# Steel beam assortment problem

### From Glossary

A steel corporation manufactures structured beams of a standard length, but a variety of strengths. There is a known demand of each type of strength, but a stronger one may fulfill demand (or part thereof) for another beam (but not conversely). The manufacture of each type of steel beam involves a fixed charge for its setup. In addition, there is a shipping cost proportional to the difference in the demanded strength and the actual strength, and proportional to the quantity shipped.

Let = number of varieties of strengths = demand for beam of strength (where ) amount of beams of strength manufactured manufacturing cost of units of beam of strength (incl. fixed charge) total excess of beams of strength before fulfilling demand shipping cost

Although does not index time, the mathematical program for this problem is the same form as the production scheduling problem, using the inventory balance equations to relate and . This is valid because implies can be used to fulfill demand (Also, note that here is not a "holding cost".)