Effect of commonality on spare parts provisioning costs for capital goods

Machines at customers have to be provided with spare parts upon failure. Consider a number of groups of machines, for each of which a target aggregate fill rate or target average response time (waiting time) should be met. Between groups, commonality exists, i.e., some parts occur in the material breakdown structure of machines in multiple groups. Instead of using separate stocks per group of machines, we study the potential benefits of exploiting commonality by using a shared stock for all groups together. For this purpose, we formulate a multi-item single-site spare parts inventory model, with the objective to minimize the spare parts provisioning costs, i.e., inventory holding and transportation costs, under the condition that all service level constraints are met. We develop a heuristic solution procedure using a decomposition approach as in Dantzig-Wolfe decomposition, in order to obtain both a heuristic solution and a lower bound for the optimal costs. In a case study and a numerical experiment, we show that significant reductions in spare parts provisioning costs can be obtained by using shared stocks. Furthermore, we show how the size of the potential benefits behaves as a function of the number of groups, the percentage of commonality and the occurrence of commonality in cheap or expensive items

Near-optimal heuristics to set base stock levels in a two-echelon distribution network

We consider a continuous-review two-echelon distribution network with one central warehouse and multiple local stock points, each facing independent Poisson demand for one item. Demands are fulfilled from stock if possible and backordered otherwise. We assume base stock control with one-for-one replenishments and the goal is to minimize the inventory holding and backordering costs. Although this problem is widely studied, only enumerative procedures are known for the exact optimization. A number of heuristics exist, but they ??nd solutions that are far from optimal in some cases (over 20% error on realistic problem instances). We propose a heuristic that is computationally e??cient and ??nds solutions that are close to optimal: 0.1% error on average and less than 3.0% error at maximum on realistic problem instances in our computational experiment

Reducing costs of repairable spare parts supply systems via dynamic scheduling

We study a system consisting of one repair shop and one stockpoint, where spare parts of repairables are kept on stock to serve an installed base of systems. Part requests are met from stock if possible, and backordered otherwise. Our objective is to determine initial stock levels and a policy for scheduling repair jobs such that holding and backorder cost are minimized. We propose two dynamic scheduling rules, compare their performance with the static priority rule, and show that even when stock levels and static priorities have been optimized simultaneously, dynamic scheduling rules often reduce total cost by more than 10%

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

In this paper we analyze an MN/MN/1 queueing system with N customer classes and preemptive priorities between classes, by using matrix-analytic techniques. This leads to an exact method for the computation of the steady state joint queue length distribution. We also indicate how the method can be extended to models with multiple servers and other priority rules

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 ICT technology, so that the condition data can be collected remotely. 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 proposed. With the joint maintenance interval and 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 on a case of a wind power farm consisting of a large number of non-identical components is performed, including a sensitivity analysis. At last, our policy is compared to a corrective-maintenance-only policy

Optimal and heuristic repairable stocking and expediting in a fluctuating demand environment

We consider a single stock point for a repairable item. The repairable item is a critical component that is used in a fleet of technical systems such as trains, planes or manufacturing equipment. A number of spare repairables is purchased at the same time as the technical systems they support. Demand for those items is a Markov modulated Poisson process of which the underlying Markov process can be observed. Backorders occur when demand for a ready-for-use item cannot be fulfilled immediately. Since backorders render a system unavailable for use, there is a penalty per backorder per unit time. Upon failure, defective items are sent to a repair shop that offers the possibility of expediting repair. Expedited repairs have shorter lead times than regular repairs but are also more costly. For this system, two important decisions have to be taken: How many spare repairables to purchase initially and when to expedite repairs. We formulate the decision to use regular or expedited repair as a Markov decision process and characterize the optimal repair expediting policy for the infinite horizon average and discounted cost criteria. We find that the optimal policy may take two forms. The first form is to never expedite repair. The second form is a type of threshold policy. We provide necessary and sufficient closed-form conditions that determine what form is optimal. We also propose a heuristic repair expediting policy which we call the world driven threshold (WDT) policy. This policy is optimal in special cases and shares essential characteristics with the optimal policy otherwise. Because of its simpler structure, the WDT policy is fit for use in practice. We show how to compute optimal repairable stocking decisions in combination with either the optimal or a good WDT expediting policy. In a numerical study, we show that the WDT heuristic performs very close to optimal with an optimality gap below 0.76% for all instances in our test bed. We also compare it to more naive heuristics that do not explicitly use information regarding demand fluctuations and find that the WDT heuristic outperforms these naive heuristics by 11.85% on average and as much as 63.67% in some cases. This shows there is great value in leveraging knowledge about demand fluctuations in making repair expediting decisions

Analysis of resource pooling games via a new extension of the Erlang loss function

We study a situation where several independent service providers collaborate by pooling their resources into a joint service system. These service providers may represent such diverse organizations as hospitals that pool intensive care beds and ambulances, airline companies that share spare parts, or car rental agencies that pool rental cars. We model the service systems as Erlang loss systems that face a fixed cost rate per server and penalty costs for lost customers. We examine the allocation of costs of the pooled system amongst the participants by formulating a cooperative cost game in which each coalition optimizes the number of servers. We identify a cost allocation that is in the core of this game, giving no subset of players an incentive to split off and form a separate pooling group. Moreover, we axiomatically characterize this allocation rule and show that it can be reached through a population monotonic allocation scheme. To obtain these results, we introduce a new extension of the classic Erlang loss function to non-integral numbers of servers and establish several of its structural properties