Gjjan Geert-Jan van Houtum

Maintenance spare parts planning and control : a framework for control and agenda for future research

This paper presents a framework for planning and control of the spare parts supply chain in organisations that use and maintain high-value capital assets. Decisions in the framework are decomposed hierarchically and interfaces are described. We provide relevant literature to aid decision-making and identify open research topics. The framework can be used to increase the efficiency, consistency and sustainability of decisions on how to plan and control a spare parts supply chain. This point is illustrated by applying it in a case study. Applicability of the framework in different environments is also investigated.

Optimal Control of Serial Inventory Systems with Fixed Replenishment Intervals

We consider a single-item, periodic-review, serial inventory/production system, with linear inventory-holding and penalty costs. To facilitate shipment consolidation and capacity planning, we assume that the system has implemented fixed replenishment intervals; each stage is allowed to order only at given equidistant times. Further, for each stage except the most downstream one, the replenishment interval is assumed to be an integer multiple of the replenishment interval of the next downstream stage. This reflects the fact that the further upstream in a supply chain, the higher setup times and costs tend to be, and thus larger batches are desired. Our model with fixed replenishment intervals is a direct generalization of the serial model of Clark and Scarf (1960). For this generalized model, we prove the optimality of base-stock policies, we derive newsboy equations for the optimal base-stock levels, and we describe an efficient exact solution procedure for the case with mixed Erlang demands. Finally, we present extensions to assembly systems and to systems with a modified fill-rate constraint instead of backorder costs.

A condition-based maintenance policy for multi-component systems with a high maintenance setup cost

Condition-based maintenance (CBM) is becoming increasingly important due to the development of advanced sensor and information technology, which facilitates the remote collection of condition data. We propose a new CBM policy for multi-component systems with continuous stochastic deteriorations. To reduce the high setup cost of maintenance, a joint maintenance interval is introduced. With this interval and the control limits of components as decision variables, we develop a model for the minimization of the average long-run maintenance cost rate of the systems. Moreover, a numerical study of a production system consisting of a large number of non-identical components is presented, including a sensitivity analysis. Finally, our policy is compared to a failure-based policy and an age-based policy, in order to evaluate the cost-saving potential.

Resource Pooling and Cost Allocation Among Independent Service Providers

We study a situation where several independent service providers collaborate by complete pooling of their resources and customer streams into a joint service system. These service providers may represent such diverse organizations as hospitals that pool beds or maintenance firms that pool repairmen. We model the service systems as Erlang delay systems M/M/s queues that face a fixed cost rate per server and homogeneous delay costs for waiting customers. We examine rules to fairly allocate the collective costs of the pooled system amongst the participants by applying concepts from cooperative game theory. We consider both the case where players numbers of servers are exogenously given and the scenario where any coalition picks an optimal number of servers. By exploiting new analytical properties of the continuous extension of the classic Erlang delay function, we provide sufficient conditions for the games under consideration to possess a core allocation i.e., an allocation that gives no group of players an incentive to split off and form a separate pool and to admit a population monotonic allocation scheme whereby adding extra players does not make anyone worse off. This is not guaranteed in general, as illustrated via examples.

Joint optimization of condition-based maintenance and production lot-sizing

Due to the development of sensor technologies nowadays, condition-based maintenance (CBM) programs can be established and optimized based on the data collected through condition monitoring. The CBM activities can significantly increase the uptime of a machine. However, they should be conducted in a coordinated way with the production plan to reduce the interruptions. On the other hand, the production lot size should also be optimized by taking the CBM activities into account. Relatively fewer works have been done to investigate the impact of the CBM policy on production lot-sizing and to propose joint optimization models of both the economic manufacturing quantity (EMQ) and CBM policy. In this paper, we evaluate the average long-run cost rate of a degrading manufacturing system using renewal theory. The optimal EMQ and CBM policy can be obtained by minimizing the average long-run cost rate that includes setup cost, inventory holding cost, lost sales cost, predictive maintenance cost and corrective maintenance cost. Unlike previous works on this topic, we allow the use of continuous time and continuous state degradation processes, which broadens the application area of this model. Numerical examples are provided to illustrate the utilization of our model.

Joint queue length distribution of multi-class, single-server queues with preemptive priorities

In this paper we analyze an M/M/1 queueing system with an arbitrary number of customer classes, with class-dependent exponential service rates and preemptive priorities between classes. The queuing system can be described by a multi-dimensional Markov process, where the coordinates keep track of the number of customers of each class in the system. Based on matrix-analytic techniques and probabilistic arguments, we develop a recursive method for the exact determination of the equilibrium joint queue length distribution. The method is applied to a spare parts logistics problem to illustrate the effect of setting repair priorities on the performance of the system. We conclude by briefly indicating how the method can be extended to an M/M/1 queueing system with non-preemptive priorities between customer classes.

Redundancy Optimization for Critical Components in High-Availability Technical Systems

We consider a user who buys a number of identical technical systems e.g., medical, manufacturing, or communication systems for which she must have very high availability. In such a situation, there are typically several options that the user can choose to facilitate this availability: cold standby redundancy for critical components, buying spare parts with the systems so failed parts can be replaced quickly, and/or application of an emergency procedure to expedite repairs when there is a stock out. To these options we introduce another: the possibility of initiating an emergency shipment when stock is one. Thus, the user may choose different combinations of the redundancy decision and the timing of applications of the emergency procedure, as well as how much spare parts inventory to purchase. n nWe formulate the problem as the minimization of the total costs---acquisition, spare parts, and repair---incurred for the systems over their lifetimes, under a constraint for the total uptime of all systems. We optimally solve the problem by decomposing the multicomponent problem into single-component problems and then conducting exact analysis on these single-component problems. Using these, we construct an efficient frontier that reflects the trade-off between the uptime and the total costs of the systems. In addition, we provide a method to rank the components by the relative value of investing in redundancy. We illustrate these results through numerical examples.

A new approximate evaluation method for two-echelon inventory systems with emergency shipments

We consider the inventory control of repairable spare parts in a network consisting of a central warehouse, a central repair facility, and multiple local warehouses. Demands for spare parts occur at the local warehouses. If a local warehouse is out of stock, then an arriving demand is satisfied by an emergency shipment from the central warehouse or the central repair facility. Such emergency shipments are common practice for networks that support technical systems with high downtime costs. We develop a new evaluation method that provides accurate approximations for the key performance measures like fractions of demands supplied by the local warehouses or emergency shipments. The method can be easily incorporated in existing (greedy) heuristic optimization methods. Our method outperforms the approximate evaluation method of Muckstadt and Thomas (Manag. Sci. 26:483–494, 1980), as we show via a numerical analysis. Finally, we show that the performance of the system is virtually insensitive to the leadtime distribution of repairs at the central repair facility.

A note on maximal covering location games

In this note we introduce and analyze maximal covering location games. As the core may be empty, several sufficient conditions for core non-emptiness are presented. For each condition we provide an example showing that when the condition is not satisfied, core non-emptiness is not guaranteed.

Domain extensions of the Erlang loss function : their scalability and its applications to cooperative games

We prove that several extensions of the classic Erlang loss function to non-integral numbers of servers are scalable: the blocking probability as described by the extension decreases when the offered load and the number of servers s are increased with the same relative amount, even when scaling up from integral s to non-integral s. We use this to prove that when several Erlang loss systems pool their resources for efficiency, various corresponding cooperative games have a non-empty core.