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(demand). the method that could be used for solving the transportation problem is to directly find the optimal solution. The direct method that used in this study id the ASM method for solving the balance transportation problem and revised ASM method for solving the unbalance transportation problem. This study aims to construct a transportation model using those methods and it solution. The method on this study is to identify the transportation model, construct the transportation model matrixes, construct an algorithm table using ASM method and to determine the optimal solution of the transportation problem. The obtained result from this study was the model ASM method could determine the optimum value without using initial feasible solution. On solving the unbalance transportation problem, there is an addition of dummy cell or column step. Then reducing the cost of cell and column and change the dummy cost with the biggest cost of reduced cell or column.

ABSTRAKQuadratic Assignment Problem (QAP) merupakan salah satu perluasan dari masalah penugasan dengan menetapkan n fasilitas ke n lokasi tertentu untuk meminimalkan total biaya penugasan. QAP juga merupakan masalah optimasi kombinatorial yaitu masalah yang mempunyai himpunan solusi terhingga. Pada dasarnya solusi dari masalah kombinatorial bisa didapatkan dengan hasil yang tepat namun untuk masalah kompleks dengan ukuran data yang lebih besar cukup sulit dalam perhitungan karena waktu yang digunakan cukup lama untuk proses penyelesaian. Salah satu algoritma yang diterapkan dalam penyelesaian QAP ini adalah algoritma Ant Colony Optimization (ACO) yaitu algoritma yang meniru tingkah laku semut dalam mencari makanan dari sarang ke sumber makanan dengan bantuan komunikasi tak langsung yang disebut pheromone, sehingga pheromone ini digunakan untuk mencari solusi optimal dengan waktu yang cukup singkat. Penelitian ini menggunakan ACO untuk menyelesaikan masalah QAP dengan melibatkan rumus random proportional rule, mendapatkan solusi terkecil dan memperbaharui pheromone hingga penugasan stabil. Solusi yang didapatkan bernilai tetap sampai solusi maksimum penugasan. Memanfaatkan studi kasus pada kasus Nugent diperoleh solusi yang lebih minimal dan penempatan fasilitas kelokasi yang tepat melalui bantuan pheromone dan disimpan dalam tabu list sehingga semua fasilitas mendapatkan lokasi yang layak dengan waktu yang cukup singkat dalam penyelesaian. ABSTRACTQuadratic Assignment Problem (QAP) is one extension of the assignment problem by setting n facilities to n certain locations to minimize the total assignment costs. QAP is also a combinatorial optimization problem that is a problem that has a finite set of solutions. Basically the solution of combinatorial problems can be obtained with the right results but for complex problems with larger data sizes it is quite difficult to calculate because the time used is long enough for the completion process. One of the algorithms implemented in the completion of QAP is the Ant Colony Optimization (ACO) algorithm is an algorithm that mimics the behavior of ants in finding food from the nest to a food source with the help of indirect communication called pheromone, so that pheromone is used to find optimal solutions with quite a short time. in this research ACO is used to solve the QAP problem by using a random proportional of rule formula then getting the smallest solution and renewing the pheromone until the assignment is stable and the solution obtained is fixed until the maximum assignment solution. The results obtained to complete the Quadratic Assignment Problem with the Ant Colony Optimization algorithm to get a solution to the QAP problems tested in the Nugent case resulted in a more minimal

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Dengue Hemorrhagic Fever (DHF) is a disease caused by an arbovirus that enters the human body through the Aedes aegypti or Aedes albopictus mosquito. Dengue Hemorrhagic Fever (DHF) is characterized by symptoms of dengue fever; headache; reddish skin that looks like measles; and muscle and joint pain. In some patients, dengue fever can turn into one of two life-threatening forms that lead to decreased immunity. Various ways have been done to prevent the cause of DHF, but the results have not been optimal. The problem of the spread of the dengue virus can also be modeled mathematically and through the stability of the equilibrium point, the dynamics or behavior of the model can be determined. DHF spread can be suppressed by giving control in the form of treatment. This type of treatment is given to infected individuals. This treatment can be controlled optimally by applying the Pontryagin maximum principle. Pontryagin's maximum principle is the optimal control solution in accordance with the objective of maximizing the performance index. The purpose of this study is to discuss a mathematical model for the transmission of the dengue virus in the human body. As an effort to inhibit dengue virus replication, treatment control is used in the model, starting from the formation of a model from determining assumptions, parameters so that the SIV-T model is obtained, determining stability analysis, and then involving optimal