Jacobs Manufacturing produces a popular custom accessory for pick-up trucks at plants in Huntington, WV and Bakersfield, CA, and ships them to distributors in Dallas, Texas; Chicago, Illinois; Denver, Colorado; and Atlanta, Georgia. The plants in Huntington, and Bakersfield have, respectively, the capacity to produce 3,000 and 4,000 units per month. For the month of October, costs of shipping a carton of 10 units from each plant to each distributor are summarized in the following table:
Shipping Cost per Container
Dallas Chicago Denver Atlanta
Huntington $19 $15 $14 $12
Bakersfield $16 $18 $11 $13
Each distributor has ordered 1,500 units of Jacobs' product for October and 2,000 units for November.
In any month, Jacobs can send each distributor up to 500 units more than they have ordered if Jacobs provides a $2 per unit discount on the excess (which the distributor must hold in inventory from 1 month to the next).
Given that November demand exceeds production capacity for the same month, it is imperative that additional units get produced and shipped in October. How can you modify your formulation to determine the least costly production and transportation plan for October and November simultaneously? (It might help to revisit your drawn network and add nodes and arcs as necessary.)
Sample Solution