Simultaneous optimization of price and quantity at the example of production program planning in dairies

Due to a separate dealing with decisions about production prices, the effects of the classical production program planning for dairies based on linear optimization are limited. A simultaneous planning of production prices and production quantities for a dairy results in a programming problem with a quadratic objective function with accordingly limited opportunities for its numeric treatment as well as in difficulties to globally re-present the price-demand function. The local development of the quadratic objective function as regards the optimum of the classical programming problem allows to iteratively eliminate the square problem by a sequence of linear problems for which the corresponding price-demand functions have only to be displayed on a local basis. The computation example demonstrates that, in comparison with the classical method, the margin per kg milk can be improved by more than 1.5 Pf.. The additional input compared with the single quantity optimization is reduced, due to fully automized data treatment, to the detection of price elasticities. The method can also be used for sectoral and regional planning.