Suppose availability and purchase costs for V8 short blocks

Suppose availability and purchase costs for V8 short blocks at Juarez and New Orleans are the same as in problem #2 (without tariffs). However, suppose that HP does not pay shipping from Juarez or New Orleans. Instead, Texas HP purchases the short blocks from their suppliers (who pay all shipping costs) and then Texas HP converts them into high performance “long blocks” (a nearly functional engine) at their Texas facilities in Dallas, Austin, and Houston. After that, Texas HP incurs the costs of shipping the long blocks to three high performance automakers, who convert the long blocks into finished, drop-in ready “crate engines” for specific types of custom autos. The costs of converting short blocks into long blocks at each of the Texas facilities as well as the costs of shipping long blocks to the three automakers are given in the table below.

Production Costs

Shipping Costs (per long block)

Facility

(per long block)

Automaker 1

Automaker 2

Automaker 3

Dallas

$2900

$200

$200

$175

Austin

$3100

$300

$250

$200

Houston

$2700

$250

$200

$150

Each long block facility in Texas has a 6000 unit production limit per month. This month, automaker 1 needs 5500 long blocks, automaker 2 needs 4000 long blocks, and automaker 3 needs 5000 long blocks.

A. Formulate the (new) Texas HP problem as a transshipment problem with bounds at the transshipment locations. Make sure to include all purchasing, shipping, and production costs in your formulation. Assume no tariffs on Juarez short blocks. Use origin destination labelling for your decision variables. (You may want to diagram the network to help you formulate the problem.)

B. Solve your transshipment formulation in Excel. What is your optimal Purchasing/Production/Shipping plan as well as the optimal cost of your plan?