DETERMINATION OF THE OPTIMAL COMMODITY NOMENCLATURE BY PROFIT AND COST

Abstract

The work proposes a method of definition of commodity classifications (goods
nomenclature) based on the nomenclatural function. The advantage of the proposed method is
the possibility of definition of commodity classifications even when the profit on every single unit
of the nomenclature differs. The basis of the method is the definition of a nomenclature as a
function of the geometric mean of a set of nomenclatures. That makes possible to determine the
gain in the direct proportion to the value of the function of the nomenclature.
The purpose of the article is to outline the methodology for determining the nomenclature
while maintaining the full range of goods. This is impossible with standard optimization using the
arithmetic mean. Since the nomenclature function is a positive value, then, unlike the arithmetic
mean, any item of the nomenclature cannot be zero in the geometric mean. The proposed
technique is an alternative to the classical linear programming problem. The method’s
advantage is the absence of any additional restrictions on the parameters of the optimal
solution. In principle, such restrictions can also be introduced after analyzing the solution. There
are no nonlinear restrictions in the methodology, so the optimal solution can vary proportionally
depending on the required value of profit or cost. We propose to implement the algorithms using
the mathematical modeling program MathCad. Two variants of algorithms are considered:
optimization by cost and by profit. The aim of this work is to create the most simple algorithms.
The algorithms implement the optimization of the range of goods in its full assortment, that is, in
the absence of zero nomenclature values.
Keywords: nomenclature function, cost function, cost incentives, geometric mean,
damping vector of nomenclature, profit of unit of nomenclature, cost of unit of nomenclature.