3044hw1s09 - the other unit is lost Round the uniform...

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1 ISyE 3044 – Spring 2009 Homework #1 — Due Friday, 23 January All problems will be graded. 1. Use the Monte Carlo method discussed in class with 20 pseudo-uniform(0 , 1) numbers to compute a point estimate and an approximate 90% confidence interval for the integral μ = integraldisplay 9 0 1 1 + t dt. Use random numbers from Table A.1, p. 577 of the text by BCN&N. Read two digits at a time and place a decimal in front to obtain a uniform(0 , 1) observation. Go from left to right and then down. For example, the first three numbers are 0.94, 0.73, and 0.70. 2. Study the inventory examples in Chapter 2 of BCN&N. The use Excel to build a simulation table similar to Table 2.21 for Exercise 7 in Chapter 2. Some columns are not needed because Excel contains functions for generating observations from statistical distributions. Assume that demands can be satisfied partially (without backordering). So, if the starting inventory during a day is 2 units and the demand is 3 units, only 2 units are sold and
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Unformatted text preview: the other unit is lost. Round the uniform realizations of the lead times to the nearest integers. Conduct 5 independent replications, each starting (in day 1) with 18 units in inventory and simulating 8 weeks (56 days). Each replication terminates at the end of day 56; so you can ignore outstanding orders. ±rom each replication collect estimates for the average amount of inventory at hand at the start of each day (after potential order deliveries) and the fraction of days a demand shortage occurs. Then use the averages from the 5 replications to compute an approximate 90% conFdence interval for the mean inventory level at the start of a day and the fraction of time a shortage occurs during the time period under study. Make sure that you can perform such a simulation by hand. Note: The site http://www.bus.ualberta.ca/aingolfsson/simulation contains many Ex-cel spreadsheets with queueing simulations....
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