Abstract
An algorithm is proposed for solving the price optimization problem using inverse calculations. The algorithm includes two stages: solving the problem of unconditional optimization and solving the inverse problem using inverse calculations while minimizing changes in the arguments of the function. In this case, the solution of the inverse problem can be performed repeatedly within a given number of iterations to sequentially approach the set value of the constraint, and to determine the increment of the arguments, the values of the elements of the gradient/anti-gradient vector of the constraint function are used. To take into account the influence of the arguments on the change of the objective function, its second partial derivatives are used. Five options of the price optimization problem are considered, which nonlinear programming tasks with one restriction are. The revenue of the enterprise, the deviation of demand from the volume of production, the deviation of the sought price from its current value are considered as the objective function. It is shown that the solutions obtained in this way are consistent with the result of using classical methods (Lagrange multipliers, penalties), and the results are also compared with solving problems using the MathCad mathematical package. The advantage of the method is a simpler computer implementation, the ability to obtain a solution in fewer iterations compared to known methods. The method can also be used to solve other problems of the presented type with the following requirements for the objective function and restrictions:1) partial derivatives of the objective function of the first order – linear one-dimensional functions;2) the restriction has the form of equality;3) the constraint is linear or the constraint is quadratic, and the partial derivatives of the first order of the constraint function are one-dimensional linear functions.The article may be useful for specialists making decisions in the field of pricing policies of organizations, as well as the development of optimization models of economic facilities and decision support systems
Highlights
The main aim of the organization’s pricing policy is improvement of the financial results of its activities: maximizing revenue and profits, ensuring that sales volumes match planned values, etc
At the same time, forecasting models can take into account the interchangeability of products [9], competition in the market [10], and the limited shelf space of the store [2]
An algorithm is proposed for solving the problem of price optimization, which is a quadratic programming problem with one restriction
Summary
The main aim of the organization’s pricing policy is improvement of the financial results of its activities: maximizing revenue and profits, ensuring that sales volumes match planned values, etc. It becomes necessary to analyze factors such as consumer demand and its dependence on price, interchangeability and complementarity of goods, the number of competitors, limited resources for the production and delivery of products. One of the main factors determining price formation is customer demand. To predict its value depending on the price, models are built on the basis of statistical data. Both the volume of demand and the probability of purchase can be considered as the predicted value. At the same time, forecasting models can take into account the interchangeability of products [9], competition in the market [10], and the limited shelf space of the store [2]
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