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.

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.

Maximum Flow Problem (MFP) discusses the maximum amount of flow that can be sent from the source to sink. Edmonds-Karp algorithm is the modified version of Ford-Fulkerson algorithm to solve the MFP. This paper presents some modifications of Edmonds-Karp algorithm for solving MFP. Solution of MFP has also been illustrated by using the proposed algorithm to justify the usefulness of proposed method.

The ultimate goal of the decision maker (DM) is to take right decisions to optimize the profit or loss of the organization when the parameters of the transportation problem are ambiguous because of some uncontrollable effects. In this paper, mathematical models are proposed using fuzzy non-linear membership functions and the inverse uncertain normal distribution has been used to eliminate the uncertainty in the parameters which will help the DM to find a compromise solution of the uncertain multi-objective transportation problem (UMOTP) and to achieve the desired goals for a chosen level of confidence for the uncertain parameters. The compromise solutions of the uncertain multi-objective transportation problem are presented to obtain the DM satisfaction if the problem becomes achievable for this preferred confidence level of the parameters. Numerical illustration is given where Linear Programming Problems (LPPs) are resolved with LINGO and the graphs are designed with the help of MATLAB 18.00. J. Bangladesh Acad. Sci. 46(1); 101-115: June 2022

This paper considers a model regarding the products with finite life which allows defective items in reproduction and causes a small amount of decay. The market demand is assumed to be level dependent linear type. The model has also considered the constant production rate which stops after a desired level of inventories and that is the highest level of it. Due to the market demand, defective item and product's decay, the inventory reduces to the zero level where again the production cycle starts. With a numerical search procedure, the proof of the proposed model has been shown. The objective of the proposed model is to find out the total optimum inventory cost, optimum ordering cost and optimum ordering cycle.