Inventory Management for Preventive and Corrective Maintenance under Supply Chain Risks
Supervisors: Anna-Lena Sachs and Rob Shone (Lancaster University), and Matthew Jones and David Randell (Shell)
In production plants which require preventive and corrective maintenance, inventory management helps to ensure that there are sufficient spare parts available for the maintenance to be performed. It can be costly to order and hold spare stock, and it is typically more costly to shut down a piece of machinery due to not having enough spare parts for it to be fixed; therefore, it is ideal to strike a balance between ordering more units than necessary and not ordering enough units to fit the demand. Some difficulties, however, are that units inside each machine break unpredictably and there can be long lead times associated with ordering stock, so it is impossible to know the number of spare parts necessary to order to exactly meet the future stochastic demand. This project focuses on finding the optimal inventory and maintenance decisions that help minimise expected future costs. These decisions also improve environmental outcomes by not over-ordering stock and by conducting maintenance in a timely manner.
We can find such optimal decisions by formulating our problem as a Markov Decision Process (MDP). By solving the MDP via Dynamic Programming, we can find an optimal dynamic policy, mapping every “state” of a system to its corresponding optimal “action”. Whilst some exact methods exist to solve MDPs, such as Value Iteration, as our problem becomes larger we will experience the curse of dimensionality. This means that some large problems will be potentially infeasible to solve, and those that can be solved will take so long to find an exact optimal policy that by the time it has been found, the solution will no longer be of use. To combat the curse of dimensionality, we derive mathematical properties for the optimal solution to develop novel heuristic methods (e.g. using Approximate Dynamic Programming).
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