Handling Type-I and Type-II endogenous uncertainties in simultaneous production planning and condition-based maintenance optimization in continuous production

Abstract

This work proposes a novel stochastic programming formulation that can handle Type-I and Type-II endogenous uncertainties with the goal of simultaneously optimize production planning and condition-based maintenance of continuous production plants. A degradation model that is able to predict the Remaining Useful Life of the equipment is embedded into the optimization problem and we consider this prediction to be uncertain. Each scenario of the stochastic program represents an uncertain realization of the predicted Remaining Useful Life and has a certain probability of realization. These probabilities can be altered by the decision maker, thus rendering some predictions more likely than the others by acting on the utilization of the plant (Type-I endogenous uncertainty). The maintenance activities recover the health of the equipment and the decisions on maintenance make some scenarios not realize any more and, therefore, modify the structure of the scenario-tree (Type-II endogenous uncertainty). We present two different modelling approaches for this novel class of stochastic programs based on superstructure scenario trees and on conditional non-anticipativity constraints. For a simple generic example, we analyse the influence of the modelling approach on the computational time that is needed to solve the resulting MINLP problem with the global solver BARON. We also investigate several branching priority strategies to reduce the computational effort for this class of problems. We demonstrate the advantages that can be achieved using the proposed formulation compared to the deterministic counterpart.This work sets the ground for modelling and solving simultaneous production planning and condition-based maintenance problems. To deal with larger-scale industrial problems, additional work is required to develop custom solution techniques to reduce the computational burden.