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Simulation Modeling & Analysis Department of Industrial Engineering University of Central Florida What is Simulation? Very broad term, set of problems/approaches Generally, imitation of a system via computer Involves a model --validity? Don’t aspire to analytic solution Don’t get exact results (bad) Allows for complex, realistic models (good) Approximate answer to exact problem is better than exact answer to approximate problem Very popular, powerful approach Applications Manufacturing Supply chain and logistics Staffing Telecommunications Health care Military Consistently ranked as most useful, powerful of mathematical-modeling approaches Systems Physical facility/process, usually evolving through time May or may not exist Study its performance May be controlled in real time Models Abstraction/simplification of the system used as a proxy for the system itself Two types Physical (iconic) Mathematical - quantitative and logical assumptions Methods of Studying a System SYSTEM Experiment with the Experiment with a actual system model of the system Physical model Analytical model Mathematical model Simulation model Spreadsheets/Process maps Hybrid model Study a System vs. Model System study No question about validity May be impractical or impossible (system may not exist) High risk Model study Must be concerned with validity Generally much easier to work with Can “exercise” it for many more situations than system Analytical solution (simple model) or simulation? Simulation Alternatives Mathematical models are an equation or set of equations which attempt to give a mathematical description of some real phenomenon. It can be very simple or very complex. Linear and non linear programming. Easiest and fastest for simple problems, gives exact and optimum solutions Mathematical models are not dynamic (static) and cannot account for changes in the system over time and they cannot model variability, e.g., probabilistic processing times, dynamic resource schedules/failures, etc. Example: Transportation Problem Problem Definition Company XYZ has five distribution centers in different locations. The company would like to develop an optimum transportation plan to distribute building material to six of its customers. The inventory at each plant, the quantity required by each customer, and location of customers and plants are known. Example: Transportation Problem C6 (30) C5 (16) 30 miles C1 (16) S1 S5 1 mi (36) (8) 8 miles 1 mile 9 miles 8 miles 4 miles 30 miles S2 S4 C4 (28) 1 mile 3 miles (31) (25) C2 (13) 10 miles 15 miles C3 (25) 5 miles S3 10 miles 10 miles (28) Problem Formulation (General) Variables: Xij - where Xij is the quantity transported from plant i (i=1,2,..m) to customer j (j=1,2,…n). m n Objective function: Minimize Z= c x i 1 j 1 ij ij Where cij is the unit transportation cost between i and j Constraints: n x j 1 ij ai , i 1,2,...m m x i 1 ij b j , j 1,2,...n a: supply , b: demand Problem Formulation (Company XYZ) Variables: Xij - where Xij is the quantity transported from plant i (i=1,2,3,4,5) to customer j (j=1,2,3,4,5,6). Assume 1 mile = $0.75 Objective function: Minimize z 6.75x11 22.5x12 45x13 63x14 14.25x15 30 x16 16.5 x21 45.75x22 68.25x23 86.25x24 10.5 x25 38.25x26 44.25x31 15x32 7.5 x33 25.5 x34 52.5 x35 67.5 x36 66.75x41 52.5 x42 15x43 3x44 74.25x45 90 x46 70.5 x51 56.25x52 18.75x53 5.25x54 78x55 93.75x56 Constraints: x11 x12 x13 x14 x15 x16 36 x21 5 x22 x23 x24 x25 x26 31 x31 x32 x33 x34 x35 x36 28 x41 x42 x43 x44 x45 x46 25 x51 x52 x53 x54 x55 x56 8 Problem Formulation (Company XYZ) Constraints: x11 x21 x31 x41 x51 x61 16 x12 x22 x32 x42 x52 x62 13 x13 x23 x33 x43 x53 x63 25 x14 x24 x34 x44 x54 x64 28 x15 x25 x35 x45 x55 x65 16 x16 x26 x36 x46 x56 x66 30 and xij 0 Problem Formulation (Table Representation) To From C1 C2 C3 C4 C5 C6 Supply S1 6.75 22.5 45 63 14.25 30 36 S2 16.5 45.75 68.25 86.25 10.5 38.25 31 S3 44.25 15 7.5 25.5 52.5 67.5 28 S4 66.75 52.5 15 3 74.25 90 25 S5 70.5 56.25 18.75 5.25 78 93.75 8 Demand 16 13 25 28 16 30 Optimum Transportation Plan Trucks From site to customer for minimum cost Total Transportation Cost = $1,859.25 Customer To C1 C2 C3 C4 C5 C6 Supply From S1 16 5 15 36 S2 16 15 31 Site S3 8 20 28 S4 5 20 25 S5 8 8 Demand 16 13 25 28 16 30 Simulation Alternatives Spreadsheets are fast, easy to use, and widely available. Any number of parameters and formulas with varying degrees of complexity can be included; at the same time these parameters and formulas can be updated quickly to test several scenarios. Spreadsheets are not very dynamic and cannot account for changes in the system over time and they neglect variability. They consider averages only (very bad) e.g., average arrival rates, average processing times, travel times, etc. Simulation Alternatives Process maps represent a common understanding of systems operations. They are easy to use, widely available, and with no need of prior mathematics or programming knowledge. Can be used to map an end-to-end business process in greater details, mainly to convey a common understanding of the “as is” process and map alternative “to be” processes. Process maps are not dynamic, cannot account for changes in the system over time, and do not represent any variability. . Is Simulation a Better Method? Yes, because Simulation fulfills other methods shortfalls and weaknesses Simulation is dynamic and account for changes in the system over time. Simulation models variability, far beyond averages. The following demonstration shows the power of simulation methodology over other competitive methodologies. The demonstration mainly shows that averages used by others method are not enough and always mislead decision makers. Demonstration: Claims Department Assume an insurance company with a claim department of 3 employees; each claim is processed by the three employees. Insurance claims arrive at the claims department every 10 minutes (inter-arrival time) for processing. When a claim arrives, it takes 1 min. to transfer the claim to the first employee. If the first employee is not free, the claim waits on his desk. When the first employee becomes free, it takes 10 min to process the claim. When the first employee finishes working on the claim, the claim is transferred to the second employee for further processing. This transfer takes 1 min. Once the second employee is available, it takes 10 min to complete his portion of the process. When the second employee finishes, the claim is transferred to the third and final employee. This transfer takes 1 min. Once the third employee is available, it takes 10 min to perform his portion of the process. When the third employee finishes, the claim is complete and is transferred to the mailroom where it is sent to the customer with the approval or disapproval decision. Claims Department Spreadsheet Formula B3+B4+…+B9 = 34 Process map Claims arrival Process 1 Process 2 Process 3 1 min 1 min 1 min 1 min exit 1 claim/10 min 10 min 10 min 10 min Simple graphical representation 0 0 0 Arri vi ng Cl ai m s Fi ni s hed Cl ai m s 0 Proc es s /em pl oyee 1 Proc es s /em pl oyee 2 Proc es s /em pl oyee 3 0 Question What is your best estimate for the minimum, average, and maximum times for cycle time, i.e. a claim to arrive at the department, process through all 3 employees, and finally arrive at the mailroom, exiting the system Modeling Claims Department Using Arena Transfer time = 1 min Inter-arrival time = 10 min Create 1 Assign arrive time Transf er to employee1 0 Transfer time = 1 min Claim processing Transf er to employee1 by employee_1 employee2 0 processing time = 10 Transfer time = 1 min min Claim processing Transf er to employee2 by employee_2 employee3 0 Transfer time = 1 min processing time = 10 Claim processing Transf er to min employee3 by employee_3 mailroom 0 processing time = 10 Averages mailroom send to client min Record 1 0 Simulation Run (Averages) Simulation Output (Averages) From the animation and the output Queues are not building Cycle time is not fluctuating, No problems in the system. This output is similar to using a static tool like a spreadsheet or a process map. In Reality “Averages Kill” In reality, the arrival of the claims and department operations would never work in perfect rhythm, there is variability. Variability occurs in every day situations and in any business. This is where the power of simulation over other methods arises. Variability and its effect on business operations and decision making will be demonstrated in the claims department simulation model. Claims Department Model with Variability Transfer time = Inter-arrival time = Exponential (1) Exponential (10) Create 1 Assign arrive time Transf er to employee1 0 Transfer time = employee1 Claim processing Transf er to Exponential (1) by employee_1 employee2 0 processing time = Transfer time = 1 min Normal distribution Exponential (1) Mean=10 , Std.dev 2 employee2 Claim processing Transf er to by employee_2 employee3 0 processing time = Transfer time = 1 min Triangular distribution Exponential (1) Claim processing Transf er to employee3 Min=8, Mode=10, by employee_3 mailroom Max=12 0 processing time = Uniform distribution mailroom Record 1 send to client Distributions Min = 8, Max = 12 0 Question What is your estimates of the minimum, average, and maximum cycle time for this system. Simulation Run (Distributions) Simulation Output (Distributions) From the animation and the output Queues are building, especially at process 1 Cycle time is fluctuating, There are problems in the system. This output is not similar to using a static tool like a spreadsheet, a process map, or even simulation run based on averages Comparison of Simulation Models Comparison of Simulation Output Averages Distributions (Variability) “A little bit” of Statistics We ran the model 1 time only, i.e. 1 replication. This is not statistically correct. Since, we introduced variability in the model We have to make the output “statistically correct” and we need to be confident about the output values. This can be done by running the simulation model several times (replications), then take the average of these replications and build a confidence interval around the mean. The simulation output then will include the average, halfwidth, min., and max. Average ± halfwidth gives the confidence interval. Simulation Output (Distributions, 30 replications) I have output! Then what? Look at the output, analyze them, brainstorm Identify possible reasons, e.g. under staffing Identify possible alternative solutions, e.g. increase number of employees Perform what-if analysis of the possible alternatives in your laboratory (simulation model) Compare and select best alternative In the claims department example: Analyze: Queues are building Possible reason: Department under staffed Possible solution: Increase staffing level What-if more employees added: next slide Simulation Output (Distributions, 30 replications, increase staffing level) The Cycle time decreases as number of employees/process increases Claims to be processes wait time decreases as number of employees/process increases The best alternative is (2, 2, 2), i.e. assigning 2 employees for each process Simulation Output (Cont.) Number in queue and wait time in queue decreases as number of employees/process increases The best alternative is (2, 2, 2), i.e. assigning 2 employees for each process Simulation Modeling Process Problem definition Problem and Real System Objectives Model scope and level of details Conceptual model More runs/scenarios Modeling & Data collection Conclusions and Running and Simulation Model implementation analyzing the model Simulation Modeling Process Planning the Study 1. Defining Objectives/Problem Definition 2. Identifying Constraints 3. Preparing Simulation Specification 4. Developing a schedule 3.1 Scope of model 3.2 Level of details Defining the system Model Building 5. Determining and CollectingPrimary Data 6. Conceptual Model Required Development 7. Determining Data Required 8. Selection of data sources 6.1. Conceptual Model Validation 9. Data Collection 9.1. Data Validation 10. Modeling required assumptions Converting data & assumptions to useful Form Model Translation No Validated? Verified? No Yes No Experimental Design “As is” model Running & Analyzing of Output Scenario 1 Scenario 2 Scenario 3 MoreRuns? Yes “What if” analysis Yes DifferentScenarios Scenario n No Documentation & Implementation of best Scenario Reportring the results Discrete Event Simulation Provides trade-off analysis Without DES analysis, process design is a “Black Box” Provides approximate answers to exact problems Better than exact answers to approximate problems Usually get random output Advantages and Disadvantages of Simulation Modeling Advantages: Flexibility to model things as they are (even if messy) Allows for uncertainty, non-stationarity in modeling Disadvantages: Don’t get simple closed-form formulas Don’t get exact answers, only estimates Is Simulation that Simple? NO The case demonstrated is a very simple example. The complexity of simulation models increases with the complexity of the problem, scope of the problem, and the level of details simulation modeling solutions is applied for problems with varying degrees of complexity Real World Simulation Applications Orlando International Airport (OIA) Objectives of the simulation study Capacity analysis of the key passenger processing components within the North Terminal Complex Determine the various bottlenecks and problems that would impede the processing of additional passengers per year. Detailed analysis of agent and electronic ticketing Detailed analysis of security check points Develop a GUI tool for the simulation model to enable the airport authority to use the model without prior simulation knowledge and to conduct unlimited “What if” analysis. Data Collection Flight schedules Passengers arrival rates and behavior Agent Ticketing time Electronic ticketing time Security check time Vertical and Horizontal transports flow time Facilities usage time Proportions of various events Data sources Time and motion study Questionnaires Airlines Airport authority Data Analysis/Input modeling Statistical analysis of data using statistical analysis software e.g. Minitab Test of hypothesis Two sample t-test ANOVA …etc. For example, statistical analysis of the ticketing time data collected to answer the question: is the passenger grouping significant? Data Analysis/Input modeling Grouping is significant Airport Model GUI Excel Arena Flight schedule (Airport model) Seat Count Airport Model Model Output Time in system Average and standard deviation of time in system Ticketing time Average and standard deviation of Ticketing time Average and standard deviation of E-ticketing time Waiting Time Average and standard deviation of waiting time in queue Maximum waiting time in queue Number waiting in queues Average and standard deviation of number waiting in queue Maximum number waiting in queue Passengers Count Airport Resources utilization OIA simulation model GUI An easy to use graphical user interface was developed and integrated with the simulation model and Excel sheets. The graphical user interface is used to: Input model data and parameters Populate/load the simulation model Run the simulation model Obtain and customize model output On-line help Model Validation The following approaches were used to validate the model: Regular interaction with airport SME to validate assumptions and results. The model results were compared to the actual system by running the model using June data and comparing the results obtained to the results visually observed within the real system. Ran numerous test scenarios

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posted: | 7/23/2011 |

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