Bragg\'s Bakery is building a new automated bakery in downtown Sandusky. Here ar

Question

Bragg's Bakery is building a new automated bakery in downtown Sandusky. Here are the activities that need to be completed to get the new bakery built and the equipment installed. Identify the critical path. CircleDotA-C-D-F bigcircA-B-D-F bigcircA-C-E-F What is the normal project length? What is the project length if all activities are crashed to their minimum? Bragg's loses $4,600 in profit per week for every week the bakery is not completed. How many weeks will the project take if we are willing to pay crashing cost as long as it is less than $4,600 for crashing individual activity?

Explanation / Answer

Activity Predecessor Activity Time ES EF LS LF Slack A None 6 0 6 0 6 0 Critical Path Activity B A 3 6 9 7 10 1 C A 4 6 10 6 10 0 Critical Path Activity D B,C 8 10 18 10 18 0 Critical Path Activity E C 5 10 15 13 18 3 F D,E 4 18 22 18 22 0 Critical Path Activity ES = E of Tail Event EF = ES + Activity Duration LF = L of Head Event LS = LF - Activity Duration Slack - LS - ES E = Earliest occurrence time for the event L = Latest allowable time for the occurrence of event Paths Weeks Duration A-B-D-F 6+3+8+4 21 A-C-D-F 6+4+8+4 22 Critical Path A-C-E-F 6+4+5+4 19 The Critical path is A-C-D-F with estimated duration of 22 weeks Normal Project Length - 22 weeks Activity Normal Time Crash Time Crash Cost/Week Reduction a b c a-b A 6 2 $3,500.00 4 B 3 2 $3,400.00 1 C 4 3 $4,700.00 1 D 8 6 $2,400.00 2 E 5 4 $3,200.00 1 F 4 3 $2,300.00 1 New Duration of Each Path Paths Weeks Duration A-B-D-F 2+2+6+3 13 A-C-D-F 2+3+6+3 14 Critical Path A-C-E-F 2+3+4+3 12 Project Length is 14 weeks if all the activities are crashed to their minimum The objective to shorten the project time frame is to complete the work earlier than its orginal time. Since, Activity B and E have slack, it doesn't make sense to complete those activities earlier. It is ideally the activities on critical path which needs to be reduced initially Path Table Duration After Crashing Stages Path Initial Stage 1 Stage 2 Stage 2 A-B-D-F 21 20 18 14 A-C-D-F 22 21 19 15 A-C-E-F 19 18 18 14 1. Stage 1 - Crashing Activity F by 1 day as it has least slope Crash Cost = $2300 which within $4600 2. Stage 2 - Crashing Activity D by 2 days as D has next least low slope Crash Cost = $2400 which is within $4600 3. Stage - Ideally the least cost next is with activity E and B, but both have slack So next activity to be crashed is A for 4 days = $3500 which is withi $4600 4. Next Crashing is for Activity C, however it has crash cost of amount higher than $4600 As such, crashing won't happen, the project will take 15 weeks

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