To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Management OPIM 310-Lecture #9 Instructor: Jose Cruz

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Elements of Project Management Project team Project team Individuals from different departments within company Individuals from different departments within company Matrix organization Matrix organization Team structure with members from different functional areas depending on skills needed Team structure with members from different functional areas depending on skills needed Project manager Project manager Leader of project team Leader of project team

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Planning Statement of work Statement of work Written description of goals, work & time frame of project Written description of goals, work & time frame of project Activities require labor, resources & time Activities require labor, resources & time Precedence relationship shows sequential relationship of project activities Precedence relationship shows sequential relationship of project activities

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Planning Statement of work Statement of work written description of goals, work & time frame of project written description of goals, work & time frame of project Activities require labor, resources & time Activities require labor, resources & time Precedence relationship shows sequential relationship of project activities Precedence relationship shows sequential relationship of project activities Construct formsPour concrete 132 Simplified Project Network

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Elements of Project Planning Define project objective(s) Define project objective(s) Identify activities Identify activities Establish precedence relationships Establish precedence relationships Make time estimates Make time estimates Determine project completion time Determine project completion time Compare project schedule objectives Compare project schedule objectives Determine resource requirements to meet objective Determine resource requirements to meet objective

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Work Breakdown Structure Hierarchical organization of work to be done on a project Hierarchical organization of work to be done on a project Project broken down into modules Project broken down into modules Modules subdivided into subcomponents, activities, and tasks Modules subdivided into subcomponents, activities, and tasks Identifies individual tasks, workloads, and resource requirements Identifies individual tasks, workloads, and resource requirements

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Work Breakdown Structure Hierarchical organization of work to be done on a project Hierarchical organization of work to be done on a project Project broken down into modules Project broken down into modules Modules subdivided into subcomponents, activities, and tasks Modules subdivided into subcomponents, activities, and tasks Identifies individual tasks, workloads, and resource requirements Identifies individual tasks, workloads, and resource requirements Dinner PastaSauceSaladBreadWineSetting TableAtmosphere PurchasePurchasePurchasePurchasePurchaseSet tableLight candles Boil waterAdd tomatoWashButter topOpenTurn on music sauce/pastelettuce CookSautéDrainSliceTaste onion & garliclettuce DrainCoolTearHeatServe meatballslettuce Add Serve Add spices croutons/ Serve dressing Cook sauceMixServe Figure 6.1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Control All activities identified and included All activities identified and included Completed in proper sequence Completed in proper sequence Resource needs identified Resource needs identified Schedule adjusted Schedule adjusted Maintain schedule and budget Maintain schedule and budget Complete on time Complete on time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. A Gantt Chart Popular tool for project scheduling Popular tool for project scheduling Graph with bar for representing the time for each task Graph with bar for representing the time for each task Provides visual display of project schedule Provides visual display of project schedule Also shows slack for activities Also shows slack for activities Amount of time activity can be delayed without delaying project Amount of time activity can be delayed without delaying project

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. A Gantt Chart |||||||||| Activity Design house and obtain financing Lay foundation Order and receive materials Build house Select paint Select carpet Finish work MonthMonth Figure 6.2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. CPM/PERT Critical Path Method (CPM) Critical Path Method (CPM) DuPont & Remington-Rand (1956) DuPont & Remington-Rand (1956) Deterministic task times Deterministic task times Activity-on-node network construction Activity-on-node network construction Project Eval. & Review Technique (PERT) Project Eval. & Review Technique (PERT) US Navy, Booz, Allen & Hamilton US Navy, Booz, Allen & Hamilton Multiple task time estimates Multiple task time estimates Activity-on-arrow network construction Activity-on-arrow network construction

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. The Project Network Network consists of branches & nodes 132 BranchNode Figure 6.3

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Network Construction In AON, nodes represent activities & arrows show precedence relationships In AON, nodes represent activities & arrows show precedence relationships In AOA, arrows represent activities & nodes are events for points in time In AOA, arrows represent activities & nodes are events for points in time An event is the completion or beginning of an activity An event is the completion or beginning of an activity A dummy shows precedence for two activities with same start & end nodes A dummy shows precedence for two activities with same start & end nodes

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Network for a House Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house Figure 6.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Concurrent Activities 23 Lay foundation Order material (a)Incorrect precedence relationship (b)Correct precedence relationship 3 42 Dummy Layfoundation Order material 1 20 Figure 6.5

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Critical Path A path is a sequence of connected activities running from start to end node in network A path is a sequence of connected activities running from start to end node in network The critical path is the path with the longest duration in the network The critical path is the path with the longest duration in the network Project cannot be completed in less than the time of the critical path Project cannot be completed in less than the time of the critical path

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. The Critical Path A: = 9 months B: = 8 months C: = 8 months D: = 7 months Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. The Critical Path A: = 9 months B: = 8 months C: = 8 months D: = 7 months Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house The Critical Path

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. The Critical Path Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house Start at 3 months Start at 5 months 1 Finish at 9 months Start at 8 months Figure 6.6 Activity Start Times

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Early Times ES - earliest time activity can start ES - earliest time activity can start Forward pass starts at beginning of CPM/PERT network to determine ES times Forward pass starts at beginning of CPM/PERT network to determine ES times EF = ES + activity time EF = ES + activity time ES ij = maximum (EF i ) ES ij = maximum (EF i ) EF ij = ES ij - t ij EF ij = ES ij - t ij ES 12 = 0 ES 12 = 0 EF 12 = ES 12 - t 12 = = 3 months EF 12 = ES 12 - t 12 = = 3 months Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Computing Early Times ES 23 = max EF 2 = 3 months ES 23 = max EF 2 = 3 months ES 46 = max EF 4 = max 5,4 = 5 months ES 46 = max EF 4 = max 5,4 = 5 months EF 46 = ES 46 - t 46 = = 8 months EF 46 = ES 46 - t 46 = = 8 months EF 67 = 9 months, the project duration EF 67 = 9 months, the project duration Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Computing Early Times Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house (ES = 0, EF = 3) (ES = 5, EF = 8) (ES = 3, EF = 5) (ES = 3, EF = 4) (ES = 5, EF = 6)(ES = 6, EF = 7) (ES = 8, EF = 9) (ES = 5, EF = 5) Early Start and Finish Times

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Late Times LS - latest time activity can start & not delay project LS - latest time activity can start & not delay project Backward pass starts at end of CPM/PERT network to determine LS times Backward pass starts at end of CPM/PERT network to determine LS times LF = LS + activity time LF = LS + activity time LS ij = LF ij - t ij LS ij = LF ij - t ij LF ij = minimum (LS j ) LF ij = minimum (LS j )

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Computing Late Times LF 67 = 9 months LF 67 = 9 months LS 67 = LF 67 - t 67 = = 8 months LS 67 = LF 67 - t 67 = = 8 months LF 56 = minimum (LS 6 ) = 8 months LF 56 = minimum (LS 6 ) = 8 months LS 56 = LF 56 - t 56 = = 7 months LS 56 = LF 56 - t 56 = = 7 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LS 24 = LF 24 - t 24 = = 4 months LS 24 = LF 24 - t 24 = = 4 months Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Computing Late Times LF 67 = 9 months LF 67 = 9 months LS 67 = LF 67 - t 67 = = 8 months LS 67 = LF 67 - t 67 = = 8 months LF 56 = minimum (LS 6 ) = 8 months LF 56 = minimum (LS 6 ) = 8 months LS 56 = LF 56 - t 56 = = 7 months LS 56 = LF 56 - t 56 = = 7 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LF 24 = minimum (LS 4 ) = min(5, 6) = 5 months LS 24 = LF 24 - t 24 = = 4 months LS 24 = LF 24 - t 24 = = 4 months Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house ES = 3, EF = 5 LS = 3, LF = 5 ( ) ES = 5, EF = 8 LS = 5, LF = 8 ( ) ES = 3, EF = 4 LS = 4, LF = 5 ( ) ES = 0, EF = 3 LS = 0, LF = 3 ( ) ES = 5, EF = 5 LS = 5, LF = 5 ( ) ES = 5, EF = 6 LS = 6, LF = 7 ( ) ES = 8, EF = 9 LS = 8, LF = 9 ( ) ES = 6, EF = 7 LS =7, LF = 8 ( ) Early and Late Start and Finish Times Figure 6.9

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Activity Slack Activities on critical path have ES = LS & EF = LF Activities on critical path have ES = LS & EF = LF Activities not on critical path have slack Activities not on critical path have slack S ij = LS ij - ES ij S ij = LS ij - ES ij S ij = LF ij - EF ij S ij = LF ij - EF ij S 24 = LS 24 - ES 24 = = 1 month S 24 = LS 24 - ES 24 = = 1 month

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Activity Slack Data Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house ActivityLSESLFEFSlacks * * * * * * Critical path

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Activity Slack Data Lay foundation Design house and obtain financing Order and receive materials Dummy Finish work Select carpet Select paint Build house ActivityLSESLFEFSlacks * * * * * * Critical path Figure 6.10 Activity Slack S = 0 S = 1 S = 0

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Probabilistic Time Estimates Reflect uncertainty of activity times Reflect uncertainty of activity times Beta distribution is used in PERT Beta distribution is used in PERT a = optimistic estimate m = most likely time estimate b = pessimistic time estimate where Mean (expected time): t = a + 4 m + b 6 Variance:  2 = b - a 6 2

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Example Beta Distributions P(time) Time amtbamtb m = t Time Time ba Figure 6.11

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company System changeover Manual Testing Dummy System Training Dummy System Testing Orientation Position recruiting System development Equipment installation Equipment testing and modification Final debugging Job training a b cde f g h i jk l m Example 6.1

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Activity Estimates TIME ESTIMATES (WKS)MEAN TIMEVARIANCE ACTIVITY ambt 

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved Early and Late Times For Activity 1-2 a = 6, m = 8, b = 10 t = = = 8 weeks a + 4 m + b (8)  2 = = = week b - a

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved Early and Late Times ACTIVITY t   ESEFLSLFS

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company Example ES = 9, EF = 16 LS = 9, LF = 16 ES = 0, EF = 8 LS = 1, LF = 9 ES = 0, EF = 6 LS = 0, LF = 6 ES = 6, EF = 9 LS = 6, LF = 9 ES = 0, EF = 3 LS = 2, LF = 5 ES = 3, EF = 7 LS = 5, LF = 9 ES = 9, EF = 13 LS = 12, LF = 16 ES = 8, EF = 8 LS = 9, LF = 9 ES = 13, EF = 13 LS = 16, LF = 16 ES = 3, EF = 5 LS = 14, LF = 16 ES = 16, EF = 25 LS = 21, LF = 25 ES = 13, EF = 17 LS = 21, LF = 25 ES = 8, EF = 13 LS = 16, LF =

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Company Example ES = 9, EF = 16 LS = 9, LF = 16 ES = 0, EF = 8 LS = 1, LF = 9 ES = 0, EF = 6 LS = 0, LF = 6 ES = 6, EF = 9 LS = 6, LF = 9 ES = 0, EF = 3 LS = 2, LF = 5 ES = 3, EF = 7 LS = 5, LF = 9 ES = 9, EF = 13 LS = 12, LF = 16 ES = 8, EF = 8 LS = 9, LF = 9 ES = 13, EF = 13 LS = 16, LF = 16 ES = 3, EF = 5 LS = 14, LF = 16 ES = 16, EF = 25 LS = 21, LF = 25 ES = 13, EF = 17 LS = 21, LF = 25 ES = 8, EF = 13 LS = 16, LF =  2 =  2 +  2 +  2 +  2 = = 6.89 weeks Total project variance

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Probabilistic Network Analysis Determine probability that project is completed within specified time where  = t p = project mean time  =project standard deviation x =proposed project time Z =number of standard deviations x is from mean Z =Z =Z =Z = x -  

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Distribution Of Project Time

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Distribution Of Project Time  = t p Timex ZZProbability Figure 6.12

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Example What is the probability that the project is completed within 30 weeks? Example 6.2  = 25 Time (weeks) x = 30 P( x  30 weeks)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Example What is the probability that the project is completed within 30 weeks? Example 6.2  = 25 Time (weeks) x = 30 P( x  30 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = 1.91 x -  

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Example What is the probability that the project is completed within 30 weeks? Example 6.2  = 25 Time (weeks) x = 30 P( x  30 weeks)  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = 1.91 x -   From Table A.1, a Z score of 1.91 corresponds to a probability of Thus P(30) = =

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Example What is the probability that the project is completed within 22 weeks? Example 6.3  = 25 Time (weeks) x = 22 P( x  22 weeks)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Example What is the probability that the project is completed within 22 weeks? Example 6.3  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = x -    = 25 Time (weeks) x = 22 P( x  22 weeks)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Southern Textile Example What is the probability that the project is completed within 22 weeks? Example 6.3  2 = 6.89 weeks  = 6.89  = 2.62 weeks Z = = = x -   From Table A.1, a Z score of corresponds to a probability of Thus P(22) = =  = 25 Time (weeks) x = 22 P( x  22 weeks)

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Project Crashing Crashing is reducing project time by expending additional resources Crashing is reducing project time by expending additional resources Crash time is an amount of time an activity is reduced Crash time is an amount of time an activity is reduced Crash cost is the cost of reducing the activity time Crash cost is the cost of reducing the activity time Goal is to reduce project duration at minimum cost Goal is to reduce project duration at minimum cost

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Housebuilding Network Figure 6.15

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved Housebuilding Network $7,000 – $6,000 – $5,000 – $4,000 – $3,000 – $2,000 – $1,000 – – ||||||| Weeks Normal activity Normal time Normal cost

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved Housebuilding Network $7,000 – $6,000 – $5,000 – $4,000 – $3,000 – $2,000 – $1,000 – – ||||||| Weeks Crash cost Crashed activity Normal activity Normal timeCrash time Normal cost

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved Housebuilding Network $7,000 – $6,000 – $5,000 – $4,000 – $3,000 – $2,000 – $1,000 – – ||||||| Weeks Crash cost Crashed activity Normal activity Normal timeCrash time Normal cost Slope = crash cost per week Total crash cost$2,000 Total crash time5 = = $400 per week Figure 6.16

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Activity and Crash Data TOTAL NORMALCRASHALLOWABLECRASH TIMETIMENORMALCRASHCRASH TIMECOST PER ACTIVITY(WEEKS)(WEEKS)COSTCOST(WEEKS)WEEK $3,000$5,0005$ ,0003, ,0007,00013, , ,00071,00037, , ,00022,00017,000 $75,000$110,700 Example 6.4

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Activity and Crash Data TOTAL NORMALCRASHALLOWABLECRASH TIMETIMENORMALCRASHCRASH TIMECOST PER ACTIVITY(WEEKS)(WEEKS)COSTCOST(WEEKS)WEEK $3,000$5,0005$ ,0003, ,0007,00013, , ,00071,00037, , ,00022,00017,000 $75,000$110,700 Example $400 $500 $3,000$7,000 $200 $7,000

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Activity and Crash Data TOTAL NORMALCRASHALLOWABLECRASH TIMETIMENORMALCRASHCRASH TIMECOST PER ACTIVITY(WEEKS)(WEEKS)COSTCOST(WEEKS)WEEK $3,000$5,0005$ ,0003, ,0007,00013, , ,00071,00037, , ,00022,00017,000 $75,000$110,700 Example $400 $500 $3,000$7,000 $200 $7,000

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Activity and Crash Data TOTAL NORMALCRASHALLOWABLECRASH TIMETIMENORMALCRASHCRASH TIMECOST PER ACTIVITY(WEEKS)(WEEKS)COSTCOST(WEEKS)WEEK $3,000$5,0005$ ,0003, ,0007,00013, , ,00071,00037, , ,00022,00017,000 $75,000$110,700 Example $500 $3,000$7,000 $200 $7,000 Crash cost = $2,000

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Activity and Crash Data TOTAL NORMALCRASHALLOWABLECRASH TIMETIMENORMALCRASHCRASH TIMECOST PER ACTIVITY(WEEKS)(WEEKS)COSTCOST(WEEKS)WEEK $3,000$5,0005$ ,0003, ,0007,00013, , ,00071,00037, , ,00022,00017,000 $75,000$110,700 Example $500 $3,000$7,000 $200 $7,000 Crash cost = $2,000

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Normal Activity and Crash Data TOTAL NORMALCRASHALLOWABLECRASH TIMETIMENORMALCRASHCRASH TIMECOST PER ACTIVITY(WEEKS)(WEEKS)COSTCOST(WEEKS)WEEK $3,000$5,0005$ ,0003, ,0007,00013, , ,00071,00037, , ,00022,00017,000 $75,000$110,700 Example $500 $3,000$7,000 $200 $7,000 Crash cost = $2,000 + $500 = $2,500

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Crashing costs increase as project duration decreases Crashing costs increase as project duration decreases Indirect costs increase as project duration increases Indirect costs increase as project duration increases Reduce project length as long as crashing costs are less than indirect costs Reduce project length as long as crashing costs are less than indirect costs Time-Cost Relationship

To Accompany Russell and Taylor, Operations Management, 4th Edition,  2003 Prentice-Hall, Inc. All rights reserved. Time-Cost Tradeoff Cost ($) Project duration CrashingTime Minimum cost = optimal project time Total project cost Indirect cost Direct cost Figure 6.17