We consider a maintenance service provider that services geographically dispersed customers with its local service engineers. Traditionally, when a system failure is reported, a service engineer makes a diagnostic visit to the customer's location to perform corrective maintenance. If spare parts are required, they are ordered and a second visit is scheduled at a later date to complete the corrective maintenance. In this paper, the service provider can proactively send spare parts to the customer to avoid the costly second visit. Motivated by a real-world problem in the high-tech industry, our model considers the cost of a second visit, fixed shipment costs, retrieval costs for the parts that are sent to the customer, and send-back costs for the parts that are sent but not used for corrective maintenance. The uncertainty in the set of parts required for corrective maintenance is modeled with a general distribution that can capture the dependencies between demands for different spare parts. We formulate an integer linear program to find the optimal set of spare parts that minimizes the expected total cost. We derive analytical results for the structure of the optimal policy and compare the optimal policy with two benchmark policies from practice. We observe that the policies from practice often find the optimal policy, and a new heuristic policy that exploits the structure of the optimal policy, on average, performs better than the benchmark policies.

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Thanks to Industry 4.0 technologies, predictive algorithms can provide advance demand information on spare parts demand. Understanding how the goodness of predictions affects on-hand inventory and costs is important for decision makers before integrating these models into existing systems. We consider a spare parts inventory problem for multiple technical systems that are supported by one local stockpoint. Each system has a single critical component that is subject to random failures. Signals are generated to predict component failures. The signal that corresponds to a failure is generated a certain amount of time before the failure, referred to as the demand lead time. However, not every signal results in a failure and some failures are undetected. A component is replaced from the stock when a failure occurs. In case of stock-outs, an emergency shipment takes place. We formulate a discrete-time Markov decision process model to optimize the replenishment decisions with the objective of minimizing the long-run average cost per period. We investigate the effect of precision (i.e., the fraction of true signals among all signals) and sensitivity (i.e., the fraction of detected failures among all failures) of the predictions and the demand lead time on the costs, order-up-to levels, average on-hand inventory and emergency shipments under the optimal policy. In the worst case, the precision, sensitivity or demand lead time is zero. We show analytically that the optimal policy and optimal costs only depend on the sensitivity and the demand lead time through their product. In numerical experiments, we observe a Pareto principle for the reduction of costs in precision (e.g., a 30% perfectness in precision brings a 70% reduction in optimal cost compared to the worst case) and an inverse Pareto principle in the product of sensitivity and demand lead time (e.g., 70% perfectness in the sensitivity or demand lead time only brings 30% reduction in optimal cost compared to the worst case). Finally, we observe that the local spare parts stock only becomes superfluous when the signals are really close to perfect.@en

A popular method in machine learning for super-vised classification is a decision tree. In this work we propose a new framework to learn fuzzy decision trees using mathematical programming. More specifically, we encode the problem of constructing fuzzy decision trees using a Mixed Integer Linear Programming (MIP) model, which can be solved by any optimization solver. We compare the performance of our method with the performance of off-the-shelf decision tree algorithm CART and Fuzzy Inference Systems (FIS) using benchmark data-sets. Our initial results are promising and show the advantages of using non-crisp boundaries for improving classification accuracy on testing data.@en

In this work, we propose a re-enactment simulation-based optimization method to determine the minimal total buffer capacity in an assembly line required to meet a target throughput. A distinguishing feature is the use of real-time event traces, in a fast fluid flow simulation model. Employing real-time event traces avoids the necessity to make restrictive modeling assumptions. The fluid simulation is combined with a multi start search algorithm. To demonstrate its effectiveness, the method is applied to a real-world use case in lead frame based semiconductor back-end manufacturing. This use case considers an assembly line consisting of six machines, for which the proposed method determines optimal buffer size configurations within several minutes of computational time.

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