Algoritma Criss-crosss dan Branch and Bound dalam Pemrograman Linier Integer, Studi Kasus: Produksi Pangan

Dalam laporan analisis situasi pangan dan gizi tahun 2014 oleh badan ketahanan pangan dan penyuluhan Daerah Istimewa Yogyakarta terdapat 16 desa yang resiko pangan dan gisi tergolong waspada dan 26 desa yang resiko pangan dan gisi tergolong rawan, efisiensi penggunaan bahan baku pangan menjadi sangat penting peranannya. Efisiensi bahan baku bisa digunakan juga untuk mencapai keuntungan dalam industry makanan.Dalam penelitian ini masalah pangan tersebut dipandan dan diformulasikan dengan menggunakan pemrograman linier yang diselesaikan dengan model integer. Algoritma criss-crosss yang dikombinasikan dengan algoritma branch and bound diusulkan dalam penyelesaian masalah integer linier programming. Penelitian ini berfokus pada penerapan kedua algoritma tersebut dalam studi kasus produksi makanan dan pencarian kondisi batasan yang sesuai.Penelitian ini berhasil menerapkan penggabungan algoritma criss-crosss dan branch and bound. Penelitian ini mendefinisikan 4 batasan yang dapat diperhatikan untuk mengurangi pencabangan dalam pencarian nilai intege

Approximation of the Whole Pareto-Optimal Set for the Vector Optimization Problem

In multi objective optimization problems several objective functions have to be minimized simultaneously. In this work, we present a new computational method for the numerical solution of the linearly constrained, convex multi objective optimization problem. We propose some technique to find joint decreasing direction for unconstrained and linearly constrained case as well. Based on these results we introduce a method using subdivision technique to approximate the whole Pareto-optimal set of the linearly constrained, convex multi objective optimization problem. Finally, we illustrate computations of our algorithm by solving the Markowitz-model on real data

New criss-cross type algorithms for linear complementarity problems with sufficient matrices

We generalize new criss-cross type algorithms for linear complementarity problems (LCPs) given with sufficient matrices. Most LCP solvers require a priori information about the input matrix. The sufficiency of a matrix is hard to be checked (no polynomial time method is known). Our algorithm is similar to Zhang's linear programming and Akkeles¸, Balogh and Ille´s's criss-cross type algorithm for LCP-QP problems. We modify our basic algorithm in such a way that it can start with any matrix M , without having any information about the properties of the matrix (sufficiency, bisymmetry, positive definiteness, etc.) in advance. Even in this case, our algorithm terminates with one of the following cases in a finite number of steps: it solves the LCP problem, it solves its dual problem or it gives a certificate that the input matrix is not sufficient, thus cycling can occur. Although our algorithm is more general than that of Akkeles¸, Balogh and Ille´s's, the finiteness proof has been simplified. Furthermore, the finiteness proof of our algorithm gives a new, constructive proof to Fukuda and Terlaky's LCP duality theorem as well