A Simplex-Type Algorithm for General Transportation Problems: An Alternative to Stepping-Stone

This paper re-examines use of the linear programming (LP) formulation to solve the transportation problem (TP). The proposed method is a general-purpose algorithm which uses only one operation, the Gauss Jordan pivoting used in the simplex method. The final tableau can be used for post-optimality analysis of TP. This algorithm appears to be faster than simplex, more general than stepping-stone and simpler than both in solving general TP. A numerical example illustrates the methodology. It is assumed the reader is familiar with simplex terminology.     

Synthesis of oligonucleotides containing thiazole and thiazole N-oxide nucleobases

[reaction: see text] The thiazole C-nucleoside analogue was synthesized by the Hantzsch cyclization method to form the thiazole ring and was then converted to the thiazole N-oxide C-nucleoside analogue by peracid oxidation of the heterocycle nitrogen. Incorporation of the thiazole and thiazole N-oxide phosphoramidites into DNA was successful though significant deoxygenation of the N-oxide occurred during DNA assembly. The mechanism proposed for the reduction of the thiazole N-oxide to thiazole involves the formation of an N-oxide phosphite ester.     

Radical of filters in BL‐algebras

In this paper, the notion of the radical of a filter in BL‐algebras is defined and several characterizations of the radical of a filter are given. Also we prove that A/F is an MV‐algebra if and only if D_s(A) ? F. After that we define the notion of semi maximal filter in BL‐algebras and we state and prove some theorems which determine the relationship between this notion and the other types of filters of a BL‐algebra. Moreover, we prove that A/F is a semi simple BL‐algebra if and only if F is a semi maximal filter of A. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

An implementation of Lagrangian decomposition in solving a multi-item production scheduling problem with changeover cost and restrictions

This paper considers a production system where several products are manufactured over several time periods with specified demand levels. The minimal changeover and holding cost problem is formulated as a mixed integer program model. An efficient heuristic method is proposed by decomposing the problem into a pair of network subproblems. Some computational results showing the efficiency of the method are presented for a set of test problems. Finally, extensions to the general problem are discussed.     

A warm-start dual simplex solution algorithm for the minimum flow networks with postoptimality analyses

This paper presents an algorithm for finding the minimum flow in general (s, t) networks with m directed arcs. The minimum flow problem (MFP) arises in many transportation and communication systems. Here, we construct a linear programming (LP) formulation of MFP and develop a simplex-type algorithm to find a minflow. Unlike other simplex-like algorithms, the algorithm developed here starts with an incomplete Basic Variable Set (BVS) initially and then fills-up the BVS completely while pushing toward an optimal vertex. If this results in pushing too far into infeasibility, the next step pulls the solution back to feasibility. Both phases use the Gauss-Jordan pivoting transformation used in the standard simplex and dual simplex algorithms.

The proposed approach has some common features with Dantzig's self-dual simplex algorithm. We have avoided, however, the need for extra variables (slack and surplus) for equality constraints, as well as an artificial constraint for the self-dual algorithm for initial phase and the dual simplex, respectively. The proposed Push phase takes at most 2m − 1 iterations to complete a tree (this augmentation may not be feasible). An infeasible path to the optimal solution contains at most 2m − 1 iterations; therefore in theory, the algorithm needs a sequence of at most 4m − 2 iterations.

Furthermore, the algorithm developed here makes available the full power of LP perturbation analysis and facilitates introducing network structural changes and side constraints also. It can also detect clerical errors in data entry which may make the problem infeasible or unbounded. It is assumed that the reader is familiar with LP terminology.     

Some results in BL ‐algebras

We define the set of double complemented elements in BL‐algebras and state and prove some theorems which determines properties of these sets. We introduce the notion of an almost top element and study the properties of these elements (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Types of Filters in BE-algebras

In this paper, we introduce some types of filters in BE-algebras and state some theorems which determine the relationship between these filters and other filters of a BE-algebra and by some examples we show that these notions are different.     

(α,β)-fuzzy Subalgebras of Q-algebras

In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets,the notion of (α,β)-fuzzy Q-algebras,the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q.Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras.The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined,and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.     

Smarandache n-Structure on CI-Algebras

In this paper, the notions of CI-algebras, Smarandache CI-algebra, Q-Smarandache filters and Q-Smarandache ideals are introduced. We show that a nonempty subset F of a CI-algebra X is a Q-Smarandache filter if and only if ${A(x,y) \subseteq F}$ , which A(x, y) is a Q-Smarandache upper set. Finally, we introduced the concepts of Smarandache BE-algebra, Smarandache dual BCK-algebra and Smarandache n-structure on CI-algebra.