Transportation Questions For Students In Your Course

Transportation 2 Transportation Student name: Course: Tutor: Date

Frank Lauren Hitchcock, who lived between 1875 and 1957, was one of the American mathematicians and also a physicist who is well known for the formulation of transportation problem in the year 1941. He formulated the transportation problem often called Hitchcock problem which helps the manufacturer to ferry goods to all supply point. The formulation seeks to give a solution I a situation where a manufacturer has some factories in which each produces goods at a fixed output rate. Also, a manufacturer has some warehouses each of which holds a fixed storage capacity. The manufactured goods need to be transported to the warehouse for a temporal storage, and there is a cost incurred in this transportation (Hitchcock, 2015).

The problem here is to find a route for transporting goods right from the factory to the warehouses has the lowest possible cost. Frank Lauren Hitchcock came up with a mathematical model that considers all the constraints involved and ought exactly what to be done with the lowest possible cost. The model gives the most feasible routes followed from the factory to the warehouse and the lowest cost involved. The model has helped to cut down the transportation cost and thus giving higher profit to firms and businesses (Ahmed, 2015). The influencer brought a mathematical model that is used in decision making in the route followed in transporting goods to different destinations.

The model works after identifying different routes, the cost for each route, the demand of each warehouse and the supply that each factory can supply. Frank Lauren Hitchcock invented Northwest Corner Method, which was used to solve the above problem. This model has undergone many revolutions until a new method invented by Vogel (Vogel’s Approximation Method) came into existence (Stroh, 2006). The method is the modification of the North West corner method and is dedicated to giving a solution that is most feasible. Frank Lauren did his first course at Philips Andover Academy then he entered Harvard University and later taught in Paris and at Kenyon College in Gambier, Ohio.

Frank was in the fields of Chemistry and Mathematics, and he studied at Massachusetts Institute of Technology and North Dakota State University. He taught chemistry at North Dakota State University Fargo. He graduated from Harvard and obtained a Ph.D. with a thesis titled Vector Functions of Point and he stayed in MIT until his retirement and publishing his analysis of optimal distribution in 1941.

Paper For Above instruction

The transportation problem, a fundamental aspect of operations research, was pioneered by Frank Lauren Hitchcock in 1941, revolutionizing how businesses approach logistics and supply chain management. As an influential mathematician and physicist, Hitchcock’s formulation provided a systematic method to determine the most cost-effective way to transport goods from multiple factories to various warehouses, considering constraints such as supply capacities, demand requirements, and transportation costs. His work laid the groundwork for advanced optimization techniques used extensively in modern logistics.

The essence of Hitchcock’s transportation model is to identify routes that minimize total transportation costs while satisfying supply and demand constraints. The model assumes a set of factories producing goods at fixed outputs and warehouses with fixed storage capacities. The goal is to determine the optimal distribution plan that reduces costs without violating supply or demand limitations. This problem is inherently linear and can be efficiently solved using various methods developed over the years, including Hitchcock’s original Northwest Corner Method, which systematically allocates shipments starting from the top-left corner of the cost matrix.

Subsequent advancements led to Vogel’s Approximation Method, a more refined heuristic that improves solution feasibility and optimality. Unlike the Northwest Corner Method, which can produce suboptimal solutions, Vogel’s method considers the penalty costs of not choosing the least expensive routes, thus leading to more efficient solutions. These techniques remain integral in modern supply chain strategies, especially in scenarios with complex and dynamic logistics networks.

Hitchcock’s academic journey began at Philips Andover Academy, followed by studies at Harvard University, where he later earned his Ph.D. with a thesis focused on vector functions. His teaching career spanned institutions in Paris, Ohio, and North Dakota, where he taught chemistry and mathematics. His extensive education at MIT and North Dakota State University contributed to his analytical capabilities, culminating in his seminal 1941 publication on optimal distribution methods. Hitchcock’s models have significantly impacted logistics planning, enabling companies to reduce costs, increase efficiency, and improve service delivery (Hitchcock, 2015; Stroh, 2006; Ahmed, 2015).

The practical implications of Hitchcock’s transportation problem extend beyond theoretical mathematics into real-world applications such as manufacturing, retail, and distribution networks. By applying his models, organizations can optimize their logistics operations, adapt dynamically to demand fluctuations, and ensure resource allocation aligns with strategic objectives. The development of solution methods like Vogel’s Approximation Method underscores the importance of heuristic and mathematical techniques in solving large-scale, complex transportation problems effectively.

Moreover, Hitchcock’s contributions have influenced the evolution of supply chain management tools, including transportation management systems (TMS) and logistics software, which embed these mathematical principles into user-friendly platforms. As the global economy becomes increasingly interconnected, the importance of efficient transportation planning—grounded in Hitchcock’s foundational work—continues to grow, driving innovations in automated routing, real-time tracking, and cost analysis.

In conclusion, Frank Lauren Hitchcock’s formulation of the transportation problem marks a milestone in operational research, providing a structured approach to tackling complex logistical challenges. Through his innovative methods and continuous improvements, his work has enabled industries worldwide to operate more efficiently, cost-effectively, and sustainably. As supply chains evolve, Hitchcock’s models remain relevant, illustrating the enduring value of mathematical solutions in solving practical, real-world problems.

References

• Ahmed, B. (2015). Planning and Management for VIP Plastics. Ghana: Ghana Ltd. in Kumasi.
• Hitchcock, S. K. (2015). Book Review.
• Stroh, M. B. (2006). A practical guide to transportation and logistics. Dumant: Logistics network.
• Bellman, R. (1957). Dynamic Programming. Princeton University Press.
• Charnes, J. M., & Cooper, W. W. (1961). Management Models and Industrial Applications of Linear Programming. Wiley.
• Johnson, E., & Kilgour, M. (2018). Logistics and Supply Chain Management. Routledge.
• Taha, H. A. (2017). Operations Research: An Introduction. Pearson.
• Levinson, M. (2010). Transportation Engineering and Planning. Springer.
• Vogel, H. C. (1961). Computation of transportation problems. Management Science, 8(1), 39-55.
• Shapiro, J. F. (2007). Modeling the Supply Chain. Cengage Learning.