Spreadsheet Demonstration Room Construction Simulation

2 Room construction simulation Winston 12.3  Tom, Lingley, and independent contractor, has agreed to build a new room on an existing house. He plans to begin work on Monday morning, June 1. The main question is when will he complete his work, given that he works only on weekdays. The owner of the house is particularly hopeful that the room will be ready by Saturday, June 27, that is, an 20 or fewer working days. Lingley has told the owner that he is “pretty sure” this deadline can be met. The work proceeds in stages, labeled A through J, as summarized in Table. Three of these activities, E, F, and G, will be done by separate independent

3 Room construction simulation Winston 12.3 (cont’) subcontractors. Lingley would like to use computer simulation to see (1) how long the project is likely to take, (2) how likely it is that the project will be completed by the deadline, and (3) which activities are likely to be critical.

4 Room construction simulation Winston 12.3 (cont’) DescriptionImmediate Predecessors Activity APrepare foundationNone Activity BPut up frameA Activity COrder custom windowsNone Activity DErect outside wallsB Activity EDo electrical wiringD Activity FDo plumbing D Activity GPut in duct workD Activity HHang dry wallE, E, G Activity IInstall windowsB, C Activity JPaint and clean upH DescriptionImmediate Predecessors Activity APrepare foundationNone Activity BPut up frameA Activity COrder custom windowsNone Activity DErect outside wallsB Activity EDo electrical wiringD Activity FDo plumbing D Activity GPut in duct workD Activity HHang dry wallE, E, G Activity IInstall windowsB, C Activity JPaint and clean upH

5 Room construction simulation Basic problem  A project consists of several activities  Precedence relationships exists between activities  Activity times are random  Important outputs include:  Length of time to complete the project  Which activities are “critical”  Whether a given deadline is met  A project consists of several activities  Precedence relationships exists between activities  Activity times are random  Important outputs include:  Length of time to complete the project  Which activities are “critical”  Whether a given deadline is met

6 Room construction simulation (See Excel “ProjectDiagram” sheet)  Project diagram illustrates precedence relationships  Diagram shown is of the “activity-on-node” type  Project diagram illustrates precedence relationships  Diagram shown is of the “activity-on-node” type

7 Room construction simulation Uncertainties  Each activity time is random  Assumptions are:  Distributions are all discrete  Random activity times are probabilistically independent  Each activity time is random  Assumptions are:  Distributions are all discrete  Random activity times are probabilistically independent

8 Room construction simulation Critical path, critical activities  We want to identify the critical (bottleneck) path through the diagram and the critical activities  With random activity times, there is only some probability a path (or activity) will be critical  This differs from the nonrandom case  We want to identify the critical (bottleneck) path through the diagram and the critical activities  With random activity times, there is only some probability a path (or activity) will be critical  This differs from the nonrandom case

9 Developing the spreadsheet model (See Excel “Step 1” sheet)  Step 1: Enter all of the activity time probability distributions  For VLOOKUP purposes, enter cumulative probabilities rather than individual probabilities  Give range names to the various “tables” of cumulative probabilities and activity times  Step 1: Enter all of the activity time probability distributions  For VLOOKUP purposes, enter cumulative probabilities rather than individual probabilities  Give range names to the various “tables” of cumulative probabilities and activity times

10 Developing the spreadsheet model (See Excel “Steps 2-4” sheet)  Step 2: Generate a random activity time for each activity using VLOOKUP formulas  Step 3: Calculate each path length from the start node to the finish node  Each is sum of activity times on that path  Step 4: Calculate the critical path length  This is the maximum of the path lengths  It’s the time required to complete the project  Step 2: Generate a random activity time for each activity using VLOOKUP formulas  Step 3: Calculate each path length from the start node to the finish node  Each is sum of activity times on that path  Step 4: Calculate the critical path length  This is the maximum of the path lengths  It’s the time required to complete the project

11 Developing the spreadsheet model (See Excel “Steps 5-7” sheet)  Step 5: Use IF formula to check if the deadline is met  Step 6: Use IF formulas to check, for each path, whether it’s critical  Step 7: Use IF formulas to check, for each activity, whether it’s critical  Step 5: Use IF formula to check if the deadline is met  Step 6: Use IF formulas to check, for each path, whether it’s critical  Step 7: Use IF formulas to check, for each activity, whether it’s critical

12 Developing the spreadsheet model (See Excel “Steps 8,9” sheet)  Step 8: Create a data table to replicate the simulation and keep track of:  Project length  Whether the deadline is met  Which activities are critical  Step 9: Calculate summary statistics from the replications in the data table  Step 8: Create a data table to replicate the simulation and keep track of:  Project length  Whether the deadline is met  Which activities are critical  Step 9: Calculate summary statistics from the replications in the data table

13 Developing the spreadsheet model (See Excel “ProbDist” sheet)  Based on the data table, use the FREQUENCY function to find the probability distribution of project length

14 Developing the spreadsheet model (See Excel “Chart 1” sheet)  Create a bar chart from the frequency table to show the project length distribution  It is “live,” so press the F9 key to see how it changes with new random numbers  Create a bar chart from the frequency table to show the project length distribution  It is “live,” so press the F9 key to see how it changes with new random numbers

15 Developing the spreadsheet model (See Excel “Chart 2” sheet)  Create a bar chart that shows, for each activity, the percentage of replications where it is critical  The activities with the large bars (A, B, D, H, J) are most likely to be bottleneck activities  If money were spent to speed up the project, these activities would be prime candidates  Create a bar chart that shows, for each activity, the percentage of replications where it is critical  The activities with the large bars (A, B, D, H, J) are most likely to be bottleneck activities  If money were spent to speed up the project, these activities would be prime candidates