3. Five distinct cargo items are to be loaded on a vessel. The weight wk, volume

Question

3. Five distinct cargo items are to be loaded on a vessel. The weight wk, volume vk, and value pe of each item k are tabulated below: Item Unit weight Unit volume Unit value wk (kg vk (m3) Pk (S) 3,000 7,000 6,000 5,000 8,000 500 800 300 200 700 7 4 4 4 The maximum allowable cargo weight and volume are 11.25 tonnes and 109 m3, respectively. (a) Formulate an integer linear program (ILP) that determines the quantities of each distinct cargo item to load on the vessel so as to maximise the value of the cargo (b) Solve the ILP using MATLAB's intlinprog() function.

Explanation / Answer

A.

The formulation

The decision variables are X(k) , k = 1 to 5

X1,X2,X3,X4,X5

Z= objective function = Max of (Sum (Pk*Xk) for k = 1 to 5.

Z= Max (P1*X1+P2*X2+P3*X3+P4*X4+P5*X5)

Such that

Constraints:

Sum(Wk*Xk) for K =1 to 5 <= 11.25 (which is W1*X1+W2*X2+W3*X3+W4*X4+W5*X5 <= 11.25

Sum(Vk*Xk) for K =1 to 5 <= 109 (which is V1*X1+V2*X2+V3*X3+V4*X4+V5*X5 <= 109

Xk >= 0

Xk = Integers

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