In practice, the certainess assumption for parameters in linear ........

In practice, the certainess assumption for parameters in linear programming are difficult to pullfiled. The uncertainties are sometimes coming from subjective and intuitive policies. To solve and accommodate these problems, will be approximated by fuzzy set theory. In this article, modeling of linear programming with fuzzy set will be discussed, followed by two cases with membership function are trapezoidal and triangular. Abstract in Bahasa Indonesia : Asumsi kepastian nilai-nilai parameter, dalam pengambilan keputusan yang dimodelkan dengan programa linier, dalam praktek sering sulit dipenuhi. Ketidakpastian yang muncul kadang diakibatkan oleh suatu kebijakan yang intuitif dan subjektif. Untuk memecahkan dan mengakomodasi ketidakpastian seperti tersebut, akan didekati dengan teori himpunan fuzzy. Dalam makalah ini, pemodelan programa linier dengan teori himpunan fuzzy tersebut, akan didiskusikan dengan dua kasus, masing-masing dengan menggunakan fungsi keanggotaan linier, yaitu trapezoida dan triangular. Kata kunci: programa linier, himpunan fuzzy.

Dormitory is a very important facility which have to be provided by a university. A survey to Petra Christian University’s students has been conducted to understand the required facilities and their financial ability. Linear programming has been used to calculate number of rooms and area of each facility which could satisfy the constraints and to obtain optimum profit. Number of bedrooms, number of bathrooms, and area of each facility, such as: living room, dining room, common room, cafeteria, book shop, mini market, phone booths, sport facilities, and parking space are recommended. Since the investment is financially feasible, the dormitory could be built in the future

Our main contribution is an $O(n \log n)$ algorithm that determines with high probability a perfect matching in a random 2-out bipartite graph. We also show that this algorithm runs in $O(n)$ expected time. This algorithm can be used as a subroutine in an $O(n^2)$ heuristic for the assignment problem. When the weights in the assignment problem are independently and uniformly distributed in the interval $[0, 1]$, we prove that the expected weight of the assignment returned by this heuristic is bounded above by $3+O(n^-a)$, for some positive constant $a$.

We develop a shortest augmenting path algorithm for the linear assignment problem. It contains new initialization routines and a special implementation of Dijkstra?s shortest path method. For both dense and sparse problems computational experiments show this algorithm to be uniformly faster than the best algorithms from the literature. A Pascal implementation is presented.

We survey recent developments in the fields of bipartite matchings, linear sum assignment and bottleneck assignment problems and applications, multidimensional assignment problems, quadratic assignment problems, in particular lower bounds, special cases and asymptotic results, biquadratic and communication assignment problems.

In this paper we consider the asymmetric assignment problem and we propose a new auction algorithm for its solution. The algorithm uses in a novel way the recently proposed idea of reverse auction, where, in addition to persons bidding for objects by raising their prices, we also have objects competing for persons by essentially offering discounts. In practice, the new algorithm apparently deals better with price wars than the currently existing auction algorithms. As a result, it tends to terminate substantially (and often dramatically) faster than its competitors.