Optimal replenishment policy for deteriorating and non-deteriorating items

Abstract

The purpose of the paper is to present a model allowing the retailer to determine the optimal price of three kinds of items in a situation where the supplier provides the retailer with an interest-free loan for a contractually agreed period. The scientific aim is to verify whether an optimization problem is solvable, and determine the maximum length of the interval over which the goods can be sold with a profit in a situation where the model features two kinds of deteriorating items and one non deteriorating item. The economic theory is explained in the introductory section and serves as a basis for the drawing up of the model. Methods of analysis, synthesis, dynamic modeling and differential calculus of multivariate functions are also used. The situation where the dealer sells all his goods in time and the situation where this period is not observed are analyzed. Thanks to the exact expression of the model it is possible to assess the effect of any changes in external factors. Authors’ findings are that the used variables form compact set and analysed function is continues on this space, we can use Weistrass Theorem for additional calculation with success. Thanks to the exact expression of the model it is possible to assess the effect of any changes in external factors. The model proposed in the paper may be expanded in the future. One possibility is to consider a generalization of the model allowing for shortage of items, quantity discounts, inflation, etc.The purpose of the paper is to present a model allowing the retailer to determine the optimal price of three kinds of items in a situation where the supplier provides the retailer with an interest-free loan for a contractually agreed period. The scientific aim is to verify whether an optimization problem is solvable, and determine the maximum length of the interval over which the goods can be sold with a profit in a situation where the model features two kinds of deteriorating items and one non deteriorating item. The economic theory is explained in the introductory section and serves as a basis for the drawing up of the model. Methods of analysis, synthesis, dynamic modeling and differential calculus of multivariate functions are also used. The situation where the dealer sells all his goods in time and the situation where this period is not observed are analyzed. Thanks to the exact expression of the model it is possible to assess the effect of any changes in external factors. Authors’ findings are that the used variables form compact set and analysed function is continues on this space, we can use Weistrass Theorem for additional calculation with success. Thanks to the exact expression of the model it is possible to assess the effect of any changes in external factors. The model proposed in the paper may be expanded in the future. One possibility is to consider a generalization of the model allowing for shortage of items, quantity discounts, inflation, etc.