Determining optimal transportation allocation using linear programming methods.

Abstract

The transportation problem is a subset of the broader linear programming (L.P.) technique developed to assist managers in making decisions. It has been used in real-life applications to minimise total transportation costs by satisfying destination and source requirements. The study aimed to minimise the delivery of items from the plant to the dealer's location by determining the optimal allocation of inventory from suppliers to dealers in the Malaysian cities of Seremban, Johor Bahru, Kuala Lumpur/Selangor and Penang. Meanwhile, the specific objectives of the study were: (i) to formulate transportation problems using the L.P., (ii) to identify a basic feasible solution (BFS), and (iii) to do an optimality analysis. A case study of an operations research problem involving the optimisation of distribution costs and the effective delivery system of inventory by utilising transportation models, namely the North-West Corner Rule (NWCR), Simplex method, and Vogel's Approximation Method (VAM) are presented and discussed. The efficiency and effectiveness of the transportation problem algorithm are determined using the Excel Solver. The excel solution and sensitivity analysis provide information about the optimal distribution strategy for their products. The results indicated that the delivery cost is reduced when the transportation problem algorithm is used. It saved up to RM50,605.21, or 78.91 per cent of the cost, and it can be concluded that the profit margin is higher than with the previous strategies. Among all transportation models, VAM and Simplex methods are considered the best methods since they produce the ideal results, whereas the North-West Corner Rule is considered the simplest method but produces the worst results. In conclusion, this study could assist the distributors in reducing shipping costs and ensuring that the inventory is distributed efficiently.