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Gattuso
Gattuso
21.08.2019 • 
Mathematics

Formulate a linear programming (lp) model to solve for the earliest start and earliest finish times (in weeks above) for the above project activities. you have to include 1) variable definition 2) objective function 3) constraints 4) lp solution output from qm for windows. do not simply turn in your pert/cpm results for chart above.
ii. (50 points) formulate another linear programming (lp) model to solve for the latest start and latest finish times for this project, using the project completion time from part i above as your set target finish date. again, you have to include 1) variable definition 2) objective function 3) constraints 4) lp solution output from qm for windows.
hints on extra credit:
- problem i is to use a lp model to determine the earliest start and earliest finish times
for each activity. since earliest implies "smallest", so there must be something for you to
minimize.
- problem ii is also a lp model which involves determining the the latest start and latest
finish times for each activity. since latest implies "largest", so there must be something for you to maximize. but you must remember adding a constraint to fix the finish time (an additional variable) to the value (? weeks) you solve in the first lp model above.
- thus you need to define 4 variables for each activity i (e.g., esi, efi, lsi, lfi) to capture these timings.
- each node implies a constraint -- for instance, there must be a connection between the finish time and start time for each activity, i.e., efi > = esi + activity time(i); and each arc implies a constraint -- for instance, if there is an arc from a to c which means c can not be started until a is finished, then esc > = efa.
- the main idea is, after you use the management scientist's lp module to solve the lp models you just formulate, you are supposed to get the exact answers as what you got through pert algorithm in chapter 10 (see slide 23). if you don't get that matched up, something is wrong with your lp model formulation.
- very much common sense. also attach your printout from lp module of qm for windows when you turn the extra credit hw in.

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