a minimum distance. Four shipping highway routes from Surabaya to Eastern Indonesia Region, namely route T-13 (Tanjung Perak-Rote (Ndao)-Sabu (Biu)- Tanjung Perak), T-14 (Tanjung Perak-Lembata (Lewoleba)-Tabilota/Larantuka-Tanjung Perak), T-15 (Cape Perak-Makassar (Soekarno Hatta)-Jailolo-Morotai (Daruba)-Tanjung Perak), and T-18 (Tanjung Perak-Badas-Bima-Merauke (Kelapa Lima)-Tanjung Perak) combined into 1 (one) route from Tanjung Perak to Merauke, resulting in 1 (one) optimal route with the minimum distance obtained from the smallest value at each stage . This study uses quantitative methods and Multistage Graph problem-solving techniques with Dynamic Programming backward or bottom-up methods, and primary data collection through interviews and secondary data such as: documents/journals/books. The selected optimal route is (Tanjung Perak-Makassar-Tabilota/Larantuka-Sabu (Biu)-Merauke (Kelapa Lima)) with a distance from Tanjung Perak to Makassar is 437 Nm. Makassar to Tabilota/Larantuka is 340 Nm. Tabilota/Larantuka to Sabu (Biu) is 163.8 Nm. Sabu (Biu) to Merauke (Kelapa Lima) is 1261.24 Nm. So that the total shipping distance from Tanjung Perak to Merauke is 2202.04 Nm.


INTRODUCTION
State defense, which is also known as national defense, is a combination of forces (civil and military) of a State that guarantees its territorial integrity, protects its people, and/or safeguards its interests. There are 2 (two) types of national defense groups, namely: military defense and non-military/non-military defense (Indonesian Defense White Paper, 2015). To achieve national goals, Indonesia's state defense is built on a universal defense system. Universal defense essentially refers to defense that applies to all citizens based on their respective roles, duties and obligations. The involvement of every citizen is motivated by a sense of love for the motherland and a shared desire to defend it, including government policies in the field of maritime defense related to the idea of a global maritime axis. According to the Presidential Regulation of the Republic of Indonesia Number 16 of 2017 concerning Indonesian Maritime Policy, Indonesia is actually becoming a sovereign, modern, strong and independent maritime country capable of making a beneficial contribution to the oceans. The Global Maritime Axis is Indonesia's destination. Indonesia's maritime strategy prioritizes national interests, national security and defense, [ 44] as well as regional and global peace (Zaccone et al, 2018;Zhang et al, 2016).
Presidential Regulation of the Republic of Indonesia Number 34 of 2022 regulates the Indonesian Marine Policy Action Plan 2021-2025. On February 22, 2022, President Joko Widodo signed this Perpres. Programs and activities under the KKI action plan are arranged in a matrix format according to the seven pillars of the KKI. One of the seven pillars is marine resource management and human resource development. The other six pillars are maritime governance and institutions, maritime economy, improving infrastructure and welfare, management of marine areas and protection of the marine environment, as well as maritime culture and maritime diplomacy. The sea highway program is part of the fourth pillar, namely the pillars of the maritime economy, infrastructure, and increasing welfare, one of the seven pillars of the KKI. In order to increase connections and development in an Indo-centric way, the government is implementing a marine and maritime infrastructure development and development program (Kamalanathsharma et al., 2013;Kusuma et al., 2019;Theocharis et al., 2019).
The aim of the Sea Highway Program is to grow the maritime economy by turning the sea into a production and marketing center between Indonesian territory and the islands and surrounding areas. The guiding concept for the Sea Highway program is to support accessibility with delivery connectivity, availability, and affordability of the different costs needed by the community. The government hopes that the sea highway program can reduce logistics costs which are the main cause of price disparities between Java and other islands. As a result, it is possible to maintain stable prices for commodities and goods across the region. The implementation of the sea highway program from Surabaya to eastern Indonesia with a quantitative approach is the only focus of this study and uses dynamic programming calculations. The purpose of this study is to analyze the determination of sea toll routes in Eastern Indonesia (KTI) to obtain the optimal route with the minimum mileage.

MET ODE
Multistage Graph problem solving techniques with Dynamic Programming and primary data collection through interviews and secondary data such as: documents/journals/books. In this study the authors use the Dynamic Programming method backward or bottom -up . _ There are several important things in the backward method, namely: 1. Principle: analysis is performed by calculating the path (path) from the source to a node 2. Formula: 3. The calculation starts from the nodes in stage 3. 4. bcost ( i,j ) means the length of the backward path from the source ( s ) to the node j on stage i . 5. c ( l,j ) means the path length of the node l to node j .
Calculation of dynamic programming or dynamic programming backward method , namely calculating the distance backwards (from source ). Let X 1 , X 2 , X 3 , X 4 be vertices l visited at step k ( k = 1, 2, 3, 4). Then the route to be followed is: 1→ X 1 → X 2 → X 3 → X 4 in this case X 4 = 11. Merauke. Step (k) is the procedure for selecting the next node destination (there are 4 stages). Graph nodes represent the state( s ) connected to each step. Shortest route from state ( s ) toX 4 on step k is represented by the recurrence relationship shown below : Information: x = decision variable at stage k ( k = 1, 2, 3) C = weight ( cost ) side from s tox [ 45] f ( s , x ) = total weight of the path from s tox f ( s ) = minimum value of i f ( s , x ) The purpose of backward dynamic programming is to get f 1 (1) by searching for f 4 ( s ),

RESULTS AND DISCUSSION
In this study, it was limited to 4 sea highway routes from Surabaya to Eastern Indonesia, namely T-13 (Tanjung Perak-Rote (Ndao)-Sabu (Biu)-Tanjung Perak) using the KM ship. Kendhaga Nusantara 11, T-14 (Tanjung Perak-Lembata (Lewoleba)-Tabilota/Larantuka-Tanjung Perak) using the KM ship. Kendhaga Nusantara 7, T-15 (Cape Perak-Makassar (Soekarno Hatta)-Jailolo-Morotai (Daruba)-Tanjung Perak) using the KM ship. Nusantara 3 Logistics, and T-18 (Tanjung Perak-Badas-Bima-Merauke (Kelapa Lima)-Tanjung Perak) use the KM ship. Logistik Nusantara 2 which will be combined into 1 route from Tanjung Perak to Merauke. So as to produce several alternative routes, in this case the author provides numbering of these routes to determine the optimal route with the minimum distance using dynamic programming calculations or the backward dynamic programming method as shown in Figure   In Figure 1 there are several alternative routes from Tanjung Perak to Merauke which are colored to facilitate the grouping of stages as shown in Figure 2. Stages 4 namely the Bima, Badas, and Sabu (Biu) areas to Merauke are colored yellow on the route. Stage 3 namely the Lembata area to Merauke via Bima, Badas, and Sabu (Biu) are colored black on the route. Then Tabilota/Larantuka headed for Merauke via Bima, Badas, and Sabu (Biu) colored orange. Then Rote (Ndao) goes to Merauke via Bima, Badas, and Sabu (Biu) is colored blue on the route. The stage 2 is the Makassar area to Merauke via Lembata, Tabilota/Larantuka, Rote (Ndao) is colored purple on the route. Then Jailolo headed for Merauke via Lembata, Tabilota/Larantuka, Rote (Ndao) was given a green color on the route. Then Morotai headed for Merauke via Lembata, Tabilota/Larantuka, Rote (Ndao) was colored red on the route. The stage 1 , namely the Tanjung Perak area to Merauke via Makassar, Jailolo, Morotai, is colored gold on the route. The existing path Dinamika Bahari: Journal of Maritime Dynamics -May 2023, 4(1), 43-50 [ 46] graph is first segmented while finalizing the solution to identify the shortest path or route and get the optimal solution at each stage. Figure 2 shows there are 4 stages from Tanjung Perak to Merauke on the shipping chart. To determine the best route from Tanjung Perak to Merauke , there are 2 (two) things that need to be done , namely: 1. In stage n, choose a decision variable (n=1,2,3,4) as the area that must be taken. So the total route is 1 →Tanjung Perak and Merauke 4 →.
2. When the tracer/browser arrives at state s, ready to proceed to stage n, select ( f s ) , x as the total policy cost of the next stage, and choose as the next goal .