Laut Tawar Lake is located in Aceh Tengah District is the largest lake in Aceh Province. The lake, located at an altitude of 1230 meters above sea level, produces about 13 species of freshwater fish. Fish depik (Rasbora tawarensis), eyas (Rasbora sp.), and relo (Rasbora sp.) are endemic species of Laut Tawar Lake. This study aims to estimate the potential of fish production based on the value of morphoedaphic index. The observation was conducted for one year, from October 2016 until September 2017. The measurement of electric conductivity value of lake waters was conducted on 7 (seven) stations selected purposively in the lake area about 5870 hectares. The results showed that morphoedaphic index value of Laut Tawar Lake ranged from 5.10 to 7.84 with an average of 6.14. Potential of fish production in the lake is 33.47 kg/ha/yr with total potential of fish production of 196.49 ton/yr. The value shows a decrease of 10.93 kg/ha/yr over a period of 22 years. This decrease is caused by changes in morphometry parameters and water quality of Laut Tawar Lake.

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Penelitian ini merupakan kajian masalah transshipment tidak seimbang menggunakan metode Least Cost - Stepping Stone. Metode Least Cost - MODI juga digunakan untuk membandingkan uji  optimalitas mana yang lebih baik dalam menyelesaikan masalah transshipment ini. Hasil dari penelitian menunjukkan bahwa metode Least Cost - SteppingStone dan metode Least Cost - MODI dapat menyelesaikan masalah transshipment tidak seimbang. Menurut uji perbandingan metode MODI lebih efisien dari pada metode Stepping Stone dalam menguji optimalitas suatu masalah transshipment karena metode MODI memerlukan lebih sedikit iterasi dibandingkan dengan metode Stepping Stone. Pada Metode MODI nilai indeks perbaikan dapat dicari tanpa harus mencari loop dari setiap sel kosong, yakni hanya membutuhkan satu loop yang didapat setelah menentukan sel dengan indeks perbaikan terbesar, sedangkan pada metode Stepping Stone nilai indeks perbaikan dicari dengan membuat loop untuk setiap sel kosong pada setiap iterasi. Selain itu Metode Least Cost menghasilkan biaya transportasi yang berbeda apabila posisi penempatan biaya diubah, sedangkan dengan metode Stepping Stone biaya transportasi akan tetap sama dan optimal apabila posisi penempatan biaya diubah.   This research is a study of unbalanced transshipment problems using the Least Cost - Stepping Stone method. The Least Cost - MODI method was also used to compare which optimality test was better in solving this transshipment problem. The results of the study showed that the Least Cost - Stepping Stone method and the Least Cost - MODI method could solve unbalanced transshipment problems. According to the comparison test, the MODI method was more efficient than the Stepping Stone method in testing the optimality of a transshipment problem because the MODI method required less iteration than the Stepping Stone method. In the MODI method, the repair index value could be searched without having to search for loops from each empty cell, which only requires one loop after determining the cell with the largest repair index. On the other hand, in the Stepping Stone method, the repair index value was searched by making a loop for each empty cell at each iteration. In addition, the Least Cost method produced different transportation costs if the placement position costs were changed. Meanwhile, the Stepping Stone method transportation costs would remain the same and optimal if the placement position costs were altered.

Optimasi adalah suatu aktivitas untuk mendapatkan hasil terbaik di dalam suatu keadaan yang diberikan. Tujuan akhir dari aktivitas tersebut adalah meminimumkan usaha (effort) atau memaksimumkan manfaat (benefit) yang diinginkan. Metode pengali Lagrange merupakan metode yang digunakan untuk menangani permasalahan optimasi berkendala. Pada penelitian ini dianalisis karakteristik dari metode pengali Lagrange sehingga metode ini dapat menyelesaikan permasalahan optimasi berkendala. Metode tersebut diaplikasikan pada salah satu contoh optimasi berkendala untuk meminimumkan fungsi objektif kuadrat sehingga diperolehlah nilai minimum dari fungsi objektif kuadrat adalah -0.0403. Banyak masalah optimasi tidak dapat diselesaikan dikarenakan kendala yang membatasi fungsi objektif. Salah satu karakteristik dari metode pengali Lagrange adalah dapat mentransformasi persoalan optimasi berkendala menjadi persoalan optimasi tanpa kendala. Dengan demikian persoalan optimasi dapat diselesaikan.   Optimization is an activity to get the best results in a given situation. The ultimate goal of the activity is to minimize the effort or maximize the desired benefits. The Lagrange multiplier method is a method used to handle constrained optimization problems. This study analyzed the characteristics of the Lagrange multiplier method with the aim of solving constrained optimization problems. The method was applied to one sample of constrained optimization to minimize the objective function of squares and resulted -0.0403 as the minimum value of the objective quadratic function. Many optimization problems could not be solved due to constraints that limited objective functions. One of the characteristics of the Lagrange multiplier method was that it could transform constrained optimization problems into non-constrained ones. Thus the optimization problem could be resolved.

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