APPLICATION OF LINEAR PROGRAMMING TO TRANSPORT AND SUPPLY CHAIN PROBLEM
Abstract
This study applied linear programming techniques to optimize the distribution of rice from selected warehouses in Nigeria to the affected cities. The objective was to minimize total transportation cost while satisfying both supply and demand constraints. Data were collected from three warehouses located in Lagos, Ibadan, and Benin, with demand points at Port Harcourt, Enugu, Abuja, and Kano. A cost matrix was developed, and the problem was formulated as a transportation model. Both manual approaches such as the least cost method and MODI method, and computational tools such as Microsoft Excel Solver were used to obtain optimal allocations. The results showed a minimum transportation cost of ₦61,500 achieved by allocating 40 units from Lagos to Port Harcourt, 30 units from Lagos to Kano, 60 units from Ibadan to Abuja, and 50 units from Benin to Enugu. Graphical visualizations, including heatmaps, network flow diagrams, and stacked bar charts, were employed to illustrate the feasible solution. Simplified two-variable examples were also provided to demonstrate the concept of feasible regions and optimal points in linear programming. The findings confirm that linear programming offers a reliable decision-support tool for logistics and distribution management, enabling cost reduction while ensuring timely satisfaction of demand. The study recommends broader adoption of optimization models by logistics firms and policymakers to enhance efficiency in Nigeria’s agricultural and industrial supply chains.
Chapter One
Linear programming (LP) can be defined as a mathematical technique for determining the best allocation of a firm’s limited resources to achieve optimum goal. It is also a mathematical technique used in Operations Research (OR) or Management Sciences to solve specific types of problems such as allocation, transportation and assignment problems that permits a choice or choices between alternative courses of action (Yahya, 2004). Companies are often faced many challenges in moving or transporting their goods from sources to their various destinations due to the availability of limited resources. These resources are capital, manpower and the distances from the sources to the destinations. However, Linear Programming being the most prominent Operation Research technique, it is designed for models with linear objective and constraint functions. A Linear Programming model can be designed and solved to determine the best course of action as in a product mix subject to the available constraints. Linear programming is a term that covers a whole range of mathematical techniques that is aimed at optimizing performance in terms of combinations of resources (Lucey, 1996).One of the most widely used optimization methods in logistics is linear programming (LP), a mathematical technique designed to allocate limited resources efficiently under given constraints. LP provides a structured approach to decision-making in logistics by optimizing resource allocation, minimizing costs, and improving overall supply chain performance. Mathematical modeling and optimization methods have been widely adopted to enhance decision-making in logistics. Among these methods, linear programming (LP) has emerged as a powerful and widely used technique for solving transportation and supply chain problems. LP provides a structured approach to decision-making, enabling companies to allocate resources efficiently, minimize operational costs, and improve service levels, (Taha,2017)
Project Details
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