Convert the next MATLAB code to a LP problem

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Alejandro Vazquez
Alejandro Vazquez 2020-12-8
编辑： Alejandro Vazquez 2020-12-8
Hello,
I am trying to convert the next MATLAB code problem into an LP model problem.
MATLAB CODE:
Create and solve an optimization problem using named index variables. The problem is to maximize the profit-weighted flow of fruit to various airports, subject to constraints on the weighted flows.
Coding-
rng(0) % For reproducibility
p = optimproblem('ObjectiveSense', 'maximize');
flow = optimvar('flow', ...
{'apples', 'oranges', 'bananas', 'berries'}, {'NYC', 'BOS', 'LAX'}, ...
'LowerBound',0,'Type','integer');
p.Objective = sum(sum(rand(4,3).*flow));
p.Constraints.NYC = rand(1,4)*flow(:,'NYC') <= 10;
p.Constraints.BOS = rand(1,4)*flow(:,'BOS') <= 12;
p.Constraints.LAX = rand(1,4)*flow(:,'LAX') <= 35;
sol = solve(p);
Solving problem using intlinprog.
LP: Optimal objective value is -1027.472366.
Heuristics: Found 1 solution using ZI round.
Upper bound is -1027.233133.
Relative gap is 0.00%.
Optimal solution found.
Intlinprog stopped at the root node because the objective value is within a gap tolerance of the optimal value, options.AbsoluteGapTolerance = 0 (the default value). The intcon variables are integer within tolerance, options.IntegerTolerance = 1e-05 (the default value).
Find the optimal flow of oranges and berries to New York and Los Angeles.
[idxFruit,idxAirports] = findindex(flow, {'oranges','berries'}, {'NYC', 'LAX'})
idxFruit = 1×2
2 4
idxAirports = 1×2
1 3
orangeBerries = sol.flow(idxFruit, idxAirports)
orangeBerries = 2×2
0 980.0000
70.0000 0
This display means that no oranges are going to NYC, 70 berries are going to NYC, 980 oranges are going to LAX, and no berries are going to LAX.
List the optimal flow of the following:
Fruit Airports
----- --------
Berries NYC
Apples BOS
Oranges LAX
idx = findindex(flow, {'berries', 'apples', 'oranges'}, {'NYC', 'BOS', 'LAX'})
idx = 1×3
4 5 10
optimalFlow = sol.flow(idx)
optimalFlow = 1×3
70.0000 28.0000 980.0000
This display means that 70 berries are going to NYC, 28 apples are going to BOS, and 980 oranges are going to LAX.

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