The Application of Functions of Several Variables Analysis in an Optimal Replenishment Policy for Deteriorating Items

摘要

Very often must be taken into account the gradual deterioration of goods in inventory management. This fact is not taken into account in multiple management systems. Traditional inventory models at the same time assume that a retailer pays for the goods the moment they are received. Nowadays, however, it is becoming a common practice that a supplier offers a retailer the option to pay for the goods with a certain delay. If the retailer is not able to meet his obligations within the deadline, he is charges an interest. In this study we introduce a newly constructed suitable model which enables a retailer to set an optimal price of deteriorating goods under permissible delay in payments, and to determine the maximum repayment term. We considered a deterministic inventory model with time-dependent demand, holding costs variable in time where deterioration is directly proportional to the time. The model is based on the assumption of time-dependent demand and has been developed for deteriorating goods. The paper further analyses a situation in which the retailer sell all the goods in time, and a situation in which the deadline was not met. Further assumption is that the inventory is depleted only by demand. The scientific aim is to verify if such an optimizing problem can be solved. Theoretical results are illustrated with numerical example for the model. Results show that the developer model is capable of solving the theoretical problem illustrated by an example. It helps to the retailer to set the selling price and the replenishment interval in order to maximize profit. 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, Taylor series). 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, time value of money, inflation etc.