Designing Multi-state Systems and Selecting Equipment Suppliers Based on Availability

 This study aims to propose an approach for optimizing equipment suppliers in multi-state systems. The proposed solution examined in the water supply system (FWS) of heat recovery boiler (HRSG), manufactured by Mapna Boiler Engineering and Manufacturing Company. The assumed system consists of two main subsystems, equipped with three and two pieces in the first and second subsystems. With the failure of any equipment, if spare equipment is available in the warehouse, this equipment will replace the disabled equipment. Still, the unreplaced equipment decreases the capacity of the system. The system works until the number of healthy devices in each subsystem is more than the specific limits; otherwise, the system stops completely.This research aims to minimize total cost in two phases of construction and operation of an industrial system. The cost of building the system is the same as the cost of purchasing equipment from suppliers. The operating cost included maintaining spare equipment, reducing capacity, and shutting down the system. The quality of installed and spared equipment can vary. The holding cost of spared equipment sourced from different suppliers may also vary due to the differences in value, insurance costs, and maintenance conditions. This research aims to provide an approach for selecting suppliers of leading equipment, extensions, and spare parts. It is important to note that the use of quality equipment increases the cost of the construction phase. On the other hand, it improves the probability of failure and, consequently, the cost of reducing capacity and shutting down the system during the operation phase. This model minimizes the system's total cost in two phases of construction and operation based on the availability criterion.

Design/methodology/approach: 

The initial step was drawing the block diagram of system reliability. This step resulted in the determined failure effect of each component on the state of the system. Then, the Markov-chain develops a parametric model of the probability of the system under different situations. The Markov-chain results summarized the likelihood of the system under any full-load, half-load, or failed states. The mathematical model used the results of the obtained coefficients to calculate the costs of purchasing and maintaining the major and spared equipment and the expected costs of reducing the capacity and stopping in the desired period. The final model used such results in the form of a constraint set in a sizable mathematical programming model solved by GAMS software.

 The model aims to minimize all system costs, including construction cost (purchase) and operating cost (i.e., maintenance, half-load, and shutdown). The analysis of the results indicated that considering the total cost of construction and operation phases in a single model more effectively, optimizes the overall system cost. The model’s solution results implied the cost of capacity reduction as the highest cost because the system under study would be in a semi-load condition for a long time. The results also highlighted that the change in equipment maintenance cost did not affect the other costs of the system, and it only caused a linear shift in maintenance cost and total cost. However, when the increased cost was too much, the supplier selection strategy changed. The mathematical model suggested buying some equipment from another supplier to minimize the total cost, which reduced total maintenance cost instead of increasing it. Change of the hourly cost of the system half-load working affected the consequence of system capacity reduction only. It had little effect on other expenses until the cost-per-hour of capacity reduction significantly reduced. In case of an optimal response, the suppliers of some equipment changed, which resulted in modified additional cost values. The change in the hourly cost of half-load working had little effect on the optimal response. Only a significant reduction in this cost changed some equipment suppliers and affected the other expenses. The change in the hourly cost of downtime resulted in purchasing equipment from other suppliers, which changed other expenses.

Rearch limitations/implications: 

The lack of failure information registration system in the country's power plants was the most critical limitation in collecting necessary information and developing a computational model. For future research, the resulting model can be closer to the real situation by considering equipment and uncertainty's repairability and changing the failure rate over time.

Practical implications:

 Applying the proposed approach reduced the cost of construction and operation of power plants in the country. Practitioners can use this approach in selecting the system equipment with different prices and technical specifications from the market.

 Social implications:

 Implementation of research results increases social welfare by increasing electricity production and reducing pollution.

 Originality/value: 

The proposed mathematical model innovatively integrates construction and operation phases costs using Markov-chain results and uses the results to optimize a typical industrial system.