A Bi-Objective Markov Decision Process Design approach to redundancy allocation with dynamic maintenance for a parallel system

TL;DR

This work addresses integrating redundancy allocation with dynamic maintenance by formulating a Bi-Objective Integrated Design and Dynamic Maintenance Problem (BO-IDDMP) within a continuous-time Markov Decision Process Design framework. A novel Approximate Pareto Population (APP) heuristic is developed to generate a rich set of Pareto-optimal designs and dynamic maintenance policies, and is shown to be orders of magnitude faster than exact MILP methods while delivering comparable or superior Pareto fronts. Key findings show that dynamic maintenance yields better-populated fronts and can dominate static, fully-active designs, especially under larger budgets and heterogeneous costs. The study advances the RAP literature by jointly optimizing design and dynamic operation, discusses real-world applicability, and outlines future extensions to more complex system structures and timing distributions.

Abstract

The reliability of a system can be improved by the addition of redundant elements, giving rise to the well-known redundancy allocation problem (RAP). We propose a novel extension to the RAP called the Bi-Objective Integrated Design and Dynamic Maintenance Problem (BO-IDDMP) which allows for future dynamic maintenance decisions to be incorporated. This leads to a problem with first-stage redundancy design decisions and second-stage sequential maintenance decisions under uncertainty. To the best of our knowledge, this is the first use of a continuous-time Markov Decision Process Design framework to formulate a problem with non-trivial dynamics, as well as its first use alongside bi-objective optimization. A general heuristic optimization methodology for bi-objective MDP Design problems is developed, and then applied to the BO-IDDMP. The efficiency and accuracy of our methodology are demonstrated against an exact mixed-integer linear programming solver. The heuristic is shown to be orders of magnitude faster in the majority of cases, and in only 2 out of 84 cases produces a solution that is dominated by the exact method. The inclusion of dynamic maintenance policies is shown to yield stronger and better-populated Pareto fronts, allowing more flexibility for the decision-maker. The impacts of varying parameters unique to our problem are also investigated.

Figures (20)

• Figure 1: Sample trajectory through the dynamic maintenance problem
• Figure 2: Illustration of APP building up the population of candidate solutions.
• Figure 3: Pareto front of candidate population.
• Figure 4: Pareto Front for Instance (14,42)
• Figure 5: Pareto Front for Instance (5,12)

Theorems & Definitions (17)

• Theorem 1
• proof
• Proposition 1
• proof
• Remark 1
• Theorem 2
• proof
• Proposition 2
• Lemma 1
• proof