Judul: Pemodelan goal programming dan dualitas bagi fungsi resiko L1 untuk optimasi portofolio serta analisis regresinya
Abstrak: Pemrograman linear merupakan alat riset operasi yang paling efektif. Model ini menyelesaikan kasus dengan cara memaksimumkan atau meminimumkan fungsi tujuan terhadap suatu susunan kendala. Hanya saja jika memiliki beberapa tujuan atau sasaran yang hendak dicapai, model ini tidak dapat menyelesaikannya. Model goal programming yang diperkenalkan oleh A. Chames & W.W. Cooper pada tahun 1961 merupakan perluasan dari model pemrograman linear yang dapat menyelesaikan masalah yang menghendaki pencapaian aneka tujuan. Salah satu penerapan model ini yang cukup menarik adalah masalah investasi portofolio. Analisis goal programming meminimumkan tingkat resiko dari masing- masing saham yang ditawarkan. Model resiko yang digunakan adalah model fungsi resiko L oleh Konno & Yamazaki (1991) yang merupakan modifikasi model fungsi resiko Markowitz. Pemodelan goal programming bagi fungsi resiko L, menghadirkan variabel deviasional, v, dan w,, yang selalu bernilai positif (syarat ketaknegatifan). Variabel deviasional, yang menampung penyimpangan atau deviasi yang akan terjadi pada fungsi kendala, akan diminimumkan di dalam fungsi tujuan. Kemudian untuk mendapatkan solusi optimal digunakan perangkat lunak Linear Interactive Discrete Optimizer (LINDO). Dualitas digunakan untuk menentukan kondisi frontier yang efisien (efficient frontier) yang merupakan tujuan utama dalam perencanaan portofolio. Kondisi ini menggambarkan keuntungan maksimum bagi sekumpulan portofolio untuk setiap level tingkat resiko. Kondisi efficient frontier akan terpenuhi jika variabel dualnya, dan y, bernilai positif. Analisis regresi dilakukan untuk menduga model keuntungan r(t) yang dibuat dalam bentuk linear, r(t) = a + bi+ &, dengan sebagai periode waktu dan & merupakan galat. Pendugaan model ini dapat juga dilakukan dengan menggunakan model goal programming yang mempunyai jumlah galat yang lebih kecil dibandingkan dengan analisis regresi. Hanya saja model goal programming tidak mampu menghitung koefisien determinasinya (R), yang mengukur proporsi keragaman. Dengan kata lain baliwa penghitungan koefisien regresi linear dengan model goal programming lebih tepat dilakukan jika fungsi yang dibangun benar-benar linear.
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Judul: Pengoptimuman Risiko dan Profit dalam Perencanaan Investasi Bank dengan Metode Goal programming dan Fuzzy Goal Programming.
Abstrak: Bank is defined as a financial institution that operates to collect funds from the public in the form of deposits and distributing the funds to the public in the form of credit, etc. Sources of bank funding come from equity capital, demand deposits, time deposits, and saving deposits. The funding will be used for a variety of financing, especially to the assets that can generate profits, such as credit, investment, etc. In the bank investment problem there are three objective functions, which minimize the risk assets, maximize the profit, and minimize the capital adequacy. In this work, the problems are formulated in the form of goal programming (GP) and fuzzy goal programming (FGP) and solved by using LINGO 11.0. GP method requires the decision maker precisely define the aspiration level of each objective function to be achieved. But in many cases the aspiration levels are not properly determined, they are intrinsically fuzzy. FGP method uses imprecise aspiration level for each fuzzy goal. The fuzzy goals are to be characterized by their respective membership functions. Therefore by determining the tolerance value for each fuzzy goal, each goal will be obtained at an interval specified tolerance. The goals are risk assets =707.5∈ 595,805 , profit =28100∈ 26695,29505 , and capital adequacy =118.5∈ 64.9,171.5 .
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Judul: Merremia dennstedt ex endlicher (Convolvulaceae) in Sumatra.
Abstrak: Merremia is a small genus in the family Convolvulaceae. Merremia is a perennial or annual herb or woody liana with stems creeping or twinning on trees or rocks, put out milky white sap when injured and some species with tubers. Merremia is often confused with genus Ipomoea, due to they have resemblance in funnel shaped or campanulate corolla and straight anther. Phenetically, some members of Merremia have yellow flower whereas Ipomoea has white, purple or purplish white. Merremia is also confused with Operculina due both have non-spinulose pollen and dehiscent capsule. Nevertheless, Operculina characterized by circumciselli capsule and Merremia characterized by valve capsule. The important character in Merremia is the spread of the hairs on corolla that can be easily observed at the mature flower bud. The genus Merremia is found in the tropical regions of both hemispheres. Merremia wildly distributed throughout the tropical regions of Asia, Africa, Australia, North and South America and approximately there were 80 species of Merremia in the world. A Total of 175 sheets (164 collection numbers) which are deposited in Herbarium Bogoriense, 97 sheets (95 collection numbers) which are deposited Andalas University Herbarium (ANDA) and 9 sheets (4 collection numbers) which are deposited in BIOTROP Herbarium (BIOT) were studied. It composed of all specimens of Merremia in Sumatra. Additional specimens were collected by the author 28 sheets (15 collection numbers) from North Sumatra, West Sumatra and Lampung, which are stored in BO and BIOT. The digital data that consist of type specimens and distributions of species from JSTOR Plant Science and Convolvulaceae Unlimited were also used here. All the hebarium specimens were studied based on their morphological characters following de Vogel (1987) and Rifai (1976). The terminology of morphological characters followed Lawrence (1955), Veldkamp (1987), Harris and Harris (1994), Hickey and King (2005) and Stearn (1983). Information on the habitat, ecology, distribution, vernacular names and uses were noted from the specimens label and literatures. Taxonomic studies in Sumatra were conducted. There are eight species, one subspecies, one varietas and two forma from nine previously species (M. cissoides, M. dissecta, M. emarginata, M. hirta, M. peltata, M. quinquefolia, M. tridentata, M. tuberosa and M. vitifolia), two subspecies (M. umbellata ssp. orientalis and M. tridentata ssp. hastata), one varietas (M. boisiana var. sumatrana) and two forma (M. hederacea f. pubescens and M. hederacea f. barbata) can be recognized. One species (M. tridentata) and subspecies (M. tridentata ssp. hastata) are excluded because they have been proposed to different new taxa Xenostegia by Austin and Staples. The existence of M. emarginata was noted as new record in Sumatra and M. cissoides was noted as new record in Indonesia. A phylogenetic analysis using PAUP*4.Ob10 was undertaken based on morphological characters, using Evolvulus nummularius and Porana volubis as the out group. The phylogenetic analysis used 35 morphological characters was resulted consistency index (CI) = 0.60, homoplasy index (HI) = 0.40, retention index (RI) = 0.56 and Rescaled consistency index (RC) = 0.34. Phylogenetic tree used morphological characters divided taxa into two groups. The separation support M. boisiana var. sumatrana, M. cissoides, M.
Keyword: Convolvulaceae, Merremia, morphology, phylogenetic, Sumatra