Question

9-30. Oilco is considering two potential drilling sites for reaching four targets (possible oil wells). The following table provides the preparation costs at each of the two sites and the cost of drilling from site i to targetj (i 1,2;j 1,2,3,4) Drilling cost ($ million) to target Site Preparation cost($ million) 2 4 Formulate the problem as an ILP, and find the optimum solution.

Answer 1

X_ij = 1 if site i is assigned to target j {in simple, X_11, X12,.......X_24}

= 0 otherwise

_Yj = 1 for site 1 & 2 {in simple Y_{1 ,} Y₂ }

objective function : (minimizing the expense in order to maximize the profit))

Hence Min Z = 5 y₁+6y₂+2x₁₁ +1x₁₂ +8 x₁₃+ 5x₁₄ + 4x₂₁ + 6x₂₂ + 3x₂₃ + 1x₂₄

_{subject to}

x₁₁ + x₂₁ = 1

x₁₂ + x₂₂ = 1

x₁₃ + x₂₃ = 1

x₁₄ + x₂₄ = 1

x₁₁ +x₁₂ + x₁₃+ x₁₄ < = My₁ (where M >=4, as only 4 targets)

x₂₁ + x₂₂ + x₂₃ + x₂₄< = My₂

default constraint X_ij,Y_j >=0 for all & j

Add slack and aritificial variables as appropriate and solve by two phase simplex method to convert Min to MAX and solve further gives Z = 18.