Math
Variables
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An integer variable $\text{plane}_i$ per plane i indicates its landing time.
$$\forall i \in [1,10],\, \text{plane}_i = [\![LT_{i,0},LT_{i,2}]\!]$$
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An integer variable $\text{earliness}_j$ per plane i indicates how early a plane lands.
$$\forall i \in [1,10],\, \text{earliness}_i = [\![0,LT_{i,1} - LT_{i,0}]\!]$$
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An integer variable $\text{tardiness}_j$ per plane i indicates how late a plane lands.
$$\forall i \in [1,10],\, \text{tardiness}_i = [\![0,LT_{i,2} - LT_{i,1}]\!]$$
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An integer variable $tot_{dev}$ totals all costs:
$$tot_{dev} = [\![0, {+\infty})$$
Remark
With the current input data, there is no need to distinguish earliness and tardiness since penalty costs are symetric. A simple distance between the target landing time and the real landing time is enough.Constraints
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One plane per runway at a time:
$$\forall i,j \in [1,10]^2,\, i\ne j, \text{plane}_{i} \ne \text{plane}_{j}$$
We saw this type of constraint before, it is an alldifferent constraint.
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the earliness of a plane i:
$$\forall i \in [1,10],\, \text{earliness}_i = max(0,-\text{plane}_i + \text{LT}_{i,1})$$
When the plane is on time or late, its earliness is equal to 0. Otherwise, a positive value is computed that corresponds to the difference between the real landing time and the target landing time.
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the tardiness of a plane i:
$$\forall i \in [1,10],\, \text{tardiness}_i = max(0,\text{plane}_i - \text{LT}_{i,1})$$
When the plane is on time or early, its tardiness is equal to 0. Otherwise, a positive value is computed that corresponds to the difference between the real landing time and the target landing time.
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the separation time required between two planes has to be satisfied:
$$\forall i,j \in [1,10]^2,\, i\ne j, (\text{plane}_{i} + \text{ST}_{i,j} \le \text{plane}_{j}) \oplus (\text{plane}_{j} + \text{ST}_{j,i} \le \text{plane}_{i})$$
If plane i lands before plane j then plane j lands at least
ST[i][j]after plane i. Otherwise, plane j lands first and plane i waits at leastST[j][i]after it to land. The two conditions cannot hold together because of the XOR logical operator. In this case a simple inequality constraint fits the need. -
the deviation cost has then to be maintained:
$$tot_{dev} = \sum_{i = 1}^{10} \text{PC}_{i,0} \cdot \text{earliness}_i + \text{PC}_{i,1} \cdot \text{tardiness}_i$$
Objective
The objective is to find a solution that minimizes tot_dev.