RUSSELL’S APPROXIMATION METHOD DAN IMPROVED VOGEL’S APPROXIMATION METHOD DALAM PENYELESAIAN MASALAH TRANSPORTASI

Distribution activities in company which related in distribution sometimes have a problems, one of the problems is transportation problem. To solve that problem can be used a transportation model to obtain the distribution route so the cost that come out is more minimum. The aim of this research is to compare the initial solution of RAM and IVAM and to know the distribution route in distribution of bottled water in the CV. Prasarana Fortuna Prima so obtained the minimum distribution costs after optimality test using MODI. The results showed that RAM gave a lower initial solution than IVAM and the initial solution of RAM was optimum after optimality test using MODI with a distribution routes is from depo Klungkung to Toko Bintang, Toko Subur, Toko Cahaya Melati, Toko Mawar Sari, and Coco Mart Ubud, from depo Kapal to CV. Sumber Jaya, Toko Sol Mandala, and Toko Kayana, from depo Mahendradatta to Toko Sinar Wangi and Toko Aris.

Kajian Masalah Transshipment Tidak Seimbang Menggunakan Metode Least Cost - Stepping Stone Dan Metode Least Cost - Modi

Penelitian ini merupakan kajian masalah transshipment tidak seimbang menggunakan metode Least Cost - Stepping Stone. Metode Least Cost - MODI juga digunakan untuk membandingkan uji optimalitas mana yang lebih baik dalam menyelesaikan masalah transshipment ini. Hasil dari penelitian menunjukkan bahwa metode Least Cost - SteppingStone dan metode Least Cost - MODI dapat menyelesaikan masalah transshipment tidak seimbang. Menurut uji perbandingan metode MODI lebih efisien dari pada metode Stepping Stone dalam menguji optimalitas suatu masalah transshipment karena metode MODI memerlukan lebih sedikit iterasi dibandingkan dengan metode Stepping Stone. Pada Metode MODI nilai indeks perbaikan dapat dicari tanpa harus mencari loop dari setiap sel kosong, yakni hanya membutuhkan satu loop yang didapat setelah menentukan sel dengan indeks perbaikan terbesar, sedangkan pada metode Stepping Stone nilai indeks perbaikan dicari dengan membuat loop untuk setiap sel kosong pada setiap iterasi. Selain itu Metode Least Cost menghasilkan biaya transportasi yang berbeda apabila posisi penempatan biaya diubah, sedangkan dengan metode Stepping Stone biaya transportasi akan tetap sama dan optimal apabila posisi penempatan biaya diubah. This research is a study of unbalanced transshipment problems using the Least Cost - Stepping Stone method. The Least Cost - MODI method was also used to compare which optimality test was better in solving this transshipment problem. The results of the study showed that the Least Cost - Stepping Stone method and the Least Cost - MODI method could solve unbalanced transshipment problems. According to the comparison test, the MODI method was more efficient than the Stepping Stone method in testing the optimality of a transshipment problem because the MODI method required less iteration than the Stepping Stone method. In the MODI method, the repair index value could be searched without having to search for loops from each empty cell, which only requires one loop after determining the cell with the largest repair index. On the other hand, in the Stepping Stone method, the repair index value was searched by making a loop for each empty cell at each iteration. In addition, the Least Cost method produced different transportation costs if the placement position costs were changed. Meanwhile, the Stepping Stone method transportation costs would remain the same and optimal if the placement position costs were altered.

Portfolio Selection and Post Optimality Test Using Goal Programming

In a practical portfolio planning process the investment decision to be taken by an investor is not simple and is influenced by several other constraints like stock price, co-moment with market, return with respect to risk, past performance and so many. In this purview, a hybrid approach is employed for portfolio selection which combines multiple methodologies like investor topology, cluster analysis, analytical hierarchy process (AHP) for ranking the assets and biogeographic-based optimization (BBO). Furthermore, with the help of goal programming (GP), performing post optimality test for betterment the result which is obtained by BBO. In the goal programming, objective is to be minimizing the weighted deviations of desire goals. Weighted deviation is known as achievement, which has two branches namely over achievement and under achievement.

The Improvement of Optimality Test over Possible Reaction Set in Bilevel Linear Optimization with Ambiguous Objective Function of the Follower

Verifying a rational response is the most crucial step in searching for an optimal solution in bilevel linear programming. Such verification is even difficult in a model with ambiguous objective function of the follower who reacts rationally to a leader’s decision. In our model, we assume that the ambiguous coefficient vector of follower lies in a convex polytope and we formulate bilevel linear programming with the ambiguous objective function of the follower as a special three-level programming problem. We use thek-th best method that sequentially enumerates a solution and examine whether it is the best of all possible reactions. The optimality test process over possible reactions in lower-level problems usually encounters degenerate bases that become obstacles to verifying the optimality of an enumerated solution efficiently. To accelerate optimality verification, we propose search strategies and the evaluation of basic possible reactions adjacent to a degenerate basic solution. We introduce these methods in both local and global optimality testing, confirming the effectiveness of our proposed methods in numerical experiments.

A Portfolio Optimality Test Based on the First-Order Stochastic Dominance Criterion

Existing approaches to testing for the efficiency of a given portfolio make strong parametric assumptions about investor preferences and return distributions. Stochastic dominance-based procedures promise a useful nonparametric alternative. However, these procedures have been limited to considering binary choices. In this paper we take a new approach that considers all diversified portfolios and thereby introduce a new concept of first-order stochastic dominance (FSD) optimality of a given portfolio relative to all possible portfolios. Using our new test, we show that the U.S. stock market portfolio is significantly FSD nonoptimal relative to benchmark portfolios formed on market capitalization and book-to-market equity ratios. Without appealing to parametric assumptions about the return distribution, we conclude that no nonsatiable investor would hold the market portfolio in the face of the attractive premia of small caps and value stocks.