(411g) Integrated Optimization of Design, Storage Sizing, and Maintenance Policy As a Markov Decision Process Considering Varying Failure Rates
- Conference: AIChE Annual Meeting
- Year: 2020
- Proceeding: 2020 Virtual AIChE Annual Meeting
- Group: Computing and Systems Technology Division
- Time: Tuesday, November 17, 2020 - 9:30am-9:45am
A number of optimization works have been reported to optimize the reliability of chemical plants. Pistikopoulos et al. (2001) and Goel et al. (2003b) formulate an MILP model for the selection of units with different reliability and the corresponding production and maintenance planning for a fixed system configuration. Terrazas-Moreno et al. (2010) formulate an MILP model using Markov chains to optimize the expected stochastic flexibility of an integrated production site by the selection of pre-specified alternative plants and the design of intermediate storage. Kim (2017) presents a reliability model for k-out-of-n systems without repair using a structured continuous-time Markov Chain, which is solved with a parallel genetic algorithm. As an improvement, our recent mixed-integer framework (Ye et al., 2019) models the stochastic failure-repair process of the superstructure of the ASU process as a continuous-time Markov Chain, and simultaneously optimizes the redundancy selection and the maintenance policy.
This work extends the idea of our aforementioned recent work (Ye et al., 2019) to incorporate liquid storage as another strategy for increasing reliability besides considering redundant equipment and condition-based maintenance. To be specific, three strategies over design and maintenance are considered to increase the availability of the system. For design, we can install parallel units for certain processing stages, such that when the primary units fail, other units can fill in its place in order to reduce system downtime. Another design strategy for reliability is to store liquid products which can be vaporized to meet pipeline demands during plant downtimes. Furthermore, we propose to capture equipment failure rate (bathtub deterioration/failure) and condition-based maintenance with a discrete-time Markov Decision Process. The bathtub curve is discretized into three âworking statesâ of the unit with different failure rates: 1. Infant, 2. Stable, and 3. Worn-out. When a unit is not working, there are three other possible states: 4. Stand-by, 5. Stopped, and 6. Failed. One and only one action is to be assigned to each state, which is the main decision to make in terms of the maintenance policy.
We embed the optimal condition of Markov Decision Processes and the stationary probability distribution conditions of the reduced Markov Chain into an MINLP (DMP) model that considers the economic trade-off among all major decisions. In order to make the model solvable, we propose a standard linearization for the bilinear terms of binary variables and continuous variables, and a reformulation of the objective function that potentially provides a stronger relaxation of the objective. An example based on the reliable design of a real-world air separation unit is used to demonstrate how to extract the model parameters from the raw data. We attempted to solve the MINLP (DMP) directly with several global solvers and found that they would not solve in reasonable amount of time. Therefore, we propose an algorithm that consists of two phases, Enumeration and Bounding, and Rewards Iteration. The validity of the bounding is based on the earlier introduced reformulation of the objective function. Resolving the example shows that the two-phase algorithm greatly reduces the required computational effort. The algorithm also has consistent performance over 20 randomly generated problems based on the original example of 4 processing stages. Another group of 20 random problems of 6 processing stages are also solved and show good computational results.