Fixed-Charge Optimization

Generic Situation:

A very difficult decision that has to be made by a production line manager is determining fixed cost. A fixed cost is a new cost that will result if a particular action is taken to fulfill a need. For instance, the setup cost required to prepare a machine or production line to produce a different kind of product.

Example:

Gannon & CO. produces three products that must all undergo different degrees of machining, grinding, and assembly summarized below:

OperationProduct-1Product-2Product-3Total Hours Available
Machining236600
Grinding634300
Assembly5 62400
HOURS REQUIRED TO CREATE FINISHED PRODUCT

Tom Gannon's bean counters have determined that each unit of Product 1 will contribute a $48 profit, each unit of Product 2 $55, and Product 3 $50. However the setup costs for these three products are: $1,000 for Product 1, $800 for Product 2, and $900 for Product 3. Marketing is positive it can sell all that are made so Tom must determine the most profitable mix of products to produce.

Profit Maximizing Solution:

The optimal production schedule is to produce 0 units of Product 1, 56 units of Product 2, and 32 units of Product 3. No other production schedule will produce a higher profit for Gannon & CO.