Dynamic Inventory Management Model for Equipment Replacement with Probabilistic Distribution of Failures

Abstract

The article deals with the issues of inventory management modeling of components to ensure the prompt replacement of deep-water pump installations for the oilfield industry in case of equipment failure. The review of literary sources on the subject of the study and the problem statement is given. The rationale for choosing a mathematical model for problem solution is given. The task of dynamic inventory management is to provide the necessary stock with minimal temporary losses from forced downtime at minimal component storage and supply cost for repair or replacement. The planning horizon is divided into several time periods where optimal amount of inventory is to be ensured. It is indicated that when planning stocks in the case of a large number of pieces of equipment operating under different conditions, it is advisable to use a probabilistic approach. An event distribution function is set for probabilistic flow of equipment shutdown. The problem is solved for each segment defining the margin value by means of the Wilson model for deterministic flow of events. The results of simulation modeling on the shutdowns of electric drive centrifugal pump installations at the wells of the Vyngapurovskoye field are presented. A histogram of equipment shutdown frequencies for various time intervals is given. An exponential best approximation function is constructed to approximate the number of stops from installation time to equipment stop, the function coefficients and the standard approximation error are calculated. The characteristic curve of the relative proportion of the operating equipment requiring replacement, as well as the planned number of installations supplied for equipment replacement, with time is given. The dynamics of safety margin changes, which ensures the guaranteed replacement of failed equipment on time with respect to time, is presented.