Finding an initial basic feasible solution is the prime requirement to obtain an optimal solution for the transportation problems. In this article, a new approach is proposed to find an initial basic feasible solution for the transportation problems. The method is also illustrated with numerical examples.
Treatment of the labile compound [Re 2 (CO) 8 (MeCN) 2 ] with 2-vinylpyridine in refluxing benzene affords exclusively the new compound [Re 2 (CO) 8 (l-g 1 :g 2 -NC 5 H 4 CH@CH 2 )] (1) in 39% yield in which the l-g 1 :g 2 -vinylpyridine ligand is coordinated to one Re atom through the nitrogen and to the other Re atom via the olefinic double bond. Reaction of [Re 2 (CO) 8 (MeCN) 2 ] with morpholine in refluxing benzene furnishes two compounds, [Re 2 (CO) 9 (g 1 -NC 4 H 9 O)] (2) and [Re 2 (CO) 8 (g 1 -NC 4 H 9 O) 2 ] (3) in 5% and 29% yields, respectively. Reaction of [Re 2 (CO) 8 (MeCN) 2 ] with 1-methylimidazole gives [Re 2 (CO) 8 {g 1 -NC 3 H 3 N(CH 3 )} 2 ] (4) and the mononuclear compound fac-[ReCl(CO) 3 {g 1 -NC 3 H 3 N(CH 3 )} 2 ] (5) in 18% and 26% yields, respectively. In the disubstituted compounds 2 and 4, the heterocyclic ligands occupy equatorial coordination sites. The mononuclear compound 5 consists of three CO groups, two N coordinated g 1 -1-methylimidazole ligands and a terminal Cl ligand. The XRD structures of complexes 1, 3 and 5 are reported.
Reactions of the labile compound [Re 2 (CO) 8 (MeCN) 2 ] with thiazole and 4-methylthiazole in refluxing benzene afforded the new compounds [Re 2 (CO) 7 {l-2,3-g 2 -C 3 H(R)NS}{g 1 -NC 3 H 2 (4-R)S}(l-H)] (1, R = H; 2, R = CH 3 ), [Re 2 (CO) 6 {l-2,3-g 2 -C 3 H(R)NS}{g 1 -NC 3 H 2 (4-R)S} 2 (l-H)] (3, R = H; 4, R = CH 3 ) and fac-[Re(CO) 3 (Cl){g 1 -NC 3 H 2 (4-R)S} 2 ] (5, R = H; 6, R = CH 3 ). Compounds 1 and 2 contain two rhenium atoms, one bridging thiazolide ligand, coordinated through the C(2) and N atoms and a g 1 -thiazole ligand coordinated through the nitrogen atom to the same Re as the thiazolide nitrogen. Compounds 3 and 4 contain a Re 2 (CO) 6 group with one bridging thiazolide ligand coordinated through the C(2) and N atoms and two N-coordinated g 1 -thiazole ligands, each coordinated to one Re atom. A hydride ligand, formed by oxidative-addition of C(2)-H bond of the ligand, bridges Re-Re bond opposite the thiazolide ligand in compounds 1-4. Compound 5 contains a single rhenium atom with three carbonyl ligands, two N-coordinated g 1 -thiazole ligands and a terminal Cl ligand. Treatment of both 1 and 2 with 5 equiv. of thiazole and 4-methylthiazole in the presence of Me 3 NO in refluxing benzene afforded 3 and 4, respectively. Further activation of the coordinated g 1 -thiazole ligands in 1-4 is, however, unsuccessful and results only nonspecific decomposition. The single-crystal XRD structures of 1-5 are reported.
Industries require planning in transporting their products from production centres to the users end with minimal transporting cost to maximize profit. This process is known as Transportation Problem which is used to analyze and minimize transportation cost. This problem is well discussed in operation research for its wide application in various fields, such as scheduling, personnel assignment, product mix problems and many others, so that this problem is really not confined to transportation or distribution only. In the solution procedure of a transportation problem, finding an initial basic feasible solution is the prerequisite to obtain the optimal solution. Again, development is a continuous and endless process to find the best among the bests. The growing complexity of management calls for development of sound methods and techniques for solution of the problems. Considering these factors, this research aims to propose an algorithm "Incessant Allocation Method" to obtain an initial basic feasible solution for the transportation problems. Several numbers of numerical problems are also solved to justify the method. Obtained results show that the proposed algorithm is effective in solving transportation problems.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.