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.