EST ECT LST LCT (Earliest Start (Earliest Activity (Latest Start (Latest Completion Slack The network diagram assuming normal activity times is shown below. Time) Completion Time) Time) Time) A1 0 1 1 D.1 A 2 3 7 E.3. D 0 5 2 2 B,4 C 0 O 0 G.1 D 3 E 4 7 4 8 3 A.3 7 0 F 7 lo Z 10 0 F,4 G 5 10 7 12 8 10 3 10 12 0 (f) What is the LCT (latest completion time) of G (in hours)? 10 (1) Path You will want to fill in the missing entries in the table below. That will help you to answer the questions that follow. Slack (weeks) Path Time (weeks) (g) Can you delay D without impacting G? YES or NO? No (1) (h) How much delay (in hours) can you have in A2 without delaying the project? |(1) (i) How much delay (in hours) can you have in A2 without impacting F? (a) What is the minimum project duration (in weeks)? (1) (1) (j) If Al takes 4 hours to complete, how much delay (in hours) can you have in D without delaying the project? 2 (1) You will want to fill in the table below to show clearly the sequence of activities to crash to reduce the duration of the project by a total of four weeks, one week at a time, always at the minimum direct cost. That will help you to answer the questions that follow. Question 2. (8 points) Consider the following project where all times are in weeks. Normal Crash Normal Crash Cost Weekly Crash Path Time (weeks) Normal After you crash these activities Activity Predecessors Time Time Cost S (000) S (000) Cost S (000) A 3 1 46 68 11 Path B A 4 2 48 60 6 C A 3 1 12 20 4 D B. C 1 1 24 24 E D 3 3 18 18 F B. C 4 1 19 25 2 G E. F 1 1 10 10 The costs above are direct costs, i.e. each cost is associated with an individual activity. Normal Cost corresponds to Normal Time. Crash Time is the minimum time an activity will require. Crash Cost corresponds to Crash Time. 3 Project Duration (weeks) Incremental Direct Cost ($000) (b) Suppose that the normal project duration is x weeks. Which activities should you crash to reduce the project duration to (x-1) weeks? (1) (I) (c) Which activities should you crash to reduce the project duration from (x-1) to (x-2) weeks? (1) (d) Which activities should you crash to reduce the project duration from (x-2) to (x-3) weeks? (1) (e) Which activities should you crash to reduce the project duration from (x-3) to (x-4) weeks? (f) What is the optimal project duration (in weeks) if indirect (overhead) project costs accumulate at the rate of $7,000 per week? (1) (g) Suppose that indirect (overhead) project costs accumulate at the rate of $9,000 per week and there is a fine of $3,000 per week for every week by which the project duration exceeds 9 weeks? (i) What is the optimal project duration (in weeks)? (ii) What is the optimal project cost (direct plus indirect plus fine) (in S)? 5 (1) (1)