SIMULATION. Simulation. advantages (cont.) Advantages

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1 SIMULATION Simulation Advantages. Simulation is relatively straightforward and flexible.. Simulation can be used to analyze large and complex real-world situations that cannot be solved by conventional operations management models. advantages (cont.). Simulation allows for the inclusion of real-world complications that most models cannot permit. Simulation can use any probability distribution that the user defines; it does not require standard distributions.. Time Compression is possible with simulation. The effects of policies over many months or years can be obtained by computer simulation in a short time.

2 advantages (cont.). Simulation allows what-if types of questions. Managers like to know in advance what options will be most attractive. With a computerized model, a manager can try out several policy decisions within a matter of minutes.. Simulations do not interfere with the realworld system. It may be too disruptive, for example, actually to experiment with new policies or ideas in a hospital, school, or manufacturing plant. advantages (cont.). Simulation allows us to study the interactive effect of individual components or variables in order to determine which ones are important. Disadvantages. Good simulation models can be very expensive; they may take years to develop.. Simulation does not generate optimal solutions to problems as does linear programming. It is a trial-and-error approach that may produce different solutions in repeated runs.

3 Disadvantages (cont.). Managers must generate all of the conditions and constraints for solutions that they want to examine. The simulation model does not produce answers by itself.. Each simulation model is unique. Its solutions and inferences are not usually transferable to other problems. Uses of Simulation. Determine (improved) operating conditions. system design. Demonstrate how proposed change in policy will work; compare new policy to existing one system analysis. Train operating personnel to make better decisions regarding utilization of new info. simulation games Components of Simulation,QSXWYDUV. Exogenous variables. Parameters LPXODWLRQ 0RGHO. Identities. Operating equations XWSXWYDUV. Endogenous variables (performance)

4 Types of Simulation Simulation. Fixed-time increment (time slicing) Times are at fixed regular increments (ex: car rental, inventory model). Variable-time increment (event sequencing) Times are measured as they happen in variable increments (ex: restaurant) Simulation Swapcraft Door-to-Door Simulation. Salesperson visits about 0 houses per night. 0/0 chance that someone answers door. 0/0 chance that it s a woman vs. man. If man answers door, % chance of buying parts, % chance of buying part. If woman answers door, % chance of buying part. Swapcraft pays $ per part sold Simulation Quarter Dime Nickel Penny Outcome Heads Tails Heads Tails Heads Heads Others Heads Tails Others Heads Tails No one home Woman answers part sold 0 parts sold Man answers parts sold part sold 0 parts sold

5 Exercise Class Exercise entrance lane Car Car Car Exit Waiting area Note: Customers balk if more than cars in line Monte Carlo Simulation (Fixed time increments). Set up probability distributions for the exogenous variables. Build cumulative probability distributions. Establish an interval of random numbers for each exogenous variable. Generate a set of random numbers. Simulate the situation for many trials

6 Components of Simulation,QSXWYDUV. Exogenous variables. Parameters LPXODWLRQ 0RGHO. Identities. Operating equations XWSXWYDUV. Endogenous variables (performance) Number of customers arriving every min. 0 Probability size Small Medium Large Probability Average time to fill order min. min. 9 min. Average profit $..0.00

7 Monte Carlo Simulation. Set up probability distributions for the exogenous variables. Build cumulative probability distributions. Establish an interval of random numbers for each exogenous variable. Generate a set of random numbers. Simulate the situation for many trials customers arriving every min. Prob Cumulative Prob Interval 0<<= <<= <<=0. 0.<<= <<=.00 size Small Medium Large Cumulative Probability probability Interval <<= <<= <<=.00

8 Monte Carlo Simulation. Set up probability distributions for the exogenous variables. Build cumulative probability distributions. Establish an interval of random numbers for each exogenous variable. Generate a set of random numbers. Simulate the situation for many trials Period New Period 8 completed? Profit 8

9 Period. New Period. New Period New. yes 9

10 Period New. yes. Period New. yes. Med Period New. yes. Med 0 0

11 Period New. yes. Med 0 Period completed? No Profit Period completed? Profit No ---

12 Period. New. yes. Med 0 Period New. yes. Med 0. Period New. yes. Med 0. no

13 Period New. yes. Med 0. no Period New. yes. Med 0. no Period New. yes. Med 0. no

14 Period completed? Profit No --- Yes().0 Period New. yes. Med 0. no Period New. yes. Med 0. no

15 Period New. yes. Med 0. no yes Period New. yes. Med 0. no yes. Period New. yes. Med 0. no yes. Small

16 Period New. yes. Med 0. no yes. Small 0 Period New. yes. Med 0. no yes. Small 0 Period completed? Profit No --- Yes().0 Yes().

17 Period.9 New. yes. Med 0. no yes. Small 0 Period New. yes. Med 0. no yes. Small 0.9 Period New. yes. Med 0. no yes. Small 0.9 yes

18 Period New. yes. Med 0. no yes. Small 0.9 yes.0 Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0 8

19 Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0 Period completed? Profit No --- Yes().0 Yes(). No Period completed? Profit No --- Yes().0 Yes(). No --- 9

20 Period.8 New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0 Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no 0

21 Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no Period New. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no

22 Period completed? Profit No --- Yes().0 Yes(). No --- Yes() Period completed? Profit No --- Yes().0 Yes(). No --- Yes().0 Period. New avail? Lost Number waiting. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no

23 Period New avail? Lost Number waiting. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no Period New avail? Lost Number waiting. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no yes Period New avail? Lost Number waiting. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no yes.89

24 Period New avail? Lost Number waiting. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no yes.89 Large Period New avail? Lost Number waiting. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no yes.89 Large Period New avail? Lost Number waiting. yes. Med 0. no yes. Small 0.9 yes.0 Med 0.8 no yes.89 Large 0

25 Period completed? Profit No --- Yes().0 Yes(). No --- Yes().0 No --- Total revenue = $. Average revenue per period =./ = $0. Average profit per customer =./ = $. Opportunity cost due to balking = (.) = $.0 Total profit =..0 = $. Servers side by side entrance Car Car Waiting area lanes Car Car Exit Note: Customers balk if more than cars in line

26 New avail? Period Pds- 8 Pds- Period 8 Lost Number completed? Profit waiting Servers single line entrance lanes Car Car Car Car Exit Waiting area Note: Customers balk if more than cars in line