The increasing importance of Maintenance and a cleaner environment besides the relations between them has encouraged the current authors to investigate a mathematical Markovian model for the condition-based Maintenance problem while considering environmental e ects. In this paper, the problem of proposing a Maintenance optimal policy for a partially observable, stochastically deteriorating system is studied in order to maximize the average pro t of the system with sustainability aspects. The modeling of this Condition-Based Sustainable Maintenance (CBSM) problem is done by mathematical methods such as Partially Observable Markov Decision Process (POMDP) and Bayesian theory. A new exact method, called accelerated vector pruning method, and other popular estimating and exact methods are applied and compared for solving the presented CBSM model, and several managerial conclusions are obtained.

Joint optimal inventory control and preventive Maintenance is a rich area of academic research that is still in its infancy and has the potential to affect manufacturing systems' performance. Also, due to uncertainties in demand, Maintenance and inventory loss are virtually unavoidable. Therefore, determining the optimal amount of inventory storage, the time to create an additional inventory for storage, and the time of Maintenance operations is a concern of many manufacturers. In this paper, a joint optimization model has been developed. In which, for the proximity of reality, demand is considered as an uncertain parameter. The strategy is such that the production component is placed under Maintenance as soon as it reaches the 𝑚 level or in the event of a malfunction earlier than 𝑚 , stopped system and placed under Maintenance and repairs. Inventory of 𝐴 period with level ℎ is created, which during Maintenance operations, stochastic demand will be provided. Finally, a model for joint optimization of Maintenance and inventory control with random failure is used that minimize the cost and create the maximum level of accessibility. A numerical study is conducted to show the effectiveness and applicability of the proposed integrated model. An accurate algorithm is provided to solve the model. The results show that the model is generally sensitive to the cost.

A major competitive advantage of production and service systems is establishing a proper Maintenance policy. Therefore, Maintenance managers should make Maintenance decisions that best fit their systems. Multi-criterion decision-making methods can take into account a number of aspects associated with the competitiveness factors of a system. This paper presents a multi-criterion decision-aided Maintenance model with three criteria that have more influence on decision making: reliability, Maintenance cost, and Maintenance downtime. The Bayesian approach has been applied to confront Maintenance failure data shortage. Therefore, the model seeks to make the best compromise between these three criteria and establish replacement intervals using Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE II), integrating the Bayesian approach with regard to the preference of the decision maker to the problem. Finally, using a numerical application, the model has been illustrated, and for a visual realization and an illustrative sensitivity analysis, PROMETHEE GAIA (the visual interactive module) has been used. Use of PROMETHEE II and PROMETHEE GAIA has been made with Decision Lab software. A sensitivity analysis has been made to verify the robustness of certain parameters of the model.