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"Dynamic Dial a Ride Problem with Time Windows (DDARPTW) merupakan masalah pencarian rute optimal untuk melayani sejumlah pelanggan yang ingin dijemput di suatu tempat dan diantar ke tempat lainnya dengan data permintaan penumpang yang dapat bertambah selama periode perjalanan. Solusi yang ingin didapatkan adalah suatu rute dengan tingkat ketidakpuasan pelanggan yang minimum. Tugas akhir ini membahas penggunaan algoritma 2 tahap pada DDARPTW serta implementasinya pada data sebanyak 56 pelanggan dengan menggunakan perangkat lunak. Penentuan solusi awal pada tugas akhir ini menggunakan metode insertion heuristic dan tahap pertama menggunakan metode local search yaitu 2-opt arc swap untuk memberikan perbaikan pada nilai fungsi tujuan serta tahap kedua menggunakan metode simple insertion untuk melakukan penambahan pelanggan baru dalam periode perjalanan.

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Dynamic Dial a Ride Problem with Time Windows (DDARPTW) is a problem of finding an optimal route to serve a number of customers who want to be picked up in a certaint place and delivered to other place. Data of passenger's demand could be added during the trip period. The obtained solution is a route with minimum level of customer dissatisfaction.

This mini thesis explores the use of two phase algorithm and its implementation on the data of 56 customers using a software. The initial solution is constructed by insertion heuristic method and the first phase use 2-opt arc swap local search which provides improvements to the value of the objective function and the second phase uses a simple insertion method to add new customer in the trip period."

"Aircraft landing problem (ALP) merupakan suatu permasalahan pesawat terbang dalam menemukan jadwal yang optimal untuk pendaratan pesawat terbang. Objektivitas dari ALP adalah meminimumkan total biaya pinalti dari pesawat pada single runway maupun multiple runway. Dalam permasalahan ini terdapat beberapa hal penting yang harus dipertimbangkan yaitu kepentingan pemisahan waktu antara pesawat terbang dan interval waktu (time window) yang harus diperhatikan demi kepentingan keselamatan penumpang. Pertama, akan diberikan pemodelan matematis dari ALP dengan fungsi objektif yang linear. Kedua, akan digunakan pendekatan solusi heuristik yaitu Algoritma Ant Colony Optimization (ACO) dalam mencari solusi ALP yang optimal.

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Aircraft landing problem (ALP) describes the aircraft problem of finding an optimal schedule of aircrafts landing. The objective of ALP is to minimize total penalty restrictive cost of aircraft in a single runway or multiple runways. This problem considers few certain constraints, such as the necessary separation time between aircrafts and time window that should be concerned for passenger safety. In the first part, will be presented a mathematical formulation of the problem with linear objective function. The second part is heuristic solution approaches with Ant Colony Optimization Algorithm to solve ALP."

"The objective of the present study is to find out the effect of problem-based performance assessment and instructional models on the students' metacognition in mathematics at senior high schools. The study was conducted in SMU in Jakarta. There were 120 first grade students as the sample of the study, selected through multistage random sampling. The data were gathered by using a metacognition scale. Data analysis was done by using the two way analysis of variance. The results of the study are: (1) In general, problem-based performance assessment effects students' metacognition mathematics, (2) Learning models affect the students' metacognition in mathematics; in which the cooperative learning model is more effective in improving the students' metacognition than the classical learning model, (3) There is an interaction effect between problem-based performance assessment and instructional models. Such interaction show that problem solving performance assessment is more effective in improving students' metacognition in mathematics if it is combined with cooperative learning model; while problem posing performance assessment is more effective if it is combined with classical learning model."

"ABSTRAKRobust Knapsack Problem (RKP) adalah variasi dari masalah Knapsack, dimana dalam hal ini bobot dari setiap item belum diketahui secara pasti, dan hanya diketahui terletak dalam sebuah interval tentu. Pada RKP akan dicari solusi optimal yang merupakan keuntungan optimal yang akan didapatkan, dan item-item mana saja yang diletakkan ke dalam Knapsack sehingga menghasilkan solusi optimal. Terdapat dua metode alternatif yang akan dijelaskan untuk mencari solusi optimal pada RKP, yang kemudian dibandingkan efisiensi dari kedua metode tersebut dengan dilihat dari running time masing-masing metode. Sedangkan untuk mencari himpunan item-item yang menghasilkan solusi optimal pada RKP akan digunakan metode partisi rekursif, dimana ide awalnya adalah dengan mempartisi himpunan item menjadi dua subhimpunan item.

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ABSTRACTRobust Knapsack Problem (RKP) is a variation of the Knapsack Problem, where in this case the weight of each item is not exactly known in advance, but belongs to a given interval. On RKP, it will be sought optimal solution, which is the optimal benefit to be gained, and set of items placed into the Knapsack. There are two methods that will be discussed to find optimal solution in RKP, and then the efficiency of the two alternative methods will be compared with their running time. Whereas, to search the set of items that build optimal solutions in the RKP will be used recursive partitioning method. The main idea of this method is dividing the set of items into two subsets of items."

"ABSTRAKThe two-sided Lagrange-Sylvester interpolation problem is solved in the frame-work of H2 functions. The extra Hilbert-space structure allows us to give self-contained and independent arguments. "

"Hazardous material (hazmat) merupakan material yang berpotensi membahayakan manusia, infrastruktur dan lingkungan (US DOT, 2004). Karena berpotensi membahayakan, maka pada pengangkutan hazmat perlu memperhatikan risiko yang mungkin timbul (baik risiko jiwa maupun harta benda) selain mempertimbangkan faktor biaya, sehingga permasalahan pengangkutan hazmat termasuk ke dalam permasalahan multi obyektif.Salah satu cara untuk menangani permasalahan multi obyektif adalah dengan menerapkan konsep optimasi Pareto, yaitu konsep yang mengatakan bahwa suatu solusi dikatakan optimal jika tidak mungkin lagi meningkatkan suatu nilai fungsi tujuan tanpa mengurangi nilai fungsi tujuan yang lain. Konsep tersebut bekerja untuk menemukan himpunan solusi non-dominated dengan menerapkan aturan dominan pareto (pareto dominance rule).Pada skripsi ini akan dibahas masalah pemilihan rute kendaraan untuk mengangkut hazmat dengan memperhatikan waktu pelayanan (time windows) yang telah ditentukan yang dimodelkan ke dalam Hazmat Vehicle Routing Problem with Time windows (HVRPTW). Rute yang terpilih merupakan jalur non dominated, yaitu jalur dengan tingkat risiko dan biaya perjalanan yang paling kecil. Untuk memilih rute tersebut digunakan metode Multi-Objective Ant Colony System yang merupakan pengembangan dari metode Ant Colony System, yaitu metode yang mengadaptasi perilaku semut dalam mencari makanan dengan bantuan pheromone (zat kimia aromatik yang dikeluarkan oleh spesies semut).

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Hazardous materials (hazmat) is defined by any substance or material which capable of causing harm to human, property and environment (US DOT, 2004). Therefore, in every hazmat transportation needs to pay attention to possible risks (both life and property risk) in addition to considering the cost factor. So that the problem of transporting hazmat belongs to the multi-objective problems.

The best approach to deal with multi objective problem is to apply the concept of Pareto optimization. This concept declare that an optimal solution is if there is no possibility to increase the value of objective function without eliminate the value of others objective function. This concept works to determine a set of non-dominated solutions applying conditions of Pareto dominance.

This research discuss about the problem of route selection of vehicles for transporting hazmat with focusing on service time (time windows) that has been determined and known as Hazmat Vehicle Routing Problem with Time Windows (HVRPTW). A non-dominated paths as selected path is the path with the smallest amount of risk and scheduled time. The route is selected by using Multi-Objective Ant Colony System algorithm which is the development of Ant Colony System methods that belongs to Ant Colony Optimization. This method adapts the behavior of ants in looking for feed helped by a pheromone (a chemical released by the aromatic species of ants)."