Functions of several variables analysis applied in inventory management

Abstract

In many cases a retailer is not capable of settling an invoice immediately upon receiving it and is given an option by the supplier to settle the invoice within a definite period. The retailer can sell the goods before the deadline, accumulate revenue and earn interest. If the retailer is not able to meet his obligations within the deadline, he is charged an interest. This paper introduces a newly constructed model which enables a retailer to set an optimal price of goods under permissible delay in payments, and to determine the maximum term of payment. The model is based on the assumption of time-dependent demand and has been developed for non-deteriorating goods. The paper further analyzes a situation in which the retailer sell all the goods in time, and a situation in which the deadline was not met. Theoretical results are demonstrated by an illustrative example. The authors of the paper used methods of analysis and synthesis, and the method of mathematical analysis (differential calculus of multivariable functions, solution of ordinary differential equations).The model suggested in the paper can be expanded in the future. One option is generalization of the model, allowing for the lack of goods, bulk discounts, etc.

Keywords

• inventory management
• EOQ model
• non-deteriorating goods
• local extremes
• multivariable functions