Quantitative Techniques for Decision Making in Construction

9.SIMULATION I

r' nh SIMOLATIorf I / \ 9.1 Introductio n Simulation i s the process of conducting experiments with a model of the system that is being studied or designed. I t is a powerful techniqu e for both analyzing and synthesizing engineering and other natural systems. The simulation procedur e i s basically an iterative procedure an d may be described a s an input-output stud y with feedbac k provide d t o guide th e changes in the input parameters. The inputs define the set of events and conditions to which the system can be subjected in the real world, and the outputs predict the system xesponse. B y studying the outputs at the end of each simulation run, one can learn more about the system behavior and may adjust th e inputs accordingly. Simulation models can be broadly grouped into three types: • Iconi c • Analo g • Analytica l Iconic model s are physical replicas of the real systems on a reduced scale. This type of model is common in engineering, e.g. In aircraft design , wind tunnels are used to simulate the environment around an aircraft in flight. I n 1 26 QUANTITATIV E TECHNIQUE FOR DECISION MAKING IN CONSTRUCTION the design of large engineering structures, such as skyscrapers, dams, bridges, and airports , thxee-dimensional axchitectuxal models are often prepare d t o provide a realistic view of the design. A simulation model, in which the real system is modeled through a completely different physica l media , i s called a n analo g model . I n studying th e response of engineering structures to various intensities of earthquakes, it is impossible to build a small model of the earthquake zone using rocks and soils and t o generate earthquake s a t th e comman d o f the experimenter . However, if the dynamic property of quake waves is known, an instrument may be constructed to generate a similar type of force motion. For problems in which th e characteristics o f the system components an d system structure can be mathematically defined, the n an analytical mode l constitutes a powerful simulatio n tool . I t may be composed of systems of equations, boundary constraints, and heuristic rules, as well as numerical data. This chapter onl y focuses o n the method of simulation calle d the Mont e Carlo Simulation, an analytical model. 9.2 Wha t I s Monte Carlo Simulation? When we use the word "simulation", we refer t o any analytical metho d meant to imitate a real-life system , especially when other analyses are too mathematically complex or too difficult t o reproduce. One typ e o f simulation i s Monte Carl o simulation , whic h randoml y generates values for uncertain variables over and over to simulate a model. At the core of simulation is random numbe r generation. The compute r generates a sequence of numbers, called random numbers or pseudorandom numbers. The numbers generated are considered t o be absolutely rando m and without a pattern. Becaus e of the element of chance, we often cal l it a Monte Carlo simulation. A Monte Carlo simulation is therefore a probabilistic model involving an element of chance and, hence, it is not deterministic. The random behavio r i n games of chance is similar t o how Monte Carl o simulation selects variable values at random to simulate a model. Whe n we roll a die, we know that either a 1, 2, 3, 4, 5, or 6 will come up, but we don't know which for any particular roll. It' s the same with the variables that have a known range of values but an uncertain value for any particular tim e or SIMULATION! 1 2 7 event (e.g. interest rates, staffing needs , stock prices, inventory, phone calls per minute). A n analogy to the above example of rolling a die is the generation of rando m numbers . W e will se e in th e example s i n thi s chapte r ho w simulations are performed by generating random numbers. However , before we go to the examples, let us take a note of the limitations o f the Mont e Carlo simulation technique . 9.3 Limitation s Despite th e man y application s an d advantages , th e followin g ar e som e limitations of computer simulations...