SIMULATION TECHNIQUES

1. SIMULATION TECHNIQUES

2. Introduction What is digital simulation? • Design a model for a real or proposed system • Execute the model on a computer • Analyze the execution output Purpose of digital simulation • Evaluate the behavior of the system under different sets of conditions by using the models to carry out groups of experiments

3. Advantage of digital simulation • Cost reduction and time saving: draw inference about new systems without actually building them and evaluate changes in existing systems without actually disturbing them. • The only tool that will allow system interactions to be analyzed for complex systems. • Permits managers to visualize the operation of a new or existing system under a variety of conditions.

4. Objective of the course • Digital simulation modeling using SIMAN/ARENA • System Applications of digital simulation • Performance analysis of manufacturing and service systems and processes

5. What is a system? A collection of elements that cooperate to accomplish some stated objectives. • Examples: • Bank tellers + customer queues • Supermarket cashiers + customer queues • Hospital emergency room + patients • Machines + parts • Cities + Highways • Telephones + connection networks • Materials + handling equipment

6. What is a model? A collection of symbols and ideas that approximately represent the functional relationship of the elements in a system. Examples: • Queuing models: queues, servers, interarrival times, service times, distributions,... • Network models: nodes, links, traveling times, capacities,...

7. Types of Simulation • Discrete simulation: State of system changes only at “discrete event” times. Examples: Customers arrive at a bank branch; parts moving in a production systems; trucks travel on a highway network; … • Continuous simulation: State of system represented by algebraic or differential equations with variables that change continuously over time. Examples: Nuclear reactions; chemical processes; ocean waves, etc. • Mixed simulation: The system has discrete elements as well as continue elements. Examples: Metal moulding and casting, ecosystems, etc. • Dynamic simulation: The system status changes over time. • Stochastic simulation: Models operate with random inputs.

8. What simulation can do for you: • Provide estimates of the statistics of system performance • Evaluate the effects of system condition changes What simulation cannot do for you: • It cannot optimize the system’s performance; it can only describe the system behavior under the given conditions • It cannot provide accurate simulation results if the data and the model are not accurate

9. Modeling strategy • Start with simple models and evolve to complex ones • Focus on important issues and screen out unimportant issues

10. People Involved in a Simulation Project • Simulationproject team • System design team • Data/information sources • Implementation team • Contractors • Decision maker/management • Establish Responsibility • Project manager • Representatives from each major groups • Project milestones and checkpoints

11. Stages of Simulation Modeling and Analysis • Identify Problem • State Objectives • Collect/Prepare Data • Formulate Model • Verify/Validate Model • Modify/Refine Model (Repeat the previous two steps if necessary) • Simulation Experiment Design • Simulation Execution • Output Analysis and Interpretation of Results • Conclusions and Implementation

12. Machine (Server) Arriving Blank Parts Departing Finished Parts 7 6 5 4 Queue (FIFO) Part in Service A Simple Processing System • General intent: • Estimate expected production • Waiting time in queue, queue length, proportion of time machine is busy • Time units • Can use different units in different places … must declare • Be careful to check the units when specifying inputs • Declare base time units for internal calculations, outputs • Be reasonable (interpretation, roundoff error)

13. Model Specifics • Initially (time 0) empty and idle • Base time units: minutes • Input data (assume given for now …), in minutes: Part Number Arrival Time Interarrival Time Service Time 1 0.00 1.73 2.90 2 1.73 1.35 1.76 3 3.08 0.71 3.39 4 3.79 0.62 4.52 5 4.41 14.28 4.46 6 18.69 0.70 4.36 7 19.39 15.52 2.07 8 34.91 3.15 3.36 9 38.06 1.76 2.37 10 39.82 1.00 5.38 11 40.82 . . . . . . . . . . • Stop when 20 minutes of (simulated) time have passed

14. Output Performance Measures • Total production of parts over the run (P) • Average waiting time of parts in queue: • Maximum waiting time of parts in queue: N = no. of parts completing queue wait WQi = waiting time in queue of ith part Know: WQ1 = 0 (why?) N> 1 (why?)

15. Output Performance Measures • Time-average number of parts in queue: • Maximum number of parts in queue: • Average and maximum total time in system of parts (a.k.a. cycle time): Q(t) = number of parts in queue at time t TSi = time in system of part i

16. Output Performance Measures • Utilization of the machine (proportion of time busy) • Many others possible (information overload?)

17. Simulation by Hand:Setup

18. Simulation by Hand:t = 0.00, Initialize

19. Simulation by Hand:t = 0.00, Arrival of Part 1 1

20. Simulation by Hand:t = 1.73, Arrival of Part 2 2 1

21. Simulation by Hand:t = 2.90, Departure of Part 1 2

22. Simulation by Hand:t = 3.08, Arrival of Part 3 3 2

23. Simulation by Hand:t = 3.79, Arrival of Part 4 4 3 2

24. Simulation by Hand:t = 4.41, Arrival of Part 5 5 4 3 2

25. Simulation by Hand:t = 4.66, Departure of Part 2 5 4 3

26. Simulation by Hand:t = 8.05, Departure of Part 3 5 4

27. Simulation by Hand:t = 12.57, Departure of Part 4 5

28. Simulation by Hand:t = 17.03, Departure of Part 5

29. Simulation by Hand:t = 18.69, Arrival of Part 6 6

30. Simulation by Hand:t = 19.39, Arrival of Part 7 7 6

31. Simulation by Hand:t = 20.00, The End 7 6

32. Simulation by Hand:Finishing Up • Average waiting time in queue: • Time-average number in queue: • Utilization of drill press:

33. Comparing Alternatives • Usually, simulation is used for more than just a single model “configuration” • Often want to compare alternatives, select or search for the best (via some criterion) • Simple processing system: What would happen if the arrival rate were to double? • Cut interarrival times in half • Rerun the model for double-time arrivals • Make five replications

34. Results: Original vs. Double-Time Arrivals • Original – circles • Double-time – triangles • Replication 1 – filled in • Replications 2-5 – hollow • Note variability • Danger of making decisions based on one (first) replication • Hard to see if there are really differences • Need: Statistical analysis of simulation output data

35. SIMAN SIMULATION LANGUAGE A complete SIMAN model consists of a MODEL frame and an EXPERIMENT frame. • The Model Frame:Describes the logical flow of events within the system. The program should have the extension MOD (i.e., filename.MOD). Statements in the MODEL file are called BLOCKS. • The Experiment Frame:Specifies the experimental conditions for executing the model. The program should have the extension EXP (i.e., filename.EXP). Statements in the EXPERIMENT file are called ELEMENTS.

36. TEXT NAME.MOD NAME.M SIMAN RUNTIME PROCEDURE TEXT NAME.EXP MODEL EXPMT NAME.E LINKER NAME.P SIMAN NAME.OUT

37. BASIC SIMAN MODELING • ENTITIES: Items that flow through a system, such as customers, parts, trucks, etc. • QUEUES: Waiting areas where the movement of entities is temporarily suspended. • RESOURCES: System components that may be allocated to entities, such as machines, workers, bank tellers, etc. • ATTRIBUTES: Represent values associated with individual entities, such as job type, arrival times, etc. • GLOBAL VARIABLES: Represent values that describe the state of the system, such as number of job in the system, number of machines available, shift number, etc.

38. Type 1 arrivals Out Type 2 arrivals Buffer Machine Example 1: The single Machine Problem A single-Machine job shop processes two distinct products (or part types). Type 1 parts arrive every 10 minutes and require 4 minutes to process on the machine. Type 2 parts begin to arrive at time 5 and continue arriving every 6 minutes thereafter. Each type 2 part requires 3 minutes to process. Determine the number of parts of each type that are processed in one 8-hour shift.

39. MODELING STRATEGY • Individual parts are entities • JobType and ProcessTime are attributes • Buffer is a queue • Machine is a resource • Time units are in minutes

40. FLOW LOGIC • CREATE arriving jobs • ASSIGN values to ProcessTime and JobType • QUEUE the jobs for the machine in the Buffer • SEIZE the machine • DELAY by ProcessTime • RELEASE the machine • COUNT the JobType completed • DISPOSE of the finished jobs

41. THE EXPERIMENT FILE: SM.EXP BEGIN; ;Single machine job shop PROJECT, Single Machine, CIS 441; ATTRIBUTES: 1, JobType: 2, ProcessTime; RESOURCES: 1, Machine, capacity(1); QUEUES: 1, Buffer; COUNTERS: 1, Type 1 Job Count: 2, Type 2 Job Count; REPLICATE, 1, 0, 480; END;

43. THE SIMULATION RESULTS: SM.OUT Project: Single Machine Analyst: CIS 441 Simulation run ended at time: 480.0 COUNTERS Identifier Count Limit Type 1 Job Count 48 Infinite Type 2 Job Count 79 Infinite

44. Example 2: Modified SM Problem Modify the single machine model such that the time between arrivals is exponentially distributed with means of 10 minutes and 6 minutes for job types 1 and 2 respectively. The processing times are uniformly distributed between 2 and 6 minutes for part type 1 and between 1.5 and 4.5 minutes for part type 2. Collect statistics on the machine utilization, number of jobs waiting, job flowtime, and time between exits.

45. THE EXPERIMENT FILE: SM2.EXP BEGIN; ;Modified single machine job shop PROJECT, Single Machine, CIS 441; ATTRIBUTES: JobType: ProcessTime: ArrTime; RESOURCES: Machine; QUEUES: Buffer; COUNTERS: Type 1 Job Count: Type 2 Job Count; TALLIES: Flowtime: ExitPeriod; DSTATS: NQ(Buffer), Queue Length: NR(Machine), Machine Utilization; REPLICATE, 1, 0, 480; END;

47. THE SIMULATION RESULTS: SM2.OUT Project: Single Machine Analyst: CIS 441 Simulation run ended at time: 480.0 TALLY VARIABLES Identifier Average Variation Minimum Maximum Observations Flowtime 7.6548 .56697 1.5940 18.866 116 ExitPeriod 4.1138 .61447 1.5089 18.022 115 DISCRETE CHANGE VARIABLES Identifier Average Variation Minimum Maximum Final Value Queue Length 1.0583 1.1847 .00000 5.0000 1.0000 Machine Utilization .80701 .48902 .00000 1.0000 1.0000 COUNTERS Identifier Count Limit Type 1 Job Count 43 Infinite Type 2 Job Count 73 Infinite

48. HW #1 • Reading Chapters 1 and 2 • 2-4 • 2-5 • Consider a manufacturing system comprising two different machines and a single operator who is shared between the two machines. Parts arrive with an exponentially distributed interarrival time with a mean of 3 minutes. The arriving parts are one of two types. Sixty percent of the arriving parts are type 1and are processed on machine 1. These parts require the operator for a one-minute setup operation. The remaining 40 percent are part type 2 and are processed on machine 2. These parts require the operator for a 1.5-minute setup operation. The service times (excluding the setup time) are normally distributed with a mean of 4.5 minutes and a standard deviation of 1 minute for type 1 parts and a mean of 7.5 minutes and a standard deviation of 1.5 minutes for type 2 parts. • Two different priority schemes have been proposed for allocating the operator between the two types of waiting jobs. The first scheme is to assign priority to the type 1 jobs. Under this proposal, a job type 2 setup will only be performed if there is no type 1 setups waiting to be performed. The second proposed scheme is to alternate the priority between the two job types. • Simulate each of these systems, using SIMAN language, for a 80-hour period; and collect statistics on the machine and operator utilization, the average number of parts waiting for each machine, and the average flow time for all parts.