Cost optimization, reliability, and MTTF analysis for failed excavators in hydraulic repair center using queueing theory

Abstract

In the present study, we utilize the application of queues at construction sites where excavators are used extensively. Excavators are prone to failures requiring timely repairs and maintenance. We establish a hydraulic repair center (HRC) to repair and maintain these failed excavators. The HRC is equipped with a dedicated hydraulic hose crimper (HHC) machine, which acts as the server providing repairs to the arriving failed excavators, referred to as customers. Two types of excavators are considered: crawler excavator (CE) and mini excavator (ME), with ME being given priority in repair jobs over CE. To address realistic situations, various queueing characteristics are incorporated, including a non-preemptive priority rule, a retrial orbit, etc. First, we develop a mathematical model by considering the arrival of excavators at the HRC following a Poisson process, with repair times adhering to exponential distributions. We construct the Markov model by formulating time-dependent differential-difference equations for each system state. These equations are then solved using a matrix method based on spectral theory to develop the corresponding probability distributions. Second, we establish several expressions of queueing and reliability indices. Third, a nonlinear cost function is formulated, and optimized using particle swarm optimization (PSO) algorithm and the bat algorithm (BA).