1IME 6140 Dr. Larry MallakResources Used in a Project•Time•Labor• Equipment and facilities•Money/cash flowIME 6140 Dr. Larry MallakTime as a Resource• “Crash” a project w/ OT or outside help.• Estimate on normal and crashed schedule.• Costs of crashingIME 6140 Dr. Larry MallakCalculating Probabilistic Activity Times• Three Time Estimates– pessimistic (a)– most likely (m)– optimistic (b)IME 6140 Dr. Larry MallakFigure 5-13 The Statistical Distribution of all Possible Times for an ActivityIME 6140 Dr. Larry MallakActivity Expected Time and Variance22E6)(Var6)(6)4(T⎟⎠⎞⎜⎝⎛−==−=++=ababbmaσσIME 6140 Dr. Larry Mallak95 Percent Level• Task will be aor lower 5 percent of the time• Task will be bor greater 5 percent of the time3.3)( ab −=σ2IME 6140 Dr. Larry Mallak90 Percent Level• Task will be aor lower 10 percent of the time• Task will be bor greater 10 percent of the time6.2)( ab −=σIME 6140 Dr. Larry Mallak95 Percent Level (Alternative Interpretation)• Task will be between aand b95 percent of the time92.3)( ab −=σIME 6140 Dr. Larry Mallak90 Percent Level (Alternative Interpretation)• Task will be between aand b90 percent of the time29.3)( ab −=σIME 6140 Dr. Larry MallakFigure 5-14 An AON NetworkIME 6140 Dr. Larry MallakFigure 5-15 An MSP Version of a Sample Problem NetworkIME 6140 Dr. Larry MallakFigure 5-16 A Pert/CPM Network for the Day Care Project3IME 6140 Dr. Larry MallakFigure 5-17 An MSP Calendar for the Day Care Project, 4/16/00 to 5/27/00IME 6140 Dr. Larry MallakFigure 5-21 A Gantt Chart of a Sample ProjectIME 6140 Dr. Larry MallakFigure 5-22 A Gantt Chart of Sample Project Showing Critical Path, Path Connections, Slack, EST, LST, EFT, and LFTIME 6140 Dr. Larry MallakFigure 5-23 A Gantt Chart of a Day Care Project Showing Expected Durations, Critical Path, Milestone, and Resource RequirementsIME 6140 Dr. Larry MallakFigure 5-24 A Progress Report on a Day Care Project Showing Actual Progress Versus BaselineIME 6140 Dr. Larry MallakThe Probability of Completing the Project on Time2)(µσµ−=DZ=NORMDIST(D,µ,σµ,TRUE)4IME 6140 Dr. Larry MallakFigure 5-18 The Statistical Distribution of Completion Times of the Path a-b-d-g-hIME 6140 Dr. Larry MallakSelecting Risk and Finding D2µσµZD +=NORMINV(probability,µ,σµ,TRUE)IME 6140 Dr. Larry MallakCrash Activitieson the Critical Path.• If 2 paths are critical, find common activity.• Compute cost/time slope for each activity.• Crash to minimize costs.IME 6140 Dr. Larry MallakIME 6140 Dr. Larry Mallak IME 6140 Dr. Larry Mallak5IME 6140 Dr. Larry Mallak IME 6140 Dr. Larry MallakIME 6140 Dr. Larry MallakConstrained Resource Scheduling•Heuristics• OptimizationIME 6140 Dr. Larry MallakHeuristics inResource Scheduling• As soon as possible• As late as possible• Shortest task first• Most resources first• Minimum slack first• Most critical followers• Most successorsIME 6140 Dr. Larry MallakOptimization & Scheduling Effectiveness• Schedule slippage• Resource utilization• Amount of in-process inventory• Uses linear programmingIME 6140 Dr. Larry MallakEXPEDITING A PROJECT6IME 6140 Dr. Larry MallakIntroduction• Projects Compete With One Another for Resources– resources that are not consumed– resources that are consumed• Goal of Resource Allocation is to Optimize Use of Limited Supply• Requires making trade-offs– time constrained– resource constrainedIME 6140 Dr. Larry MallakThe Critical Path Method• Normal Duration Estimates•Normal Costs• Crash Duration Estimates•Crash Costs• Crash Cost Per DayCost Normal -Cost Crash DurationCrash -Duration NormalIME 6140 Dr. Larry MallakFigure 6-1(a) Gantt Chart Crash Problem -- 21-Day ProjectIME 6140 Dr. Larry MallakFigure 6-1(b) AON Network for Sample Crash Problem -- 21-Day ProjectIME 6140 Dr. Larry MallakFigure 6-2 Gantt Chart for 20-Day Solution to Crash ProblemIME 6140 Dr. Larry MallakFigure 6-3 Gantt Chart for 19-Day Solution to Crash Problem7IME 6140 Dr. Larry MallakFigure 6-4 Gantt Chart for 18-Day Solution to Crash ProblemIME 6140 Dr. Larry MallakFigure 6-5 Gantt Chart for 16-Day Solution to Crash ProblemIME 6140 Dr. Larry MallakFigure 6-6 Project Cost Versus Project Duration for Sample Crash ProblemIME 6140 Dr. Larry MallakProbabilistic Activity Durations•Three time estimates made for both normal resource loading and crash resource loading• Variance of normal activity may be different than variance of crash timeIME 6140 Dr. Larry MallakUsing Excel’s Solver to Crash a Project•Target Cell– minimize crashing costs• By Changing Cells– amount to crash activities– time events occur•Constraints– amount each activity can be crashed– precedence relationships– complete project by specified time– nonnegativityIME 6140 Dr. Larry MallakFigure 6-7 AOA Network of Sample “Crash” Problem8IME 6140 Dr. Larry MallakFigure 6-9 Cost/Duration Graph for Sample Crashing ProjectIME 6140 Dr. Larry MallakFast-Tracking a Project• Used Primarily in Construction Industry• Building phase started before design and planning phases completed• Particularly appropriate when large proportion of work is routineIME 6140 Dr. Larry MallakRESOURCE LOADINGIME 6140 Dr. Larry MallakResource Loading• Amount of specific resources that are scheduled for use on specific activities or projects at specific times.• Usually a list or table.IME 6140 Dr. Larry MallakFigure 6-10 Action Plan and Gantt Chart for Production of a VideotapeIME 6140 Dr. Larry MallakThe Charismatic VP• Subordinates have hard time saying no to well liked boss.• Leads to overcommitted subordinates.• Problem further compounded because more experienced workers tend to be most over worked.• One solution is to set specific limits on amount of overscheduling permitted.9IME 6140 Dr. Larry MallakRESOURCE LEVELINGIME 6140 Dr. Larry MallakFigure 6-11 Gantt Chart for Videotape Project, Adjusted for Client AvailabilityIME 6140 Dr. Larry MallakFigure 6-12 Resource Overallocation Report for Scriptwriter Showing all ActivitiesIME 6140 Dr. Larry MallakFigure 6-13 Graphic Resource Overallocation Report for ScriptwriterIME 6140 Dr. Larry MallakFigure 6-14 Resource Leveled Report for Scriptwriter Showing all ActivitiesIME 6140 Dr. Larry MallakFigure 6-15 Graphic Resource Leveled Report for Scriptwriter10IME 6140 Dr. Larry MallakFigure 6-16 Daily Resource Loading Chart for Videotape Project, Scriptwriter LeveledIME 6140 Dr.