Mathematical Model of Machine Loading Problem

In order to illustrated the application of neural network upon machine loading problem we taken a straightforward model of machine loading problem or complex application mimicking actual life manufacturing is not represented to ignore confusion. For that, suppose that a set of n single-operating part types as j₁, j₂, j₃, . . . , j_n are to be processed on m identical machines as M₁, M₂, . . . , M_m. All machines are able of operating any part and each operation needs one arbitrary machine. Job j_n must be allocated one machine and the needed resources throughout the non-interrupted processing time of length p_j. Machine loading problem can after that be formulated as the given as zero-one integer programming problem as:

Here

j : job index,

i : machine index,

p_j : job processing time j,

b_i : on machine processing time available i, and

X_ij : 1, whether job j is processed on machine i, 0, or else.

Eq. 1 shows the objective function. Eqs. 2, 3 and 4 are the constraints of the machine loading problem. Eq. 2 states as the time available on every machine cannot be gone beyond. Eq. 3 limits the parts to be processed by merely one machine. At last Eq.4 condition that X_ij is a decision variable such value depends upon the assigned of parts to machines.