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How to solve the problem about VRPTW?...

van25 10 Maple 15
optimization lpsolve
January 11 2018
1 1

Hi, I do not understand how to solve errors in Maple on my project. My project is to solve Vehicle Routing Problem with Time Windows, and then the error is "Error, (in Optimization: -LPSolve) no feasible integer point found; use feasibilitytolerance option to adjust tolerance". I do not understand about feasibilitytolerance. Can anyone help me? Thankyou.

NULL

HASIL*MAPLE*UNTUK*KECAMATAN*COBLONGNULL

> 

restart
> 

with(Optimization);

[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve, QPSolve]

 (1)
> 

with(linalg);

[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, coldim, colspace, colspan, companion, concat, cond, copyinto, crossprod, curl, definite, delcols, delrows, det, diag, diverge, dotprod, eigenvals, eigenvalues, eigenvectors, eigenvects, entermatrix, equal, exponential, extend, ffgausselim, fibonacci, forwardsub, frobenius, gausselim, gaussjord, geneqns, genmatrix, grad, hadamard, hermite, hessian, hilbert, htranspose, ihermite, indexfunc, innerprod, intbasis, inverse, ismith, issimilar, iszero, jacobian, jordan, kernel, laplacian, leastsqrs, linsolve, matadd, matrix, minor, minpoly, mulcol, mulrow, multiply, norm, normalize, nullspace, orthog, permanent, pivot, potential, randmatrix, randvector, rank, ratform, row, rowdim, rowspace, rowspan, rref, scalarmul, singularvals, smith, stackmatrix, submatrix, subvector, sumbasis, swapcol, swaprow, sylvester, toeplitz, trace, transpose, vandermonde, vecpotent, vectdim, vector, wronskian]

 (2)
> 

with(ExcelTools);

[Export, Import, WorkbookData]

 (3)
> 

with(CodeTools);

[CPUTime, DecodeName, EncodeName, Profiling, RealTime, Test, Usage]

 (4)
> 

``
> 

c := convert(Import("C:\\Users\\VaniaMR\\Documents\\SEMANGAT SKRIPSI\\skripsi\\Bab-bab\\data Bandung Utara.xlsx", 6, "B2:I9"), matrix)

array( 1 .. 8, 1 .. 8, [( 5, 8 ) = (2.9), ( 4, 1 ) = (2.5), ( 2, 2 ) = (0.), ( 8, 3 ) = (3.1), ( 2, 4 ) = (1.9), ( 7, 5 ) = (3.7), ( 6, 6 ) = (0.), ( 3, 7 ) = (3.9), ( 6, 8 ) = (2.7), ( 5, 1 ) = (.28), ( 7, 3 ) = (3.9), ( 1, 2 ) = (3.2), ( 3, 4 ) = (3.7), ( 8, 5 ) = (2.9), ( 5, 6 ) = (.26), ( 2, 7 ) = (1.8), ( 3, 8 ) = (3.1), ( 6, 1 ) = (.25), ( 8, 2 ) = (1.1), ( 2, 3 ) = (2.8), ( 4, 4 ) = (0.), ( 5, 5 ) = (0.), ( 8, 6 ) = (2.7), ( 1, 7 ) = (3.5), ( 4, 8 ) = (2.3), ( 7, 1 ) = (3.5), ( 7, 2 ) = (1.8), ( 1, 3 ) = (4.1), ( 5, 4 ) = (2.7), ( 6, 5 ) = (.26), ( 7, 6 ) = (3.4), ( 8, 7 ) = (1.6), ( 1, 8 ) = (3.3), ( 8, 1 ) = (3.3), ( 6, 2 ) = (2.9), ( 4, 3 ) = (3.7), ( 6, 4 ) = (2.7), ( 3, 5 ) = (4.0), ( 2, 6 ) = (2.9), ( 7, 7 ) = (0.), ( 2, 8 ) = (1.1), ( 5, 2 ) = (3.1), ( 2, 1 ) = (3.2), ( 3, 3 ) = (0.), ( 7, 4 ) = (1.3), ( 4, 5 ) = (2.7), ( 1, 6 ) = (.25), ( 6, 7 ) = (3.4), ( 7, 8 ) = (1.6), ( 4, 2 ) = (1.9), ( 6, 3 ) = (3.8), ( 8, 4 ) = (2.3), ( 1, 1 ) = (0.), ( 1, 5 ) = (.28), ( 4, 6 ) = (2.7), ( 5, 7 ) = (3.7), ( 8, 8 ) = (0.), ( 3, 1 ) = (4.1), ( 3, 2 ) = (2.8), ( 5, 3 ) = (4.0), ( 1, 4 ) = (2.5), ( 2, 5 ) = (3.1), ( 3, 6 ) = (3.8), ( 4, 7 ) = (1.3) ] )

 (5)
> 

t := convert(Import("C:\\Users\\VaniaMR\\Documents\\SEMANGAT SKRIPSI\\skripsi\\Bab-bab\\data Bandung Utara1.xlsx", 7, "B2:I9"), matrix)

array( 1 .. 8, 1 .. 8, [( 5, 8 ) = (9.0), ( 4, 1 ) = (8.0), ( 2, 2 ) = (0.), ( 8, 3 ) = (8.0), ( 2, 4 ) = (6.0), ( 7, 5 ) = (10.0), ( 6, 6 ) = (0.), ( 3, 7 ) = (9.0), ( 6, 8 ) = (7.0), ( 5, 1 ) = (2.0), ( 7, 3 ) = (9.0), ( 1, 2 ) = (9.0), ( 3, 4 ) = (12.0), ( 8, 5 ) = (9.0), ( 5, 6 ) = (2.0), ( 2, 7 ) = (4.0), ( 3, 8 ) = (8.0), ( 6, 1 ) = (2.0), ( 8, 2 ) = (3.0), ( 2, 3 ) = (7.0), ( 4, 4 ) = (0.), ( 5, 5 ) = (0.), ( 8, 6 ) = (7.0), ( 1, 7 ) = (10.0), ( 4, 8 ) = (6.0), ( 7, 1 ) = (10.0), ( 7, 2 ) = (4.0), ( 1, 3 ) = (11.0), ( 5, 4 ) = (9.0), ( 6, 5 ) = (2.0), ( 7, 6 ) = (8.0), ( 8, 7 ) = (3.0), ( 1, 8 ) = (9.0), ( 8, 1 ) = (9.0), ( 6, 2 ) = (8.0), ( 4, 3 ) = (12.0), ( 6, 4 ) = (9.0), ( 3, 5 ) = (12.0), ( 2, 6 ) = (8.0), ( 7, 7 ) = (0.), ( 2, 8 ) = (3.0), ( 5, 2 ) = (10.0), ( 2, 1 ) = (9.0), ( 3, 3 ) = (0.), ( 7, 4 ) = (4.0), ( 4, 5 ) = (9.0), ( 1, 6 ) = (2.0), ( 6, 7 ) = (8.0), ( 7, 8 ) = (3.0), ( 4, 2 ) = (6.0), ( 6, 3 ) = (10.0), ( 8, 4 ) = (6.0), ( 1, 1 ) = (0.), ( 1, 5 ) = (2.0), ( 4, 6 ) = (9.0), ( 5, 7 ) = (10.0), ( 8, 8 ) = (0.), ( 3, 1 ) = (11.0), ( 3, 2 ) = (7.0), ( 5, 3 ) = (12.0), ( 1, 4 ) = (8.0), ( 2, 5 ) = (10.0), ( 3, 6 ) = (10.0), ( 4, 7 ) = (4.0) ] )

 (6)
> 

a := `<,>`(0, 0, 0, 0, 0, 0, 0, 0)

a := Vector(8, {(1) = 0, (2) = 0, (3) = 0, (4) = 0, (5) = 0, (6) = 0, (7) = 0, (8) = 0})

 (7)
> 

b := `<,>`(30, 30, 30, 30, 30, 30, 30, 30)

b := Vector(8, {(1) = 30, (2) = 30, (3) = 30, (4) = 30, (5) = 30, (6) = 30, (7) = 30, (8) = 30})

 (8)
> 

n := sqrt(numelems(c)):

{1, 2, 3, 4, 5, 6, 7, 8}

 (9)
> 

z := add(add(c[i, j]*x[i, j], j = N), i = N);

3.2*x[1, 2]+4.1*x[1, 3]+2.5*x[1, 4]+.28*x[1, 5]+.25*x[1, 6]+3.5*x[1, 7]+3.3*x[1, 8]+3.2*x[2, 1]+2.8*x[2, 3]+1.9*x[2, 4]+3.1*x[2, 5]+2.9*x[2, 6]+1.8*x[2, 7]+1.1*x[2, 8]+4.1*x[3, 1]+2.8*x[3, 2]+3.7*x[3, 4]+4.0*x[3, 5]+3.8*x[3, 6]+3.9*x[3, 7]+3.1*x[3, 8]+2.5*x[4, 1]+1.9*x[4, 2]+3.7*x[4, 3]+2.7*x[4, 5]+2.7*x[4, 6]+1.3*x[4, 7]+2.3*x[4, 8]+.28*x[5, 1]+3.1*x[5, 2]+4.0*x[5, 3]+2.7*x[5, 4]+.26*x[5, 6]+3.7*x[5, 7]+2.9*x[5, 8]+.25*x[6, 1]+2.9*x[6, 2]+3.8*x[6, 3]+2.7*x[6, 4]+.26*x[6, 5]+3.4*x[6, 7]+2.7*x[6, 8]+3.5*x[7, 1]+1.8*x[7, 2]+3.9*x[7, 3]+1.3*x[7, 4]+3.7*x[7, 5]+3.4*x[7, 6]+1.6*x[7, 8]+3.3*x[8, 1]+1.1*x[8, 2]+3.1*x[8, 3]+2.3*x[8, 4]+2.9*x[8, 5]+2.7*x[8, 6]+1.6*x[8, 7]

 (10)
> 

conx := seq(add(x[i, j], i = `minus`(N, {j})) = 1, j = N);

x[2, 1]+x[3, 1]+x[4, 1]+x[5, 1]+x[6, 1]+x[7, 1]+x[8, 1] = 1, x[1, 2]+x[3, 2]+x[4, 2]+x[5, 2]+x[6, 2]+x[7, 2]+x[8, 2] = 1, x[1, 3]+x[2, 3]+x[4, 3]+x[5, 3]+x[6, 3]+x[7, 3]+x[8, 3] = 1, x[1, 4]+x[2, 4]+x[3, 4]+x[5, 4]+x[6, 4]+x[7, 4]+x[8, 4] = 1, x[1, 5]+x[2, 5]+x[3, 5]+x[4, 5]+x[6, 5]+x[7, 5]+x[8, 5] = 1, x[1, 6]+x[2, 6]+x[3, 6]+x[4, 6]+x[5, 6]+x[7, 6]+x[8, 6] = 1, x[1, 7]+x[2, 7]+x[3, 7]+x[4, 7]+x[5, 7]+x[6, 7]+x[8, 7] = 1, x[1, 8]+x[2, 8]+x[3, 8]+x[4, 8]+x[5, 8]+x[6, 8]+x[7, 8] = 1

 (11)
> 

conV := seq(add(x[i, k], i = N)-add(x[k, j], j = N) = 0, k = N);

x[2, 1]+x[3, 1]+x[4, 1]+x[5, 1]+x[6, 1]+x[7, 1]+x[8, 1]-x[1, 2]-x[1, 3]-x[1, 4]-x[1, 5]-x[1, 6]-x[1, 7]-x[1, 8] = 0, x[1, 2]+x[3, 2]+x[4, 2]+x[5, 2]+x[6, 2]+x[7, 2]+x[8, 2]-x[2, 1]-x[2, 3]-x[2, 4]-x[2, 5]-x[2, 6]-x[2, 7]-x[2, 8] = 0, x[1, 3]+x[2, 3]+x[4, 3]+x[5, 3]+x[6, 3]+x[7, 3]+x[8, 3]-x[3, 1]-x[3, 2]-x[3, 4]-x[3, 5]-x[3, 6]-x[3, 7]-x[3, 8] = 0, x[1, 4]+x[2, 4]+x[3, 4]+x[5, 4]+x[6, 4]+x[7, 4]+x[8, 4]-x[4, 1]-x[4, 2]-x[4, 3]-x[4, 5]-x[4, 6]-x[4, 7]-x[4, 8] = 0, x[1, 5]+x[2, 5]+x[3, 5]+x[4, 5]+x[6, 5]+x[7, 5]+x[8, 5]-x[5, 1]-x[5, 2]-x[5, 3]-x[5, 4]-x[5, 6]-x[5, 7]-x[5, 8] = 0, x[1, 6]+x[2, 6]+x[3, 6]+x[4, 6]+x[5, 6]+x[7, 6]+x[8, 6]-x[6, 1]-x[6, 2]-x[6, 3]-x[6, 4]-x[6, 5]-x[6, 7]-x[6, 8] = 0, x[1, 7]+x[2, 7]+x[3, 7]+x[4, 7]+x[5, 7]+x[6, 7]+x[8, 7]-x[7, 1]-x[7, 2]-x[7, 3]-x[7, 4]-x[7, 5]-x[7, 6]-x[7, 8] = 0, x[1, 8]+x[2, 8]+x[3, 8]+x[4, 8]+x[5, 8]+x[6, 8]+x[7, 8]-x[8, 1]-x[8, 2]-x[8, 3]-x[8, 4]-x[8, 5]-x[8, 6]-x[8, 7] = 0

 (12)
> 

conz := add(x[i, 1], i = N) = 1;

x[1, 1]+x[2, 1]+x[3, 1]+x[4, 1]+x[5, 1]+x[6, 1]+x[7, 1]+x[8, 1] = 1

 (13)
> 

conD := add(x[1, j], j = N) = 1;

x[1, 1]+x[1, 2]+x[1, 3]+x[1, 4]+x[1, 5]+x[1, 6]+x[1, 7]+x[1, 8] = 1

 (14)
> 

conTW := seq(seq(y[i]-y[j]+max(b[i]+t[i, j]-a[j], 0)*x[i, j] <= b[i]-a[j], i = `minus`(N, {j})), j = N);

y[2]-y[1]+39.0*x[2, 1] <= 30, y[3]-y[1]+41.0*x[3, 1] <= 30, y[4]-y[1]+38.0*x[4, 1] <= 30, y[5]-y[1]+32.0*x[5, 1] <= 30, y[6]-y[1]+32.0*x[6, 1] <= 30, y[7]-y[1]+40.0*x[7, 1] <= 30, y[8]-y[1]+39.0*x[8, 1] <= 30, y[1]-y[2]+39.0*x[1, 2] <= 30, y[3]-y[2]+37.0*x[3, 2] <= 30, y[4]-y[2]+36.0*x[4, 2] <= 30, y[5]-y[2]+40.0*x[5, 2] <= 30, y[6]-y[2]+38.0*x[6, 2] <= 30, y[7]-y[2]+34.0*x[7, 2] <= 30, y[8]-y[2]+33.0*x[8, 2] <= 30, y[1]-y[3]+41.0*x[1, 3] <= 30, y[2]-y[3]+37.0*x[2, 3] <= 30, y[4]-y[3]+42.0*x[4, 3] <= 30, y[5]-y[3]+42.0*x[5, 3] <= 30, y[6]-y[3]+40.0*x[6, 3] <= 30, y[7]-y[3]+39.0*x[7, 3] <= 30, y[8]-y[3]+38.0*x[8, 3] <= 30, y[1]-y[4]+38.0*x[1, 4] <= 30, y[2]-y[4]+36.0*x[2, 4] <= 30, y[3]-y[4]+42.0*x[3, 4] <= 30, y[5]-y[4]+39.0*x[5, 4] <= 30, y[6]-y[4]+39.0*x[6, 4] <= 30, y[7]-y[4]+34.0*x[7, 4] <= 30, y[8]-y[4]+36.0*x[8, 4] <= 30, y[1]-y[5]+32.0*x[1, 5] <= 30, y[2]-y[5]+40.0*x[2, 5] <= 30, y[3]-y[5]+42.0*x[3, 5] <= 30, y[4]-y[5]+39.0*x[4, 5] <= 30, y[6]-y[5]+32.0*x[6, 5] <= 30, y[7]-y[5]+40.0*x[7, 5] <= 30, y[8]-y[5]+39.0*x[8, 5] <= 30, y[1]-y[6]+32.0*x[1, 6] <= 30, y[2]-y[6]+38.0*x[2, 6] <= 30, y[3]-y[6]+40.0*x[3, 6] <= 30, y[4]-y[6]+39.0*x[4, 6] <= 30, y[5]-y[6]+32.0*x[5, 6] <= 30, y[7]-y[6]+38.0*x[7, 6] <= 30, y[8]-y[6]+37.0*x[8, 6] <= 30, y[1]-y[7]+40.0*x[1, 7] <= 30, y[2]-y[7]+34.0*x[2, 7] <= 30, y[3]-y[7]+39.0*x[3, 7] <= 30, y[4]-y[7]+34.0*x[4, 7] <= 30, y[5]-y[7]+40.0*x[5, 7] <= 30, y[6]-y[7]+38.0*x[6, 7] <= 30, y[8]-y[7]+33.0*x[8, 7] <= 30, y[1]-y[8]+39.0*x[1, 8] <= 30, y[2]-y[8]+33.0*x[2, 8] <= 30, y[3]-y[8]+38.0*x[3, 8] <= 30, y[4]-y[8]+36.0*x[4, 8] <= 30, y[5]-y[8]+39.0*x[5, 8] <= 30, y[6]-y[8]+37.0*x[6, 8] <= 30, y[7]-y[8]+33.0*x[7, 8] <= 30

 (15)
> 

batasan1 := seq(a[i] <= y[i], i = N);

0 <= y[1], 0 <= y[2], 0 <= y[3], 0 <= y[4], 0 <= y[5], 0 <= y[6], 0 <= y[7], 0 <= y[8]

 (16)
> 

batasan2 := seq(y[i] <= b[i], i = N);

y[1] <= 30, y[2] <= 30, y[3] <= 30, y[4] <= 30, y[5] <= 30, y[6] <= 30, y[7] <= 30, y[8] <= 30

 (17)
> 

binaryvariables = {seq(seq(x[i, j], i = `minus`(N, {j})), j = N)};

binaryvariables = {x[1, 2], x[1, 3], x[1, 4], x[1, 5], x[1, 6], x[1, 7], x[1, 8], x[2, 1], x[2, 3], x[2, 4], x[2, 5], x[2, 6], x[2, 7], x[2, 8], x[3, 1], x[3, 2], x[3, 4], x[3, 5], x[3, 6], x[3, 7], x[3, 8], x[4, 1], x[4, 2], x[4, 3], x[4, 5], x[4, 6], x[4, 7], x[4, 8], x[5, 1], x[5, 2], x[5, 3], x[5, 4], x[5, 6], x[5, 7], x[5, 8], x[6, 1], x[6, 2], x[6, 3], x[6, 4], x[6, 5], x[6, 7], x[6, 8], x[7, 1], x[7, 2], x[7, 3], x[7, 4], x[7, 5], x[7, 6], x[7, 8], x[8, 1], x[8, 2], x[8, 3], x[8, 4], x[8, 5], x[8, 6], x[8, 7]}

 (18)
> 

conu := seq(seq(u[i]-u[j]+n*x[i, j] <= n-1, i = `minus`(N, {1, j})), j = `minus`(N, {1}));

u[3]-u[2]+8*x[3, 2] <= 7, u[4]-u[2]+8*x[4, 2] <= 7, u[5]-u[2]+8*x[5, 2] <= 7, u[6]-u[2]+8*x[6, 2] <= 7, u[7]-u[2]+8*x[7, 2] <= 7, u[8]-u[2]+8*x[8, 2] <= 7, u[2]-u[3]+8*x[2, 3] <= 7, u[4]-u[3]+8*x[4, 3] <= 7, u[5]-u[3]+8*x[5, 3] <= 7, u[6]-u[3]+8*x[6, 3] <= 7, u[7]-u[3]+8*x[7, 3] <= 7, u[8]-u[3]+8*x[8, 3] <= 7, u[2]-u[4]+8*x[2, 4] <= 7, u[3]-u[4]+8*x[3, 4] <= 7, u[5]-u[4]+8*x[5, 4] <= 7, u[6]-u[4]+8*x[6, 4] <= 7, u[7]-u[4]+8*x[7, 4] <= 7, u[8]-u[4]+8*x[8, 4] <= 7, u[2]-u[5]+8*x[2, 5] <= 7, u[3]-u[5]+8*x[3, 5] <= 7, u[4]-u[5]+8*x[4, 5] <= 7, u[6]-u[5]+8*x[6, 5] <= 7, u[7]-u[5]+8*x[7, 5] <= 7, u[8]-u[5]+8*x[8, 5] <= 7, u[2]-u[6]+8*x[2, 6] <= 7, u[3]-u[6]+8*x[3, 6] <= 7, u[4]-u[6]+8*x[4, 6] <= 7, u[5]-u[6]+8*x[5, 6] <= 7, u[7]-u[6]+8*x[7, 6] <= 7, u[8]-u[6]+8*x[8, 6] <= 7, u[2]-u[7]+8*x[2, 7] <= 7, u[3]-u[7]+8*x[3, 7] <= 7, u[4]-u[7]+8*x[4, 7] <= 7, u[5]-u[7]+8*x[5, 7] <= 7, u[6]-u[7]+8*x[6, 7] <= 7, u[8]-u[7]+8*x[8, 7] <= 7, u[2]-u[8]+8*x[2, 8] <= 7, u[3]-u[8]+8*x[3, 8] <= 7, u[4]-u[8]+8*x[4, 8] <= 7, u[5]-u[8]+8*x[5, 8] <= 7, u[6]-u[8]+8*x[6, 8] <= 7, u[7]-u[8]+8*x[7, 8] <= 7

 (19)
> 

Sol := Optimization[LPSolve](z, {conD, conTW, conV, conu, conx, conz, batasan1, batasan2}, binaryvariables = {seq(seq(x[i, j], i = `minus`(N, {j})), j = N)})

Error, (in Optimization:-LPSolve) no feasible integer point found; use feasibilitytolerance option to adjust tolerance

  
> 

X := eval(Matrix(n, symbol = x), {Sol[2][], seq(x[i, i] = 0, i = 1 .. n)})

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received {Sol[2][], seq(x[i, i] = 0, i = 1 .. n)}

  
> 

f := [1, 5, 6, 3, 2, 8, 7, 4, 1];

[1, 5, 6, 3, 2, 8, 7, 4, 1]

 (20)
> 

add(c[f[i], f[i+1]], i = 1 .. nops(f)-1);

13.64

 (21)
> 

``

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