Fixed charge problems with identical fixed charges

The general problem considered by this paper is a special case of the fixed-charge problem. The further condition imposed is that all variables have the same associated fixed-charge. The problem is discussed in the context of a known commercial application, that being the cutting stock problem. The situation considered is that of cutting given numbers of small rectangles from large rectangular stock-plates. In many such situations major aims are to have low stock-plate usage and a low number of setups of the cutting equipment. These represent conflicting objectives capable of being combined by the use of fixed charges upon the setups but this paper presents an alternative approach incorporating direct manipulation of the number of setups involved in the solution. This approach is compared to a solution technique for the general fixed-charge problem.