The company ULW uses three special ship to deliver three different chemical-product X, Y and Z. The transportation...

The company ULW uses three special ship to deliver three different chemical-product X, Y and Z. The transportation time of a ship to its customers is one week. Each ship has got four special compartments. First compartment has a capacitiy of 13.000 tons. The second compartment has a capacitiy of 15.000 tons. The third one has got a capacity of 16.000 tons, and the last compartment has a capacity of 16.500 tons. The chemical-product X, Y and Z cannot be mixed with each other. The weekly market demand for the product X is about 1.250.000 tons; the weekly demand for the product Y is about 1.456.000 tons and the daily market demand for the product Z is about 241.000 tons. The market prices of the three chemical-product X, Y and Z are 6,67 TL; 7,53 TL and 7,84 TL (per tons). Develop the optimal weekly loading schedule for the maximum income.

(Create only the ILP model, do not solve the problem)

Solutions

Expert Solution

Define the decision variables as follows:

X_jk = Tons of 'X' loaded in the j-th container of the k-th ship for j=1,2,3,4 and k=1,2,3
Y_jk = Tons of 'Y' loaded in the j-th container of the k-th ship for j=1,2,3,4 and k=1,2,3
Z_jk = Tons of 'Z' loaded in the j-th container of the k-th ship for j=1,2,3,4 and k=1,2,3

B_1jk = binary integer such that B_1jk =1 when X_jk > 0 for j=1,2,3,4 and k=1,2,3
B_2jk = binary integer such that B_2jk =1 when Y_jk > 0 for j=1,2,3,4 and k=1,2,3
B_3jk = binary integer such that B_3jk =1 when Z_jk > 0 for j=1,2,3,4 and k=1,2,3

Max Z = 6.67 * (X₁₁ + X₁₂ + X₁₃ + X₂₁ + X₂₂ + X₂₃ + X₃₁ + X₃₂ + X₃₃ + X₄₁ + X₄₂ + X₄₃) + 7.53 * (Y₁₁ + Y₁₂ + Y₁₃ + Y₂₁ + Y₂₂ + Y₂₃ + Y₃₁ + Y₃₂ + Y₃₃ + Y₄₁ + Y₄₂ + Y₄₃) + 7.84 * (Z₁₁ + Z₁₂ + Z₁₃ + Z₂₁ + Z₂₂ + Z₂₃ + Z₃₁ + Z₃₂ + Z₃₃ + Z₄₁ + Z₄₂ + Z₄₃)

Subject to,

X₁₁ + X₁₂ + X₁₃ + X₂₁ + X₂₂ + X₂₃ + X₃₁ + X₃₂ + X₃₃ + X₄₁ + X₄₂ + X₄₃ <= 1250000

Y₁₁ + Y₁₂ + Y₁₃ + Y₂₁ + Y₂₂ + Y₂₃ + Y₃₁ + Y₃₂ + Y₃₃ + Y₄₁ + Y₄₂ + Y₄₃ <= 1456000

Z₁₁ + Z₁₂ + Z₁₃ + Z₂₁ + Z₂₂ + Z₂₃ + Z₃₁ + Z₃₂ + Z₃₃ + Z₄₁ + Z₄₂ + Z₄₃ <= 241000*7

X_1k - 13000 * B_11k <= 0 for k=1,2,3
B_11k - X_1k <= 0 k=1,2,3

X_2k - 15000 * B_12k <= 0 for k=1,2,3
B_12k - X_2k <= 0 k=1,2,3

X_3k - 16000 * B_13k <= 0 for k=1,2,3
B_13k - X_3k <= 0 k=1,2,3

X_4k - 16500 * B_14k <= 0 for k=1,2,3
B_14k - X_4k <= 0 k=1,2,3

Y_1k - 13000 * B_21k <= 0 for k=1,2,3
B_21k - Y_1k <= 0 k=1,2,3

Y_2k - 15000 * B_22k <= 0 for k=1,2,3
B_22k - Y_2k <= 0 k=1,2,3

Y_3k - 16000 * B_23k <= 0 for k=1,2,3
B23k - Y3k <= 0 k=1,2,3

Y_4k - 16500 * B_24k <= 0 for k=1,2,3
B_24k - Y_4k <= 0 k=1,2,3

Z_1k - 13000 * B_31k <= 0 for k=1,2,3
B_31k - Z_1k <= 0 k=1,2,3

Z_2k - 15000 * B_32k <= 0 for k=1,2,3
B_32k - Z_2k <= 0 k=1,2,3

Z_3k - 16000 * B_33k <= 0 for k=1,2,3
B_33k - Z_3k <= 0 k=1,2,3

Z_4k - 16500 * B_34k <= 0 for k=1,2,3
B_34k - Z_4k <= 0 k=1,2,3

B_1jk + B_2jk + B_3jk <= 1 for j=1,2,3,4 and k=1,2,3

X_jk, Y_jk, Z_jk >= 0 for j=1,2,3,4 and k=1,2,3

B_1jk, B_2jk, B_3jk = {0, 1} for j=1,2,3,4 and k=1,2,3

keosha answered 1 year ago

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