Mathematical Models and Algorithms for Failed Equipment Planning Replacement

Abstract

For the operability of deep well pump units under the conditions of oil and gas field equipment rental, it is necessary to plan the required resources. Failed equipment must be replaced with new one. If it is possible to repair the items, they are sent to repair service points. A review of literary sources on the subject of the study and the problem statement are provided. A large number of equipment application points and real operating conditions introduce great uncertainty into planning the failed equipment replacement. The value of the failure rate is a random variable. A mathematical model to manage the process of failed equipment replacing has been developed. Fuzzy logic methods have been used to take into account the uncertainty. Characteristics of fuzzy failure flow have been determined,based on the available information on failures. To perform computational operations, algorithms for working with fuzzy variables have been developed based on, in general case, asymmetric, and parabolic membership functions. The operations of addition, subtraction, multiplication, division, and exponentiation of fuzzy numbers are determined using interval arithmetic andα-cut method. The amount of equipment stock is determined by a fuzzy number. The use of a hybrid genetic algorithm provided an optimal solution to the optimization problem equipment replacement management. The calculation results are given. When solving the fuzzy optimization problem in comparative operations, the rank of the fuzzy number was calculated. The concept of centroid defuzzification of the fuzzy number is used to determine the rank value. The diagram of the fuzzy number membership function and the diagram of the optimization problem objective function: total costs were constructed. Compared with the optimization problem clear formulation, the total costs in the fuzzy formulation turned out to be higher, also the value of the safety stock was determined .