Part Contact States
The loading, movement and unloading of parts via the manufacturing system should be scheduled through supervisory computer. In contrast along with classical scheduling, one can no longer suppose that the parts will move to subsequently machine immediately after this has finished processing. Comparatively, the part will wait on the machine till the material handler unloads this. Obviously, no part can be scheduled upon the machine under consideration till the earlier part has been unloaded.
In order to model this condition, this is essential to explicitly consider loading and unloading activities, additionally to machining activity. Assume C_{i} and D_{i} signify the load and unload operations related along with the processing operation i. the technological relationships among these operations can be presented via the pairs (C_{i}, i) and (i, D_{i}). Thus, the set of operations contains 2 | N | additional operations, and all arc set (i, j) ∈ A_{k} is changed into (C_{i}, i), (i, D_{i}), (C_{j}, j), ( j, D_{j}). The material handling resource V can be modeled like the set, S_{v}, consisting of operations that require source v.
Accordingly, in CCS M_{r} ∩ S_{v} > 0 , containing that three existing operations in set N which need both machine r and the handling resource v for execution, that is loading and unloading operations.
Specified that operation I has been loaded upon machine r, part contact constraints should make sure that no other operation is scheduled upon this machine till the unloading operation, D_{i} has been finished. Mathematically, the part contact constraints can be illustrated by the given set of constraints as:
t_{i} - t_{Ci} ≥ p_{Ci}, Λ t_{Di} - t_{i} ≥ p_{i}, n i n M_{k} , k = 1, 2, 3, ... , m . . . (4)
t_{Cj} - t_{Di} ≥ p_{Di} V t_{Ci} - t_{Dj} ≥ p_{Dj} n i, j n M_{k} , i n j, k = 1, 2, 3, . . . , m. . . (5)
t_{w} - t_{s} ≥ p_{s}, V t_{s} - t_{w} ≥ p_{w } n i, j n H v , v = 1, . . . , h . . (6)
here the constraint in Eq. (4) implies the technological relations and which no operation can be scheduled among C_{i}, i and D_{i},, the constraint in Eq. (5) shows the capacity constraints for the machine and the constraint in Eq. (6) Shows the capability constraints for the material handling resources. This is assumed that all resource processes one operation at a time.