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Solutions | Approved: 8 years ago | 101.75 kB | Comments: 0
...Problem 9.1 Define the variables as yjyjj,1,2,...,6,where...
...yjyjj,1,2,...,6,where 1 means the jth project is...
...yj 0 means the jth project is...
...project is omitted. The objective function to...
...(a) subject to the following constraints: First...
...gyy656 1 (g) The branch and bound...
...begins by solving the LP problem with...
...integer restrictions on the variables with the...
...the variables with the following result: 1...
...f $265,200 Note that several variables (,,,)yyyy1234...
...are not integers. The branch and bound...
...out with Excel. The final (optimal) integer...
...$225,000 This indicates that the project 2...
...This indicates that the project 2 with...
...project 2 with the highest net present...
...selected because of the constraints in the...
...the constraints in the problem. Note that...
...the problem. Note that the first noninteger...
...problem. Note that the first noninteger solution...
...of f than the integer solution, as...
...cap(i)*(y(i,1) + y(i,2)) The last constraint above...
...constraint above insures that, if a generator...
...spreadsheet model containing the optimal solution appears...
...solution appears below. The optimal solution turns...
...and 2 have the lowest operating costs,...
...has by far the lowest operating cost,...
...used to satisfy the remaining demand. Even...
...generator 3 has the lowest startup cost,...
...much higher than the 100MW. The first...
...than the 100MW. The first year two...
...than second year. The second year nothing...
...as defined by the variables pinv and...
...and ninv, and the equations invsplit, because...
...equations invsplit, because the costs for positive...
...inventory are different. The binary variables y...
...variables y turn the production variables prd...
...and off through the constraints “onoff”. They...
...setup times into the maxtime constraints, and...
...setup costs into the objective. The “oneprod”...
...into the objective. The “oneprod” constraints insure...
...“oneprod” constraints insure that at most one...
...in any week. The optimal solution produces...
...week. This causes the penalty cost to...
...be incurred, but the backlogged demand is...
...is satisfied in the next week (The...
...the next week (The constraint that inventory...
...week (The constraint that inventory is zero...
...is zero at the end of week...
...week 4 insures that there is no...
...backlogged demand after the fourth week). All...
...week). All of the 90 available hours...
...available per week, the problem has no...
...different values of the parameter “tavail”. 6...
...and 2 insure that y(I) = 0...
...Node 2 gives the MIP optimum. 8...
...one can see that plant 1 has...
...2 cannot satisfy the demand by itself....
...I: yy121, 1. The LP to be...
...xx2122 1 **** The solution is x1x1xx22...
...II: yy121, 0. The LP to be...
...xx1112 2 **** The solution is x1x1xx12...
...Case I gives the optimal solution to...
...optimal solution to the problem. Problem 9.10...
...problem. Problem 9.10 The solution can be...
...each extractor, assign the stream with the...
...the stream with the least cost for...
...least cost for that extractor. The optimum...
...for that extractor. The optimum pairing is...
...Node 5 gives the IP optimum. Problem...
...11 Problem 9.15 The solution is: Refinery...
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