Multiple Repair Scheduling with Optimized Cost Applying Markov Chain Model

Abstract

Concrete is one of the most significant materials when it is needed to build any structure. Its vital properties are its strength and durability which may be defined as the efficiency to endure any weathering action while maintaining its desired engineering features. Though it is one of the most durable materials, but even it reaches to its decayed state which is resulted from lack of proper maintenance. Concrete in present infrastructures has been deteriorating at a rapid rate. This situation is very expected in saline areas where concentration of chloride is severe. It is one of the main reasons for weakening the concrete. Deterioration occurs rapidly for the shortage of proper repair. If it is repaired properly, deterioration speed will slow down and can improve condition rating after several years of repairing. So, there should be taken a suitable strategy for repair of concrete. The objective of this thesis is to select an appropriate repair schedule in accordance with minimized cost. Sometimes suitable repair strategy cannot be selected for the lack of enough inspection data and shortage of revenue. Here, failure probability records of 50 years are used as the dataset. There are many models which are used to predict the condition of infrastructures such as Monte Carlo stimulation, Markov Chain Model etc. Here, Markov Chain Model is used for multiple repairs scheduling with optimized repair cost. Markov Chain Model solely relies on current state for the upcoming estimation. This model is relatively comprehensible and predicts better when it is related to evaluation of cost-utility. There are some assumptions based on this model which is followed throughout the research. Three repair matrixes which are modelled as variables. There are five states and after repairing the condition jumps to better condition state than before. Among these matrixes, some repair concrete as it is in its newer state and some repair slightly to avoid the worst state. If the repair matrix is better, then the price is much higher. Four repair schedules are created to compare among different repair matrixes based on their unit cost. Time, schedule, cost are used as the constraints here. The limitation of failure probability is taken as 0.2. It means the condition of concrete cannot cross 0.2 after repairing. If it crosses the limit, then the concrete is deteriorated so much that it will face failure. A repair schedule has to be selected which does not cross this criteria. Then excel solver uses these variables and constraints to find the solution. For specific normalized condition of concrete’s failure probability, variation of life cycle costs using multiple repair options are also shown in this report as the result. The repair schedule, which costs less but maintains the concrete from failure over the years, is taken as the desired repair schedule. The costly schedule should be avoided as much as possible. It will be useful for building concrete infrastructure in not only coastal areas but also in the areas where there is a high salinity level in groundwater. Sudden failures can be avoided using this strategy. This paper will help to sort out the desired strategy.