Goal programming model for determining the optimal production schedule considering penalties or bonuses dependent on quality

This paper presents a nonlinear integer goal programming model that optimizes a mineral production schedule while considering the penalties and bonuses based on quality variations in the final product. It involves five coal quality goals plus a profit objective in its formulation and uses the weighting method of goal programming for a solution. The goals to be sought involve the sulfur, ash, heat content, moisture content, and ash softening temperature of the blended coal product. The model is linear in its handling of most of these goals but uses a piecewise linear integer formulation for the sulfur and heat content bonus and penalty schedule. The model is applicable to any mineral product blended from several different sources and subject to a varying price dependent on blended product quality or qualities. However, it seems to be most pertinent to optimizing production schedules for coal deliveries to power plants. Accordingly, the model is applied to a hypothetical coal production problem where multiple coal mines are operated to supply a final blended product to a power plant. In this example, the price paid for the coal is assumed to be a function of five of the most important coal qualities. The problem is solved as a direct function of the coal supply contract, thus removing the necessity of determining the weighting coefficients on a subjective basis.