Model of the Impact Of Parameters Controlling Replenishment in the BS (Min-Max) Continuous Review System on the Actual Inventory Availibility

Abstract

Background: Due to random changes in demand, inventory management is still despite the development of alternative goods flow management concepts an important issue both in terms of costs of maintenance and replenishment as well as the level of service measured by inventory availability levels. There are a number of replenishment systems to be used in such conditions, but they are most often formed on the basis of two basic ones: a system based on the reorder point and based on periodic inspection. This paper refers to the former system, the BS system (min-max), in which an order is placed after reaching inventory level B (information level, reorder point) for a quantity allowing to reach level S. This system is very often used in business practice. Observations conducted under realistic conditions indicate the need to improve the classical models describing the system. This results, among other things, from the fact that the actual level of available inventory at the start of the replenishment cycle may be significantly lower than level B, resulting in lower than expected levels of customer service. Taking account of this phenomenon through model determination of the cumulative distribution function for the observed difference makes it possible to select the correct parameters to control the replenishment system in question and therefore to achieve the expected economic effects. Methods: The object of the study is to create a mathematical model allowing the determination of the required inventory level B taking into account the difference ∆ between this level and the actual level of inventory at the start of the replenishment cycle. To determine the effect of various factors such as demand distribution parameters in the adopted unit of time and the difference between level S (max) and B (min), a dedicated tool (simulator in EXCEL spreadsheet) for determining the distribution of frequency of value ∆ has been developed. Then a mathematical model allowing the determination of the distribution and its parameters as a function of the difference r = S-B for virtually any distribution of demand has been developed and implemented in a separate EXCEL spreadsheet. Results: It was found that there is the need to take into account the distribution of the difference between the information level B (the reaching or exceeding of which is a signal to place an order) and the actual level of inventory at the start of the replenishment cycle when determining the inventory replenishment control parameters in the BS system. A mathematical model allowing to determine the incidence and distribution of function of value depending on the demand distribution parameters and difference r between the S level (max) and B level (min) has been developed and used for calculations. High compatibility of results obtained from model calculations with the results obtained through simulation imitating real events has been shown. Conclusions: The model described in this paper will allow a more accurate determination of parameters that control the BS system to safeguard the required level of service and conditions relating to the volume of deliveries. Further work is required to develop an effective model solution for a general formula presented in this paper used to calculate the B parameter as a function of the required service level and the S parameter depending on the designated (e.g. economic) average delivery.