### American Journal of Mathematical and Computer Modelling

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### The Novel Efficient Method to Solve Balanced and Unbalanced Profit Maximization in Transportation Problems

Organizations must plan how to get their commodities from production centers to consumers' homes with the least amount of transportation expense to maximize profit. The Transportation Problem (TP) approach is used to evaluate and reduce the cost of transportation. There are two types of TPs. Such as cost minimization TP and profit maximization TP. Typically, the transportation technique is employed for minimization but the objective function should be maximized rather than minimized in several categories of TPs. By changing the maximizing problem into the minimization problem, these types of issues may be resolved in literature. By deducting the unit costs from the table's greatest unit cost, maximizing is changed into minimization. The first step in achieving an optimal solution is to find the initial basic feasible solution (IBFS). North-West Conner, Least Cost, and Vogel’s Approximation Methods can be used to find IBFS. The optimal solution can be obtained by using only Modified Distribution (MODI) and Stepping Stone Methods. This study proposes a novel direct method to find an optimal or near-optimal solution to profit maximization TPs. In this proposed method, maximization TP is not needed to convert minimization TP. This method is very easy and it has less implementation. In the end, by solving several illustrative examples, we compare the proposed method’s results with other existing methods.

Cost Minimization, Profit Maximization, Unit Cost, Optimal Solution, Transportation Problem

Oshan Niluminda, Uthpala Ekanayake. (2023). The Novel Efficient Method to Solve Balanced and Unbalanced Profit Maximization in Transportation Problems. American Journal of Mathematical and Computer Modelling, 8(2), 17-24. https://doi.org/10.11648/j.ajmcm.20230802.11