min Z = 154 * ∑(i=1 to 10) ∑(j=1 to 5) C_ij * X_ij
约束条件:
1. 每个卸点j的产量要求:
∑(i=1 to 10) X_ij >= d_j / 154, j=1,2,3,4,5
2. 时间约束:
5 * K_ij <= (15/7)*C_ij + 8, ∀i,j
3. 质量约束(仅矿石卸点j=1,2,5):
0.285 * ∑(i) X_i1 <= ∑(i) X_i1 * e_i <= 0.305 * ∑(i) X_i1 (对于j=1)
0.285 * ∑(i) X_i2 <= ∑(i) X_i2 * e_i <= 0.305 * ∑(i) X_i2 (对于j=2)
0.285 * ∑(i) X_i5 <= ∑(i) X_i5 * e_i <= 0.305 * ∑(i) X_i5 (对于j=5)
4. 铲位数量约束:
∑(i=1 to 10) a_i <= 7
5. 物料约束(铲位i的矿石和岩石总量约束):
∑(j in {1,2,5}) X_ij <= D_i^{(1)} / 154 (矿石卸点)
∑(j in {3,4}) X_ij <= D_i^{(2)} / 154 (岩石卸点)
6. 铲位使用约束(如果铲位i没有电铲,则不能运输):
∑(j=1 to 5) X_ij <= (D_i^{(1)} + D_i^{(2)}) / 154 * a_i
∑(i=1 to 10) ∑(j=1 to 5) K_ij<=20
K_ij=((15/7)*C_ij + 8)*X_ij/475
7. 变量类型:
a_i ∈ {0,1} (二进制变量)
X_ij >= 0 (连续变量)
数据:
C_ij 矩阵(10个铲位i,5个卸点j):
j=1 j=2 j=3 j=4 j=5
i=1: 5.26, 1.90, 5.89, 0.64, 4.42
i=2: 5.19, 0.99, 5.61, 1.76, 3.86
i=3: 4.21, 1.90, 5.61, 1.27, 3.72
i=4: 4.00, 1.13, 4.56, 1.83, 3.16
i=5: 2.95, 1.27, 3.51, 2.74, 2.25
i=6: 2.74, 2.25, 3.65, 2.60, 2.81
i=7: 2.46, 1.48, 2.46, 4.21, 0.78
i=8: 1.90, 2.04, 2.46, 3.72, 1.62
i=9: 0.64, 3.09, 1.06, 5.05, 1.27
i=10:1.27, 3.51, 0.57, 6.10, 0.50
e_i(铁含量,以小数表示):
i=1:0.30, i=2:0.28, i=3:0.29, i=4:0.32, i=5:0.31, i=6:0.33, i=7:0.32, i=8:0.31, i=9:0.33, i=10:0.31
D_i^{(1)}(矿石总量):
i=1:9500, i=2:10500, i=3:10000, i=4:10500, i=5:11000, i=6:12500, i=7:10500, i=8:13000, i=9:13500, i=10:12500
D_i^{(2)}(岩石总量):
i=1:12500, i=2:11000, i=3:13500, i=4:10500, i=5:11500, i=6:13500, i=7:10500, i=8:11500, i=9:13500, i=10:12500
d_j(卸点产量要求):
j=1:12000, j=2:13000, j=3:13000, j=4:19000, j=5:13000
添加∑(j=1 to 5)Xij<=96(i=1,2,3,4,5,6,7,8,9,10) ∑(i=1 to 10)Xij<=160(i=1,2,3,4,5)
给出MATLAB求解代码