Thread: Formulating an Integer Programming problem

A manufacturer can sell product 1 at a profit of $2/unit and product 2 at a profit of $5/unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw material are needed to manufacture 1 unit of product 2. A total of 120 units of raw material are available. If any of product 1 is produced, a setup cost of $10 is incurred, and if any of product 2 is produced, a setup cost of $20 is incurred. Formulate an IP to maximize profits. For computational simplicity you can assume that it is allowed to produce fractions of product 1 or product 2 (so the numbers of products do not have to be integers).

Originally Posted by jlt1209

A manufacturer can sell product 1 at a profit of $2/unit and product 2 at a profit of $5/unit. Three units of raw material are needed to manufacture 1 unit of product 1, and 6 units of raw material are needed to manufacture 1 unit of product 2. A total of 120 units of raw material are available. If any of product 1 is produced, a setup cost of $10 is incurred, and if any of product 2 is produced, a setup cost of $20 is incurred. Formulate an IP to maximize profits. For computational simplicity you can assume that it is allowed to produce fractions of product 1 or product 2 (so the numbers of products do not have to be integers).

Let be the number of units of product 1 produced, and be the number of units of product 2.

The objective is the profit:



where is the indicator function which is if its argument is greater than and otherwise (alternativly introduce two 0-1 variables to handle the set up costs).

The nonnegativity constraints are that , and the materials constraint is:



CB