Response of Delays to Changing Delay Times To develop your understanding of how the different types of delays respond to variations in the delay time, answer the following questions.

1. Consider a model of the post office as a third-order material delay (equation (11-4)). Assume that the mailing rate is constant and that the system is in equi- librium-the mailing rate and delivery rate are equal. Without using simulation, sketch the behavior you expect if the delay time suddenly and permanently in- creases from 5 days to 10 days on day 5. Make two graphs-one showing the

mailing rate and delivery rate and the other showing what you expect to happen to the stock of letters in transit. Sketch the response you would expect if the delay time suddenly dropped from 5 to 2.5 days.

2. Now consider a firm's forecast of orders. Assume the firm uses adaptive ex- pectations to forecast orders, equation (11-6). Assume that the order rate is con- stant and that the expected order rate is equal to the order rate (the system is in equilibrium). Without using simulation, sketch the behavior you expect if the time to adjust the forecast suddenly and permanently decreases from 6 months to

3 months. 3. After you've sketched your intuitive estimates, build the models and simu- late their response to changes in the delay time. Was your intuition correct? If there are differences in the response of the material and information delays to changes in the delay times, explain why.