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Planning of Barus & Holley Addition

Planning of Barus & Holley Addition. Activity Duration, Days Predecessors. P rocurement. 215. S ite P reparation. 60. P our F oundation. 31. SP. E rect S teel . 15. P, PF. R oof, E xt. W all. 40. ES. F abricate G lass. 50. ES. I nt W alls & G l. 85. REW.

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Planning of Barus & Holley Addition

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  1. Planning of Barus & Holley Addition Activity Duration, Days Predecessors Procurement 215 Site Preparation 60 Pour Foundation 31 SP Erect Steel 15 P, PF Roof, Ext. Wall 40 ES Fabricate Glass 50 ES Int Walls & Gl. 85 REW Landscaping 55 REW Acquire Furn. 280 Install Furn. 15 IWG, AF, FG

  2. Arrow Diagram (Network) Nodes (I) = Events Arrows (I,J) = Activities (Tasks) 2 5 PF L REW SP IWG P ES FG 9 3 4 1 6 7 AF IF 8

  3. ES(I) = Earliest Start of Activities emanating from node I Forward Pass: Find ES(I) 60 270 2 5 PF L REW SP IWG P ES FG 9 3 4 1 6 7 370 215 230 280 355 0 AF IF 8 355

  4. LC(I) = Latest Completion of Activities terminating at Node I. Backward Pass: Find LC(I) 184 270 60 270 2 5 PF L REW SP IWG P ES FG 9 3 4 1 6 7 370 215 230 280 355 0 215 230 370 355 0 355 AF IF 8 355 355

  5. Determining the Critical Path An Activity (I,J) is on the Critical Path if the following three conditions are met: ES(I) = LC(I) ES(J) = LC(J) ES(J) – ES(I) = LC(J) – LC(I) = D(I,J) where D(I,J) is the duration of Activity (I,J).

  6. 8 Identify Critical Path 184 270 60 270 2 5 PF L REW SP IWG P ES FG 9 3 4 1 6 7 370 215 230 355 280 0 215 370 230 355 355 0 AF IF 355 355

  7. Determining the Slack Times (Floats) The Slack Time, ST(I,J), of an Activity (I,J) is the difference between the maximum time available to perform the Activity (i.e. LC(J) – ES(I)) and its duration D(I,J); that is, ST(I,J) = LC(J) – ES(I) – D(I,J). For Activities on the Critical Path the Slack Time is zero.

  8. 8 Determine Slack Times 184 270 60 270 2 5 L (45) SP(124) PF(124) REW IWG ES P P FG(75) 9 3 4 1 6 7 370 215 230 355 280 0 215 370 230 355 355 0 AF(75) IF 355 355

  9. Construct Time Chart 1 3 4 5 7 9 8 1 2 2 3 4 6 5 9 1 8 0 100 200 300 400 Elapsed Time, Days Critical Tasks Non-Critical Tasks

  10. Schedule Project 1 3 4 5 7 9 8 SP 1 2 PF 2 3 FG 4 6 L 5 9 AF 1 8 0 100 200 300 400 Elapsed Time, Days

  11. MODEL: SETS: TASKS / START, PROCUREMENT, SITE_PREPARATION, POUR_FOUNDATION, ERECT_STEEL, ROOF_EXT_WALL, FABRICATE_GLASS, INT_WALLS_GLASS, LANDSCAPING, ACQUIRE_FURN, INSTALL_FURN, FINISH/: TIME, ES, LS, SLACK; PRED( TASKS, TASKS) / START, SITE_PREPARATION, START, PROCUREMENT, START, ACQUIRE_FURN, SITE_PREPARATION, POUR_FOUNDATION, PROCUREMENT, ERECT_STEEL, POUR_FOUNDATION, ERECT_STEEL, ERECT_STEEL, ROOF_EXT_WALL, ERECT_STEEL, FABRICATE_GLASS, ROOF_EXT_WALL, INT_WALLS_GLASS, FABRICATE_GLASS, INSTALL_FURN, ROOF_EXT_WALL, LANDSCAPING, INT_WALLS_GLASS, INSTALL_FURN, ACQUIRE_FURN, INSTALL_FURN, LANDSCAPING, FINISH, INSTALL_FURN, FINISH /; ENDSETS LINGO Model: Tasks

  12. LINGO Model: Data DATA: TIME = 0, 215, 60, 31, 15, 40, 50, 85, 55, 280, 15 ,0; ENDDATA

  13. LINGO Model: Algorithm @FOR( TASKS( J)| J #GT# 1: ES( J) = @MAX( PRED( I, J): ES( I) + TIME( I))); @FOR( TASKS( I)| I #LT# LTASK: LS( I) = @MIN( PRED( I, J): LS( J) - TIME( I))); @FOR( TASKS( I): SLACK( I) = LS( I) - ES( I)); ES( 1) = 0; LTASK = @SIZE( TASKS); LS( LTASK) = ES( LTASK); END

  14. LINGO Solution: Input Data Feasible solution found at step: 0 Variable Value LTASK 12.00000 TIME( START) 0.0000000 TIME( PROCUREMENT) 215.0000 TIME( SITE_PREPARATION) 60.00000 TIME( POUR_FOUNDATION) 31.00000 TIME( ERECT_STEEL) 15.00000 TIME( ROOF_EXT_WALL) 40.00000 TIME( FABRICATE_GLASS) 50.00000 TIME( INT_WALLS_GLASS) 85.0000 TIME( LANDSCAPING) 55.00000 TIME( ACQUIRE_FURN) 280.0000 TIME( INSTALL_FURN) 15.0000 TIME( FINISH) 0.0000000

  15. LINGO Solution: Earliest Starts ES( START) 0.0000000 ES( PROCUREMENT) 0.0000000 ES( SITE_PREPARATION) 0.0000000 ES( POUR_FOUNDATION) 60.00000 ES( ERECT_STEEL) 215.0000 ES( ROOF_EXT_WALL) 230.0000 ES( FABRICATE_GLASS) 230.0000 ES( INT_WALLS_GLASS) 270.0000 ES( LANDSCAPING) 270.0000 ES( ACQUIRE_FURN) 0.0000000 ES( INSTALL_FURN) 355.0000 ES( FINISH) 370.0000

  16. LINGO Solution: Latest Starts Latest Start is defined by LS(I,J) = LC(I,J) – D(I,J). LS( START) 0.0000000 LS( PROCUREMENT) 0.0000000 LS( SITE_PREPARATION) 124.0000 LS( POUR_FOUNDATION) 184.0000 LS( ERECT_STEEL) 215.0000 LS( ROOF_EXT_WALL) 230.0000 LS( FABRICATE_GLASS) 305.0000 LS( INT_WALLS_GLASS) 270.0000 LS( LANDSCAPING) 315.0000 LS( ACQUIRE_FURN) 75.00000 LS( INSTALL_FURN) 355.0000 LS( FINISH) 370.0000

  17. LINGO Solution: Slack Times SLACK( START) 0.0000000 SLACK( PROCUREMENT) 0.000000 SLACK( SITE_PREPARATION) 124.0000 SLACK( POUR_FOUNDATION) 124.0000 SLACK( ERECT_STEEL) 0.0000000 SLACK( ROOF_EXT_WALL) 0.0000000 SLACK( FABRICATE_GLASS) 75.00000 SLACK( INT_WALLS_GLASS) 0.0000000 SLACK( LANDSCAPING) 45.00000 SLACK( ACQUIRE_FURN) 75.00000 SLACK( INSTALL_FURN) 0.0000000 SLACK( FINISH) 0.0000000

  18. CPM with Crashing: LINGO Model (a) MODEL: ! A CPM model with crashing; SETS: TASKS / START, PROCUREMENT, SITE_PREPARATION, POUR_FOUNDATION, ERECT_STEEL, ROOF_EXT_WALL, FABRICATE_GLASS, INT_WALLS_GLASS, LANDSCAPING, ACQUIRE_FURN, INSTALL_FURN, FINISH/: TIME, ! Normal time for task; TMIN, ! Min time at max crash; CCOST, ! Crash cost/unit time; EF, ! Earliest finish; CRASH; ! Amount of crashing;

  19. Accessing LINGO Go to: Engineering Instructional Computer Facility Prince Engineering Laboratory Balcony (Enter from Brook Street; follow corridor to third stairwell on the right, go up two flights of stairs) Logon: Name: First 6 characters of last name followed by first and second letters of first name. Password: Rightmost 6 numbers and letters of student ID number. Open Lingo: Go to the Start menu.

  20. PRINCE LAB COMPUTING FACILITY LINK TO Logon FAQ

  21. CPM with Crashing: LINGO Model (b) ! Here are the precedence relations; PRED( TASKS, TASKS)/ START, SITE_PREPARATION, START, PROCUREMENT, START, ACQUIRE_FURN, SITE_PREPARATION, POUR_FOUNDATION, PROCUREMENT, ERECT_STEEL, POUR_FOUNDATION, ERECT_STEEL, ERECT_STEEL, ROOF_EXT_WALL, ERECT_STEEL, FABRICATE_GLASS, ROOF_EXT_WALL, INT_WALLS_GLASS, FABRICATE_GLASS, INSTALL_FURN, ROOF_EXT_WALL, LANDSCAPING, INT_WALLS_GLASS, INSTALL_FURN, ACQUIRE_FURN INSTALL_FURN, LANDSCAPING, FINISH, INSTALL_FURN, FINISH /; ENDSETS

  22. CPM with Crashing: LINGO Model (c) DATA: TIME = 0, 215, 60, 31, 15, 40, 50, 85, 55, 280, 15, 0; ! Normal times; TMIN = 0, 195, 50, 28, 12, 35, 45, 50, 40, 240, 13, 0; ! Crash times; CCOST = 0, 2, 3, 3, 4, 4, 5, 3, 2, 1, 2, 0; ! Cost ($K)/day to crash; DUEDATE = 348; ! Project due date; ENDDATA

  23. CPM with Crashing: LINGO Model (d) ! The crashing LP model; ! Define earliest finish, each predecessor of a task constrains when the earliest time the task can be completed. The earliest the preceding task can be finished plus the time required for the task minus any time that could be reduced by crashing this task.; @FOR( PRED( I, J): EF( J) >= EF( I) + TIME( J) - CRASH( J) );

  24. CPM with Crashing: LINGO Model (e) ! For each task, the most it can be crashed is the regular time of that task minus minimum time for that task; @FOR( TASKS( J): CRASH( J) <= TIME( J) - TMIN( J) ); ! Meet the due date; ! This assumes that there is a single last task; EF( @SIZE( TASKS)) <= DUEDATE;

  25. CPM with Crashing: LINGO Model (f) ! Minimize the sum of crash costs; MIN = @SUM( TASKS: CCOST * CRASH); END

  26. CPM with Crashing: LINGO Solution Optimal solution found at step: 13 Objective value: 44.00000 Variable Value Reduced Cost EF( START) 0.0000000 2.000000 EF( PROCUREMENT) 195.0000 0.0000000 EF( SITE_PREPARATION) 60.00000 0.0000000 EF( POUR_FOUNDATION) 91.00000 0.0000000 EF( ERECT_STEEL) 210.0000 0.0000000 EF( ROOF_EXT_WALL) 250.0000 0.0000000 EF( FABRICATE_GLASS) 335.0000 0.0000000 EF( INT_WALLS_GLASS) 335.0000 0.0000000 EF( LANDSCAPING) 305.0000 0.0000000 EF( ACQUIRE_FURN) 280.0000 0.0000000 EF( INSTALL_FURN) 348.0000 0.0000000 EF( FINISH) 348.0000 0.0000000

  27. CPM with Crashing: LINGO Solution(Crash Times) Variable Value Reduced Cost CRASH( START) 0.0000000 0.0000000 CRASH( PROCUREMENT) 20.00000 0.0000000 CRASH( SITE_PREPARATION) 0.0000000 3.000000 CRASH( POUR_FOUNDATION) 0.0000000 3.000000 CRASH( ERECT_STEEL) 0.0000000 2.000000 CRASH( ROOF_EXT_WALL) 0.0000000 2.000000 CRASH( FABRICATE_GLASS) 0.0000000 5.000000 CRASH( INT_WALLS_GLASS) 0.0000000 1.000000 CRASH( LANDSCAPING) 0.0000000 2.000000 CRASH( ACQUIRE_FURN) 0.0000000 1.000000 CRASH( INSTALL_FURN) 2.000000 0.0000000 CRASH( FINISH) 0.0000000 0.0000000

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