Question

Figure 6S-1 Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below. Range Interarrival (min) Service (min) 0.000-0.200 3 6 0.201-0.400 6 7 0.401-0.600 9 8 0.601-0.800 12 9 0.801-1.000 15 10 The stream of random number for a Monte Carlo simulation of the system appear in this table> Interarrival Service .114 .979 .899 .297 .925 .162 .085 .574 .824 .235 .151 .593 .223 .956 .477 .845 Use the data from Figure 6S-1. What is the total time that customers must wait from 8:00 am to 9:15 am?

Answers: 18 minutes 17 minutes 20 minutes 19 minutes

Answer 1

Below is the screenshot of the calculation performed in excel to find the waiting time.

Book1 Excel File Home Insert Page Layout Formulas Data Review View Help Tell me what you want to do Wrap Text 11 A A Calibri Number Merge & Center. s-% , s:s: Conditional Format as Cell Formatting Table Styles Paste Ξ-- 00 3.0 Format Painter Font Clipboard Alignment Number Styles АЗ 82+0.001 Range Interarrival Time (min) Service Time (Min 2 0.000 0.200 3 0.201 0.400 0.401 0.600 5 0.601 0.800 12 10 0.801 1.000 15 8 Simulation 9 Customer Interarrival Interarrival Time Arrival Time Service Time Service Start Time Completion Time Waiting Time Service 10 13 10 0.114 0.979 0.899 0.297 15 39 0.925 0.162 15 39 47 0.085 0.574 36 51 51 0.824 0.235 15 0.151 0.593 0.223 10 16 0.956 76 10 17 0.477 0.845 69 76

From Above, Total Waiting Time = 20 minutes

Below is the screenshot of the formula applied -

日勺. E Book1-Excel Abhishek Rai Insert Page Layout Formulas Data Review View Help Tell me what you want to do File Σ AutoSum . 三9-2므 Wrap Text E Copy Paste Merge & Certer . $ % , 留, Conditional Format as. Cell ormatting Table Styles Insert Delete Format B 1 u . 田·ク·a--Ξ-EAE Blu-E·ク Format Painter Clear. Clipboard Font Editing Alignment Number Styles Cells F3 Service Time (Min) Range Interarrival Time (min) 0.2 B2+0.001 0.4 B3+0.001 5 B4+0.001 0.8 12 6 B5+0.001 1 15 8 Simulation 9 Customer Interarrival Interrrival Time Service Time Service Start Time Completion Time Waiting Time Service Arrival Time F10+G10 G10-E10 G11-E11 10 1 0.114 0.979 11 2 0.899 0.297 LOOKUP(B11,SAS2:SAS6,SCS2:SC$6) -D1+E10 LOOKUPIC11,SAS2.SAS6, LOOKUP(B12,SAŚ2:SA$6,SCS2:SC$6) -D12+E11FLOOKUP(C12,SAS2:SAS6,SD$2.SDS6)-MAX(H11,E12)F LOOKUP(B13,SAS2:SAS6,SCS2.SCS6)-D13+E12FLOOKUP(C13,SAS2:SAS6,SDS2:SDS6) MAX(H12,E13)F13+G13 12 3 0.925 0.162 G12-E12 -G13-E13 13 4 0.085 0.574 14 5 0.824 0.235 G14-E14 0.151 15 6 0.593 G15-E15 LOOKUP(B16,SAS2:SA$6,SC$2:5C$6) -D16+E15 =LOOKUP( B17,$AS2:$AS6,$CS2:SCS6)-D17+E16 LOOKUP(C16,SA$2.SAS6,SDS2:SDS6) -MAX(H15.E16 -F16+616 |=LOOKUP(C17,SAS2:SAS6,SDS2:SDS6)-MAX(H16,E17) -f174G17 0.956 16 7 0.223 -G16-E16 0.845 17 8 -G17-E17 0.477 SUM(110:117) 18