The Transportation Model (TM) in the application of Linear Programming (LP) is very useful in optimal distribution of goods. This paper focuses on finding Initial Basic Feasible Solutions (IBFS) to TMs hence, proposing a Demand-Based Allocation Method (DBAM) to solve the problem. This unprecedented proposal goes in contrast to the Cost-Based Resource Allocations (CBRA) associated with existing methods (including North-west Corner Rule, Least Cost Method and Vogel’s Approximation Method) which make cost cell (i.e. decision variable) selections before choosing demand and supply constraints. The proposed ‘DBAM’ on page 4 is implemented in MATLAB and has the ability to solve large-scale transportation problems to meet industrial needs. A sample of five (5) examples are presented to evaluate efficiency of the method. Initial Basic Feasible Solutions drawn from the study (according to DBAM) represent the optimal with higher accuracy, in comparison to the existing methods. Results from the study qualify the DBAM as one of the best methods to solve industrial transportation problems.

The Transportation Problem (TP) is a mathematical optimization technique which regulates the flow of items along routes by adopting an optimum guiding principle to the total shipping cost. However, instances including road hazards, traffic regulations, road construction and unexpected floods sometimes arise in transportation to ban shipments via certain routes. In formulating the TPs, potential prohibited routes are assigned a large penalty cost, M, to prevent their presence in the model solution. The arbitrary usage of the big M as a remedy for this interdiction does not go well with a good solution. In this paper, a two-phase method is proposed to solve a TP with prohibited routes. The first phase is formulated as an All-Pairs Least Cost Problem (APLCP) which assigns respectively a non-discretionary penalty cost M*ij <= M to each of n prohibited routes present using the Floyd¢s method. At phase two, the new penalty values are substituted into the original problem respectively and the resulting model is solved using the transportation algorithm. The results show that, setting this modified penalty cost ( M*) logically presents a good solution. Therefore, the discretionary usage of the M <= ∞ is not a guarantee for good model solutions. The modified cost M*<= M so attained in the sample model, is relatively less than the Big M ( <= ∞) and gives a good solution which makes the method reliable.