A New Strategy for Solving the Initial Basic Feasible Solution of the Transportation Problem Using Exponential Distribution and a New Penalty Model

One of the key concepts in operations research (OR) is the transportation problem (TP). The transportation problem involves distributing products from several sources to different destinations while minimizing shipping expenses. To achieve minimum transportation costs, the transportation problem is examined in two phases. An initial basic feasible solution (IBFS) is the first phase for achieving the lowest price, with the help of IBFS, one can calculate the optimal solution derived as the second phase. The literature review indicates that the authors developed a novel algorithm for the IBFS, incorporating several mathematical tools and some new models yet possessing certain limitations. To overcome this, we proposed a new algorithm for the IBFS, a collaborating statistical tool and a new penalty model. An exponential distribution illustrates the probability of cost or time required to reach each source to the destination. Furthermore, a novel penalty model is formulated to distribute essential supply to requisite demand. A modified distribution method (MODI) is employed to calculate the optimal solution. Eleven numerical examples were illustrated to develop the proposed algorithm. The results are compared with classical Vogel’s approximation method (VAM) and ten previously published papers. In addition, three randomly generated problems were performed. Finally, with the reduction in total transportation cost over Vogel’s approximation method, the demand-based allocation method (DBAM) and the existing ten published studies. Our suggested method of getting 10 optimal solutions in IBFS recorded a 71.42% accuracy.