Mathematical Programming Models for Cutting-Stock Problems in the Clothing Industry

The cutting-stock problem in the clothing industry does not conform to the classical representation of such problems. Waste minimization is only a subsidiary objective. The overall objective is to maximize long-run profitability, but operational planning requires limiting consideration to a series of problems covering short planning periods. This requires a more complex objective to incorporate interaction between periods. Production constraints with unique characteristics occur in the laying, cutting and sewing operations. The conventional pattern-design problem is dealt with by use of a commercial computer-aided graphical design system. The question addressed in this paper is how to combine such patterns so as to satisfy the various objectives and constraints. This leads to both integer and quadratic formulations of appropriate mathematical programming models.