1. Delays James R. Burns Fall 2010

2. 11/16/20152 Today Recitation Lecture Hands-on

3. 11/16/20153 Recitation What does it take to create a table lookup function in VENSIM The HW problem

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5. 5 Delays Delays always breed danger –Miguel de Cervantes (Don Quixote) Never do today what you can put off till tomorrow. Delay may give clearer light as to what is best to be done. –Arron Burr What does Peter Senge tell us about Delays in the book THE FIFTH DISCILPLINE?

6. 11/16/20156 Where can delays occur? In information channels (In the transmission of information) In flows (of people, resources, goods, money etc.)

7. 11/16/20157 Specific instances in which Delays can occur… aging populations, mail delays, perception delays, shipping delays, appearance delays, adjustment delays, scheduling delays and queue delays.

8. 11/16/20158 Flow Delays Pipeline (Boxcar) Exponential Third order First order

9. 11/16/20159 Some Flow Delays that we’ve already looked at

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12. 11/16/201512 Information Delays First order Smoothing

13. 11/16/201513 Recall the balancing loop structure

14. 11/16/201514 Boxcar Delay

15. 11/16/201515 Problems with Boxcar Delay Pipeline or boxcar delays are considered “pure” in the sense that no output is produced until the delay is over, or until the elapsed time is greater than the delay. Moreover, the output tends to be somewhat discontinuous, causing the model state (or, stock) trajectories to lack smoothness.

16. 11/16/201516 Exponential Delay

17. 11/16/201517 As previously mentioned, the boxcar approach tends to introduce discontinuities into the simulation model. To overcome this problem Forrester replaced the boxcars with levels or states separated by rates whose associated equations were determined to be r i = n * x i / D, where n is the order of the delay in terms of states and D is the length (in the time units of the simulation) of the delay.

18. 11/16/201518 Third-Order Exponential Delay

19. 11/16/201519 Information Delay

20. 11/16/201520 Delay functions in VENSIM DELAY3(input, delay time) – a third-order exponential delay Input should be a rate Output is returned through the name— DELAY3 Output will also be a rate—a delayed one Delay time must have consistent units with the VENSIM time variable

21. 11/16/201521 The structure of the DELAY3() function DL = delay time/3 LV1 = INTEGRAL(input-RT1, DL) RT1 = LV1/DL LV2 = INTEGRAL(RT1 – RT2, DL) RT2 = LV2/DL LV3 = INTEGRAL(RT2 – DELAY3, DL) DELAY3 = LV3/DL

22. 11/16/201522 Delay functions in VENSIM DELAY3I(input, delay time, initial value) Same as DELAY3() except each stock is loaded with an initial value of initial value/3 DELAY1(input, delay time) – a first-order exponential delay DELAY1I(input, delay time, initial value) – a first-order exponential delay with initial value)

23. 11/16/201523 More delay functions DELAY INFORMATION (input, delay time, initial value) – discrete information delay DELAY MATERIAL (input, delay time, initial value, missval) – discrete material or flow delay

24. 11/16/201524 Supply Chain 1

25. 11/16/201525 Supply Chain 2

26. 11/16/201526 Supply Chain 3

27. 11/16/201527 Supply Chain 4

28. 11/16/201528 Supply Chain 5

29. 11/16/201529 Supply Chain 6

30. 11/16/201530 Supply Chain 7

31. 11/16/201531 Supply Chain 8

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