Question 4 A local shopping mall loans out baby strollers to shoppers in order to enable shoppers with young children to have a better shopping experience. Due to limited space available at the concierge counter where the baby strollers are loaned and returned, it could only hold 3 baby strollers. The mall management conducts a simulation study to further understand the stroller's utilization. The time between successive arrivals of shoppers seeking to loan the baby stroller at the concierge is as shown in Table 4-1. The probability of stroller usage time is given in Table 4-2. Assume that the concierge counter opens at 11:00 A.M. and the first arrival is after this, based on the first inter-arrival time generated. Table 4-1 Time Between Probability Arrivals (in minutes) 15 0.3 30 0.3 45 0.2 60 0.2 Table 4-2 Usage Time Probability (in minutes) 30 0.4 60 0.3 90 0.2 120 0.1(a) Identify the corresponding interval of random numbers (in decimals) for "Time Between Arrivals" and "Usage Time" using the probability information given in Table 4-1 and Table 4-2, respectively. (If you need to draw a diagram or figure (and cannot do so in MS Word), take a picture of the image you have drawn and insert it in your answer. You are reminded that your overall file size of your submission of this TOA should not exceed 500MB. For a table, you are advised to copy the table given in the question or draw it in MS Word. For an equation, you are advised to write the equation in MS Word.) (8 marks) (b) Using the interval in Part (a), simulate the following 5 shoppers experience in loaning the baby strollers using the corresponding random numbers: 1 . Time Between Arrivals: 0.22, 0.67, 0.28, 0.73, 0.16. ii. Usage Time: 0.31, 0.97, 0.72, 0.26, 0.91 (If you need to draw a diagram or figure (and cannot do so in MS Word), take a picture of the image you have drawn and insert it in your answer. You are reminded that your overall file size of your submission of this TOA should not exceed 500MB. For a table, you are advised to copy the table given in the question or draw it in MS Word. For an equation, you are advised to write the equation in MS Word.) (5 marks)(c) Using the result in Part (b). simulate the loaning of baby strollers for the 5 consecutive shoppers using this table (copy the same table in your answer booklet) and interpret the result (in particular for situation(s) when a baby stroller is not available when the shopper arrives at the concierge). If no stroller is available at arrival, customers will leave without the loan. Time between Arrival Number of Stroller Loan Out Usage Time - Stroller Returned Arrivals - Time Stroller Time, Indicate Simulation Time, Indicate Shopper Simulation (Indicate Available clock time Results from clock time Results from clock time) (0,1,2 or 3) (NA if no stroller Part (b) (NA if no stroller Part (b) is available) is loaned) (If you need to draw a diagram or figure (and cannot do so in MS Word), take a picture of the image you have drawn and insert it in your answer. You are reminded that your overall file size of your submission of this TOA should not exceed 500MB. For a table, you are advised to copy the table given in the question or draw it in MS Word. For an equation, you are advised to write the equation in MS Word.) (12 marks)
