Discuss the transport problem using concepts from quantitative techniques or methods, indicating how you can obtain an optimal transport solution. Use an illustrative example.

The transport problem continually exists as a challenge for most business organizations around the world. In particular, this is a primary issue in the shipment and/or transit of products from different industries to specific destinations at minimal costs while simultaneously aiming to meet the limits of demand and supply. The transport problem is a linear programming model that increasingly uses both constraint and linear objective functions to develop strategic transportation solutions with the least operational costs.  

Transportation problems primarily aim to foster subsequent minimization of cost functions over a trajectory of shipping products from the supplier to a destination. Ideally, the cost function primarily denotes the expense incurred by the logistics provider in transporting a particular amount of commodities from a given supplier to a specified destination as determined in large part by customer demand. The cost of any given shipment increasingly relies on the interplay of a variety of critical factors. These factors include, amongst others, the itinerary of the shipment, the distance between the source and destination of the commodities, speed of transportation, and the number of units being transported in the shipment. Be that as it may, the main concern of transportation problems lies in determining minimal transit costs without compromising the relative capacities of demand and supply in due process.

Transportation problem occurs in one of two ways namely balanced and unbalanced forms. The former depicts the presence of equal supply and demand capacities. Most transportation problems manifest in this form as initial production units account for the demand capacities and inventory. The latter, however, denotes the presence of unequal capacities of either demand or supply. The latter form arises from an extreme rise or decline in demand.

Illustrative example with a solution

Suppose there is a successful multinational automobile supplier firm known as J&J. The present firm has its production operations set up in numerous countries and therefore gets to supply countless other automobile developers the world over. For example, suppose the firm has three plants in Malaysia located at strategic areas A, B, and C. The relative capacities of the plants mentioned above are 600, 200, 350, respectively, on a daily basis. The plant provides supplies to four clients, namely M, N, O, and P. The respective demands of said clients are 550, 200, 400, and 300 on a daily basis. The relative distance between each source and destination, issued in Km, and transport cost per unit Km are illustrated in the following table.

Solution

Attainment of strategic solutions to transportation problems is best done in steps. These steps include creating a transportation matrix, defining the objective function, and solving using the Least Possible method in Excel.

The transportation matrix above offers critical insights into the maximum number of anticipated shipments from the source to the destination.

The objective function is the sum product of the decision variables (highlighted in red) and cost per unit km. Total shipped denotes the sum of columns M, N, O, and P for relative rows. Total Demand is the sum of rows A, B, and C for relative rows.

The total cost is 22,000.

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