Assignment:
Industrial customers have contracted demands for heat pumps. These units are to be delivered from the warehouse of a central supplier to the companies. The supplier is now attempting to locate the warehouse, so as to minimize the transportation cost of the pumps to its customers. The demand is fairly constant throughout the year. The delivery is per pickup truck, one heat pump at a time, resulting in a linear cost function. Figure shows the supplier’s customers, their double-digit demands, and the single-digit distances between the customers.
A consultant of the supplier had suggested locating the warehouse between the nodes n2 and n3 at a distance of 5.4 from n2. They have based their argument on the large weights of the adjacent nodes n2 and n3 that provide a strong pull to locate the warehouse there.
(a) Without any calculations, do you agree with the consultant’s recommendation?
(b) Find a location on the network that minimizes the total delivery cost. How much more expensive was the consultant’s recommendation?
(c) Ignore now the weights at the nodes, and assume that the same graph were to be used by some planner to locate a vertex 1-center. Where would this center be located?
Provide complete and step by step solution for the question and show calculations and use formulas.