Andrei Sleptchenko

Effects of finite repair capacity in multi-echelon, multi-indenture service part supply systems

In this paper, we consider multi-echelon, multi-indenture supply systems for repairable service parts with finite repair capacity. We show that the commonly used assumption of infinite capacity may seriously affect system performance and stock allocation decisions if the repair shop utilisation is relatively high. Both for the case of item-dedicated and shared repair shops, we modify the well-known VARI-METRIC method to allocate service part stocks in the network. The repair shops are modelled by (single or multi-class) multi-server queuing systems. We validate our procedure by comparison to results from discrete event simulation. This comparison shows that the accuracy of the technique presented in this article is on average more than five times as close to simulated values as the classical VARI-METRIC technique.

Using repair priorities to reduce stock investment in spare part networks

In this paper, we examine the impact of repair priorities in spare part networks. Several heuristics for assigning priorities to items as well as optimising stock levels are developed, extending the well-known VARI-METRIC method. We model repair shops by multi-class, multi-server priority queues. A proper priority setting may lead to a significant reduction in the inventory investment required to attain a target system availability (usually 10–20%). The saving opportunities are particularly high if the utilisation of the repair shops is high and if the item types sharing the same repair shop have clearly different characteristics (price, repair time). For example, we find an investment reduction of 73% for a system with single server repair shops with an utilisation of 0.90 that handle five different item types.

Trade-off between inventory and repair capacity in spare part networks

The availability of repairable technical systems depends on the availability of (repairable) spare parts, to be influenced by (1) inventory levels and (2) repair capacity. In this paper, we present a procedure for simultaneous optimisation of these two factors. Our method is based on a modification of the well-known VARI-METRIC procedure for determining near-optimal spare part inventory levels and results for multi-class, multi-server queuing systems representing repair shops. The modification is required to avoid non-convexity problems in the optimisation procedure. To include part-time and overtime working, we allow for a non-integer repair capacity. To this end, we develop a simple approximation for queuing systems with a non-integer number of servers. Our computational experiments show that the near-optimal utilisation rate of the repair servers is usually high (0.80–0.98) and depends mainly on the relative price of the servers compared with inventory items. Further, the size of the repair shop (the minimal number of servers required for a stable system) plays its part. We also show that our optimisation procedure is robust for the choice of the step size for the server capacity.

An Exact Solution for the State Probabilities of the Multi-Class, Multi-Server Queue with Preemptive Priorities

We consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple customer types, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an exact method to estimate the steady state probabilities. Because we need iterations to calculate the steady state probabilities, the only error arises from choosing a finite number of matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the moments of the number of customers of a certain type in the system en the expected postponement time for each customer class. We illustrate our method with some numerical examples. Numerical results show that in most cases we need only a moderate number of matrix iterations (∼20) to obtain an error less than 1% when estimating key performance characteristics.

Reducing costs of spare parts supply systems via static priorities

We study static repair priorities in a system consisting of one repair shop and one stockpoint, where spare parts of multiple, critical repairables are kept on stock to serve an installed base of technical systems. Demands for ready-for-use parts occur according to Poisson processes, and are accompanied by returns of failed parts. The demands are met from stock if possible, and otherwise they are backordered and fulfilled as soon as a ready-for-use part becomes available. Returned failed parts are immediately sent into repair. The repairables are assigned to static priority classes. The repair shop is modeled as a single-server queue, where the failed parts are served according to these priority classes. We show that under a given assignment of repairables to priority classes, optimal spare parts stock levels follow from Newsvendor equations. Next, we develop fast and effective heuristics for the assignment of repairables to priority classes. Subsequently, we compare the performance of the system under these static priorities to the case with a First-Come First-Served (FCFS) service discipline. We show that in many cases static priorities reduce total inventory holding and backordering costs by more than 40%. Finally, we analyse the effect of the number of priority classes. We show that 2 priority classes suffice to obtain 90% of the maximal savings via static priorities.

On Markovian Multi-Class, Multi-Server Queueing

Multi-class multi-server queueing problems are a generalisation of the well-known M/M/k queue to arrival processes with clients of N types that require exponentially distributed service with different average service times. In this paper, we give a procedure to construct exact solutions of the stationary state equations using the special structure of these equations. Essential in this procedure is the reduction of a part of the problem to a backward second order difference equation with constant coefficients. It follows that the exact solution can be found by eigenmode decomposition. In general eigenmodes do not have a simple product structure as one might expect intuitively. Further, using the exact solution, all kinds of interesting performance measures can be computed and compared with heuristic approximations (insofar available in the literature). We provide some new approximations based on special multiplicative eigenmodes, including the dominant mode in the heavy traffic limit. We illustrate our methods with numerical results. It turns out that our approximation method is better for higher moments than some other approximations known in the literature. Moreover, we demonstrate that our theory is useful to applications where correlation between items plays a role, such as spare parts management.

Approximations for Markovian multi-class queues with preemptive priorities

We discuss the approximation of performance measures in multi-class M/M/k queues with preemptive priorities for large problem instances (many classes and servers) using class aggregation and server reduction. We compared our approximations to exact and simulation results and found that our approach yields small-to-moderate approximation errors.

Joint optimization of redundancy level and spare part inventories

We consider a “k-out-of-N” system with different standby modes. Each of the N components consists of multiple part types. Upon failure, a component can be repaired within a certain time by switching the failed part by a spare, if available. We develop both an exact and a fast approximate analysis to compute the system availability. Next, we jointly optimize the component redundancy level with the inventories of the various spare parts. We find that our approximations are very accurate and suitable for large systems. We apply our model to a case study at a public organization in Qatar, and find that we can improve the availability-to-cost ratio by reducing the redundancy level and increasing the spare part inventories. In general, high redundancy levels appear to be useful only when components are relatively cheap and part replacement times are high.

Integrated Optimization for Stock Levels and Cross-Training Schemes with Simulation-Based Genetic Algorithm

A spare part supply system for repairable spares in a repair shop is modeled as a set of heterogeneous parallel servers that have the ability to repair only certain types of repairables. The proposed model minimizes the total cost of holding inventory for spare parts, cost for backorder arising from downtime of the system due to the lack of spare parts and the cost of crosstraining for servers. Simulation-based Genetic Algorithm (GA) is proposed to optimize inventory levels and to determine the best skill assignments to servers, i.e., cross-training schemes. When methodologys performance is compared with total enumeration, tight optimality gaps are obtained.

Simulation based particle swarm optimization of cross-training policies in spare parts supply systems

We study a single location supply system for repairable spare parts. The system consists of a multi-server repair shop and inventory with ready-to-use spare parts. When a failed part is received, a new (or as-good-as-new) replacement part is sent back, and the failed part is forwarded to the repairshop. In the case of unavailability of spare parts, failed requests are backordered and fulfilled when a ready-for-use part of the same type is received from the repairshop. The repair shop has several multi-skilled parallel servers (technicians) that are capable of handling certain types of spares. In this paper, we propose a Particle Swarm Optimization heuristic combined with Discrete-Event Simulation for optimizing the cross-training policy (skill assignment scheme) while minimizing the total system cost (consisting of inventory costs, backorder penalty cost, server cost and skill cost).