مدیریت هزینه چرخه عمر با روش شبیه سازی مونت کارلو Monte Carlo simulation approach to life cycle cost management

Background Flanagan et al.’ s (1983) research showed that the capital costs of a building only represents half the total cost during its whole life, and are only slightly higher than united cleaning and care taking, replacement and maintenance, and routine servicing costs. Recently, there has been a growth in the application of public private partnerships (PPP) and private financial initiative (PFI) projects in the construction industry. As a result, the life cycle cost considerations are playing a more important role in tenders than ever before. The investors of durable buildings realised that an increased amount of money spent on initial cost can considerably reduce future costs of a building. The construction clients began to understand the importance of life cycle cost to their investment, so they require early and accurate life cycle cost advice on their project to help their financial planning and decisionmaking process. Life cycle costing is also a good assessment tool for sustainable building design (Wang et al. 2009). The construction industry is considered a riskbased industry and strong correlation has been established between project complexity and perceived risks. Although, it can also be argued that the construction industry is no different to other industries in terms of risk exposure (Loosemore et al. 2005), the growth in client expectations over the project whole life cycle dictates higher demands on the project team. As ‘value for money’ was repeatedly recorded as client main interest, it became essential to consider accurate measures and cost control in project life cycle cost analysis. Life cycle costing is one form of appraisal of how well a project meets the clients’ performance requirements (ISO 15686-5 2007). Life cycle costing is a valuable technique which is used for predicting and assessing the cost performance of constructed assets. The appropriate time to control the life cycle cost of a building is at the scheme (initial) design stage but little information is available during this stage (Wang and Horner 2007b). Kirk and Dell’Isola (1995) believe that the elemental estimating method, which breaks down building into elemental level for detailed costing, can improve the capability to cope with problems in life cycle costing and then assist earlier design decision-making. The life cycle costing process includes breaking down building to a measurable and detailed elemental level, to make life cycle assumptions, to calculate replacement cost of each element at each year according to the life cycle assumptions and finally to summarise and generate a life cycle profile over a long period of time (typically 25–۵۰ years for PFI/PPP projects) for the whole building. A typical life cycle cost structure of a building comprises of hundreds of different building elements. Each element correlates to several life cycle assumptions such as the replacement cycle, replacement cost and quantity of the element. In order to establish life cycle assumptions the quantity and unit rate of each element have to be estimated according to the design; and the life span for each of the building elements must be predicted. Every assumption is a variable in life cycle costing; therefore assumption making is the most difficult step in life cycle costing due to the complex cost breakdown structure and uncertainties in predicting future events in the long period of time. The combination of these variables can form an excessive number of different scenarios. For example, an estimator may assign 20 year life to PVC windows in a building project, but it only lasts for 16 years due to heavy usage of the building. Either overestimating or underestimating the life cycle assumptions are the risks in life cycle costing which may cause the project to be under funded in future. The life cycle costing should not only perform as a budget estimate tool, but it can also determine the project contingency and review the project cash flow in order to examine project affordability especially for PFI/PPP procurement. However, the input variables are normally given deterministic values in practical models regardless of the risks and uncertainties involved in the estimating process. As a result the deterministic model only produces a single figure as budget estimate of life cycle cost over a long period of time. The cumulative impact of inaccurate information can be drastic and the validity of the life cycle cost model can, therefore, be questioned. It is essential for project coalitions to ensure the application of robust cost estimating methods and tools. The widely used cost estimate method for life cycle cost estimate is still the deterministic model in practice. However, deterministic models cannot model life cycle costs successfully because the uncertainties of the future events affect the estimate of the life cycle cost of buildings. Mok et al. (1997) believe that traditional deterministic (most likely) cost estimation of building services is economically ineffective and reactionary in nature. They suggested implementing risk management process for this estimation. The disadvantages of traditional deterministic single-figure estimating are: (1) the contingency figure is arbitrarily arrived at, and may not be appropriate for the specific project; (2) there is a tendency to double-count risks, because some estimators are inclined to include contingencies in their best estimate; (3) a percentage addition still results in a singlefigure prediction of the estimated final cost, implying a degree of certainty that is simply not justified; (4) it does not highlight any potential for cost reduction, and may reflect the potential for ‘downside’ risk, and depending on the estimators’ attitudes and the sources of original data (Mok 1997). Loosemore et al. (2005) cited that the problem with single point estimate (especially in construction projects) is the potential variability that they hide. Life cycle cost models are normally based on the information provided by cost planner and estimators who include a level of contingency to the estimate. Taking into consideration the number of building elements over the economical life cycle of a PFI project (for instance, the cumulative impeded contingency), can wrongly contribute to the decision-making and inaccurate sums may be allocated to projects. Cost and project information and estimator’s experience can also contribute to the outcomes. The basic concepts of risk management of probability and ranging are found useful when dealing with the problem. Some theoretical non-deterministic models have been developed for estimating life cycle cost of buildings. For example, artificial neural networks (Boussabaine and Kirkham 2004), fuzzy logic approach (Wang and Horner 2007b, Wang 2009), sinking fund method (Bowles et al. 1997), coefficient method (Lavy and Shohet 2008). However, those previous researches provide little help on cost control and the determination of contingency allowance for life cycle fund of PFI projects in practice. A number of factors should be taken into consideration when building life cycle cost model. Technical factors, such as project life span, element life span, and replacement cost rates, affect the total life cycle cost of the building. External factors, such as environment, the age of the building and occupancy condition, also affects the building running costs (Lavy and Shohet 2008). Babalola and Aladegbaiye (2006) identified nine factors that have influence on project contingency. These factors are shown in Table 1. While cost information and estimator’s experience are considered technical factors, other factors have an administrative nature which governs the project environment. The analysis and discussion of life cycle cost models should consider the factors identified above. The determination of time horizon exists in aspects such as the physical, technological and economic life of projects (Dell’Isola and Kerk 1981). It depends on the client’s expectations and the characteristics of the project (El-Haram and Horner 1998). Dell’Isola and Kerk (1981) believe that 25 to 40 years is long enough to forecast future costs to capture the most important costs for economic purposes. The most commonly used concession periods in PPP/PFI procurements are 25 years and 30 years.