The production/distribution model given in the text [formulation (8.70)– (8.75)] seems to assume that all shipments must go through a warehouse (as shown in Figure 8.9). (a) Can the formulation given...

The production/distribution model given in the text [formulation (8.70)– (8.75)] seems to assume that all shipments must go through a warehouse (as shown in Figure 8.9).

(a) Can the formulation given in the text allow for direct plant-to-market shipments? If so, how? If not, modify the formulation to allow for this possibility, clearly defining any new notation that you use.

(b) Direct shipping from a plant to a market may seem to always dominate the more indirect method of shipping through a warehouse in terms of unit costs. Briefly discuss at least three reasons why this might not be so and why, even if it is so, we might want to use warehouses.