Judul: TinjauandanProyeksiHargaKomoditasPokokPanganIndonesia
Abstrak: Sufficiency of food needs for human is important because it relates to the rights of citizens and human rights. The process of production ,distribution, and consumption is strongly influenced by domestic food prices. The contribution of food prices to the inflation in Indonesia is 79,61% (Statistic Center, 2013). Fluctuations in food prices is related to biological structure of commodities and agricultural environments, time lags in decision making related to the use of inputs until sell output, market structure, and policy impact. Information of food prices can be accessed to the State Logistics Agency (Bulog), Department of Trade and Industry (Disperindag), and Statistic Center (BPS). Standardization of daily food prices report made by Ministry of Trade Indonesia through Minister Decision No.522/MPP/Kep/11/1998. This regulations do not specifically regulate the location, the quality of the commodity, and commodity branded and non-branded. this problem cause food prices data among government agencies and private companies different each other. Research on food prices fluctuation and data synergize between government agencies and private companies is important to predict the price and formulating the optimal policy in the future .Every commodities in Indonesia has different characteristics of data, average mean value, and the pattern. Therefore , the best forecasting method for one commodity not always be the best method for another commodity . Based on these problems, the objective of this study are: 1) Analyze the development of Indonesian food prices; 2) Identify synergy prices between State Logistics Agency (Bulog), Department of Industry and Trade (Disperindag) , the Statistic Center (BPS) , and results of the survey in each region; 3) Getting the best forecasting method to forecast the price of basic food commodities in Indonesia ; 4 ) Forecast the price of food commodities of Indonesia in the future . The results showed that there are 7 commodities which have increasing price significantly. Those commodities are cassava (65,44%), onions (87,50%), red chili (70,39%), beef (41,45%), eggs (33,98%) , salted fish (29,06%) and instant noodles (30,68%). Some other commodities have decreasing price. Those commodities are green beans (4,3%) , Filma cooking oil (0,80%) , and Minyakita cooking oil (5,81%). The difference between the price data from Bulog , BPS , Disperindag , and survey results up to Rp 10.177/kg for the same commodity at the same time. There are 4 best methods for forecasting Indonesian food prices. Those methods are Multiplicative winters, additive winters, quadratic trend, multiplicative decomposition, and ARIMA (Autoregressive Integrated Moving Average). Forecasting results indicate that Onion will contribute strongly effect to inflation.
Keyword: time series analysis, the synergy of data, basic food commodities

Judul: Analysis of National Strategic Food Price Volatility and Its Effect on Inflation
Abstrak: Pangan merupakan kebutuhan primer yang harus terjaga stabilitas harganya. Beberapa periode terakhir harga sejumlah komoditas pangan strategis mengalami peningkatan. Penelitian ini bertujuan untuk menganalisis tingkat volatilitas harga minyak goreng, beras, cabai merah, bawang merah dan bawang putih serta pengaruhnya terhadap inflasi. Data yang digunakan adalah data harga kelima komoditas yang diperoleh dari Pusat Informasi Harga Pangan Strategis dan data inflasi diperoleh dari Bank Indonesia. Analisis yang dilakukan yakni Coefficient of Variation untuk melihat disparitas harga di seluruh provinsi di Indonesia dan pemodelan ARCH-GARCH untuk menganalisis volatilitas. Error Correction Model digunakan untuk menganalisis pengaruh volatilitas harga pangan terhadap inflasi. Hasil penelitian menunjukkan terdapat disparitas harga pangan antar waktu dan antar wilayah di Indonesia. Volatilitas harga kelima komoditas terjadi pada data harga tingkat nasional dan pada sejumlah wilayah amatan. Volatilitas harga minyak goreng serta beras berpengaruh signifkan terhadap inflasi pada jangka panjang. Sementara pada jangka pendek, volatilitas harga cabai merah dan volatilitas bawang merah bulan sebelumnya signifikan mempengaruhi tingkat inflasi, Food is a primary necessity that requires accessibility and price stability. In recent periods, the prices of some strategic food commodities have increased. The aim of this research is to analyze the level of price volatility of cooking oil, rice, red chili, shallots, and garlic, as well as their effect on inflation. The data used include the prices of these five commodities obtained from the Strategic Food Price Information Center and the inflation rate data obtained from the Bank of Indonesia. The analysis conducted includes the Coefficient of Variation to observe price disparities across all provinces in Indonesia and the ARCH-GARCH modeling to analyze volatility. The Error Correction Model is used to analyze the effect of food price volatility on inflation. The results show that price disparities occurs over time and across regions in Indonesia. Volatility in the prices of these five commodities occurs both at the national price level and in some observed regions. The price volatility of cooking oil and rice has a significant long-term effect on inflation. Meanwhile, in the short term, price volatility of red chili and shallots from the previous month have a significant effect on the inflation rate.
Keyword: ARCH-GARH, ECM, inflasi, pangan, volatilitas

Judul: Closed Knight’s Tour pada Papan Catur Berbentuk Persegi Panjang dengan Ukuran Maksimal 8 × 8
Abstrak: Closed Knight’s Tour merupakan langkah kuda yang mengunjungi setiap kotak pada papan catur tepat satu kali dengan langkah kuda berawal dan berakhir pada kotak yang sama. Graf yang terbentuk dari closed knight’s tour dinotasikan sebagai graf G(m,n), dengan m adalah banyaknya baris dan n adalah banyaknya kolom. Graf tersebut memuat Hamiltonian cycle. Sebuah graf terhubung G adalah graf bipartite jika dan hanya jika graf tersebut tidak memiliki cycle dengan panjang ganjil. Papan catur yang memenuhi syarat cukup untuk memiliki closed knight’s tour adalah papan catur berukuran 5 × 6, 5 × 8, 6 × 6, 6 × 7, 6 × 8, 7 × 8, dan 8 × 8.
Keyword: bipartite, closed knight’s tour, hamiltonian cycle, knight’s tour, teori graf