Table 1 Indicates, parameters and decision variables.
Notations | Descriptions |
|---|---|
Indices | |
N | Set of orders and factories,\(\:N=C/\left\{0\right\}\cup\:F\). |
k, j, l | Index for orders or customers. |
g | Index for factories. |
i | Index for machines. |
h | Index for vehicles. |
Parameters | |
\(\:{p}_{ij}\) | Processing time of order j on machine i. |
\(\:{q}_{j}\) | Size of order j. |
\(\:{t}_{kj}\) | Transportation time between customers k and j. |
\(\:{T}_{gj}\) | Transportation time between the manufacturing factory g and customer j. |
\(\:{v}_{j}\) | Service time at customer j. |
G | An infinite constant. |
Decision variables | |
\(\:{X}_{kjg}\) | Binary variable. It equals to 1 if order j is processed consecutively after order k at factory g, and 0 otherwise. |
\(\:{Y}_{kjgh}\) | Binary variable. It equals to 1 if vehicle h goes from customer k to j at factory g, and 0 otherwise. |
\(\:{Z}_{jg}\) | Binary variable. It equals to 1 if order j in factory g, and 0 otherwise. |
\(\:{S}_{jig}\) | Start time of order j on machine i at factory g. |
\(\:{C}_{jig}\) | Completion time of order j on machine i at factory g. |
\(\:{C}_{g}\) | Completion time of factory g. |
\(\:{V}_{gh}\) | Departure time of vehicle h at factory g. |
\(\:{U}_{ghj}\) | Delivery time of order j on vehicle h at factory g. |
\(\:{A}_{j}\) | Arrival time at customer j. |
\(\:{L}_{j}\) | Leave time from customer j. |
