A new heuristic method of finding the initial basic feasible solution to solve the transportation problem

Abstract

Many real applications use the transportation problems for finding the optimal solution for product shipment from supply to demand. The transportation problem (TP) is related to delivering some products from the supply to the demand. The initial basic feasible solution (IBFS) is a significant step to achieve the minimal total cost (optimal solution) of the transportation problem. However, the existing methods of IBFS do not always provide a good feasible solution which can reduce the number of iterations to find the optimal solution. Therefore, it is still challenging to develop a better method of IBFS. In this paper, a new method to obtain the IBFS of transportation problem called Bilqis Chastine Erma method (BCE) was proposed. The thirty-five numerical examples were used to evaluate the performance of the proposed method. It was compared to other IBFS methods, namely: Vogel’s Approximation Method (VAM), Total Differences Method 1 (TDM1), Total opportunity cost matrix – Minimal total (TOCM-MT), and Juman & Hoque Method (JHM). The experiment results indicate that BCE obtained lower total minimal cost than VAM, TDM1, TOCM-MT, and JHM and reached the fastest solving time. It reached its optimal solution for thirty-one of thirty-five numerical examples (88.57%).

Keywords

• Transportation problem
• Initial basic feasible solution
• Optimal solution
• Minimal total cost
• Vogel’s approximation method