Judul: Analisis Volatilitas Harga Minyak Sawit dan Harga Minyak Goreng
Abstrak: Crude palm oil industry has bright prospect in vegetables oil competition. Nowadays crude palm oil is the most produced and consumed.. Indonesia is the biggest crude palm oil exporter contributing 46.2 percent of world’s total supply in 2011. One of palm oil based downstream industry which is important in Indonesia is cooking oil industry. Cooking oil is one of the important nine basic needs for people. Cooking oil consumption tends to increase and this condition has been fullfiled by domestic industry. This because Indonesia has surplus condition in cooking oil. Unfortunately this surplus condition doesnot guarantee low and stable price domestically. The aims of this research are to analyze volatility of crude palm oil price and cooking oil, to analyze effect of crude palm oil export policy to the volatility of palm oil price and cooking oil and to analyze effect of value added tax borne by government to the cooking oil volatility. Data used in this research is secondary data which is daily time series data, period January 2005 to March 2012. Volatility of palm oil price and cooking oil in this research is built on the basis of time series econometric methods called autoregressive conditional heteroscedasticity/ generalized autoregressive conditional eteroschedasticity (ARCH GARCH) Analysis results to price volatility of crude palm oil and cooking oil show different pattern. Volatility of crude palm oil is influenced by volatility of two previous periods, meanwhile volatility of cooking oil is influenced by volatility and variance last period. Volatility of cooking oil price is higher than volatility of cooking oil. Analysis results to progressive export tax policy of crude palm oil and value added tax borne by government towards cooking oil industry give different effect to price volatility. Implementation of Export tax policy to crude palm oil leads to constant price volatility of crude palm oil and cooking palm oil price until the end of analysis period, with the result that export tax policy can stabilize crude palm oil price and cooking oil. On the other hand value added tax borne by government towards cooking oil price leads to unstable price volatility of cooking oil until the end of analysis period. It can be concluded that value added tax borne by government cannot stabilize of cooking oil price
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Judul: Analysis of Price Volatility and Vertical Integration of Cooking Oil Market in Indonesia
Abstrak: Fenomena kenaikan dan penurunan harga minyak goreng yang berbeda setiap jenisnya turut berperan sebagai penyumbang angka inflasi dalam kelompok pangan bergejolak di Indonesia. Perubahan harga yang tidak stabil tersebut menjadi tantangan tersendiri bagi produsen, pedagang besar, dan pedagang eceran. Penelitian ini bertujuan menganalisis volatilitas dan hubungan integrasi vertikal pada harga minyak goreng kemasan premium, kemasan sederhana, dan kemasan curah pada setiap tingkat harga pasar di produsen, pedagang besar, dan pedagang eceran. Penelitian ini menggunakan harga minyak goreng mingguan nasional tahun 2019-2023 diperoleh dari Pusat Informasi Harga Pangan Strategis. Analisis yang dilakukan yakni Koefisien Variasi untuk melihat fluktuasi harga, model ARCH/GARCH untuk menganalisis volatilitas, dan model VECM untuk menganalisis integrasi vertikal. Hasil penelitian menunjukkan harga minyak goreng di setiap jenis kualitas memiliki perbedaan nilai fluktuasi. Volatilitas sangat tinggi terjadi pada harga minyak goreng premium dan curah di tingkat pedagang eceran, sedangkan volatilitas tinggi terjadi pada harga minyak goreng curah di tingkat pedagang besar. Hasil VECM menunjukkan terdapat hubungan jangka panjang dan jangka pendek antar variabel harga minyak goreng pada tiga tingkat pasar berbeda., The phenomenon of increasing and decreasing cooking oil prices that are different for each type contributes to the inflation rate in the volatile food group in Indonesia. The unstable price changes are a challenge for producers, wholesalers, and retailers. This study aims to analyze the volatility and vertical integration relationship in the price of premium packaged cooking oil, simple packaging, and bulk packaging at each market price level at producers, wholesalers, and retailers. This study uses weekly national cooking oil prices for 2019-2023 obtained from the Strategic Food Price Information Center. The analysis carried out is the Coefficient of Variation to see price fluctuations, ARCH/GARCH models to analyze volatility, and VECM models to analyze vertical integration. The results show that cooking oil prices in each type of quality have different fluctuation values. Very high volatility occurs in the price of premium and bulk cooking oil at the retail level, while high volatility occurs in the price of bulk cooking oil at the wholesale level. VECM results show that there are long-run and short-run relationships between cooking oil price variables at three different market levels.
Keyword: Volatilitas, harga, integrasi, minyak goreng

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