Question

In: Operations Management

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:

Xjk = 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
Yjk = 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
Zjk = 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

B1jk = binary integer such that B1jk =1 when Xjk > 0 for j=1,2,3,4 and k=1,2,3
B2jk = binary integer such that B2jk =1 when Yjk > 0 for j=1,2,3,4 and k=1,2,3
B3jk = binary integer such that B3jk =1 when Zjk > 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

X1k - 13000 * B11k <= 0 for k=1,2,3
B11k - X1k <= 0 k=1,2,3

X2k - 15000 * B12k <= 0 for k=1,2,3
B12k - X2k <= 0 k=1,2,3

X3k - 16000 * B13k <= 0 for k=1,2,3
B13k - X3k <= 0 k=1,2,3

X4k - 16500 * B14k <= 0 for k=1,2,3
B14k - X4k <= 0 k=1,2,3

Y1k - 13000 * B21k <= 0 for k=1,2,3
B21k - Y1k <= 0 k=1,2,3

Y2k - 15000 * B22k <= 0 for k=1,2,3
B22k - Y2k <= 0 k=1,2,3

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

Y4k - 16500 * B24k <= 0 for k=1,2,3
B24k - Y4k <= 0 k=1,2,3

Z1k - 13000 * B31k <= 0 for k=1,2,3
B31k - Z1k <= 0 k=1,2,3

Z2k - 15000 * B32k <= 0 for k=1,2,3
B32k - Z2k <= 0 k=1,2,3

Z3k - 16000 * B33k <= 0 for k=1,2,3
B33k - Z3k <= 0 k=1,2,3

Z4k - 16500 * B34k <= 0 for k=1,2,3
B34k - Z4k <= 0 k=1,2,3

B1jk + B2jk + B3jk <= 1 for j=1,2,3,4 and k=1,2,3

Xjk, Yjk, Zjk >= 0 for j=1,2,3,4 and k=1,2,3

B1jk, B2jk, B3jk = {0, 1} for j=1,2,3,4 and k=1,2,3


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