Implementation Of Immune System To Control Fms

A Generic Machine Loading Problem

Machine loading problem arrives beneath the broad range of flexible manufacturing system that consists of several NC or numerical control machines, and material handling device, all beneath the supervision of a centrally situated computer system.

                                                                                    Table no.8: Description of Problem Number 1

Machine loading problem deals along with the allocation of operation of chosen jobs from a pool of jobs to the described alternative machines whilst satisfying several machining and tooling constraints. The complexity connected along with machine loading problem can be gauged from the cause that for a sample machine loading problem having eight jobs and four machines; the concerned data is shown in Table no.9. Because, the existing eight jobs can be sequenced in 8! Ways and for any type of such sequencing, there exists:

1× 2 × 2 × 1 × 2 × 6× 9 × 6 = 2,592 operation-machine allocation combinations.

Thus, there will be a total of 8! × 2,592 = 104,509,440 possible allocations for eight jobs.

In order to resolve a machine loading problem, two objectives frequently taken are:

(a) Maximizing throughput, and

(b) Imbalance of minimizing systems and also this is equivalent to balance of maximizing systems.

Accurate balance is achieved if imbalance of systems becomes zero by the minimum imbalance value. For a described timeframe, the upper bound value of throughput is the total of all the probable products such could be produced in the timeframe. Thus, the upper bound throughput for the time horizon is equivalent to the total of the batch sizes of all the jobs desired to be allocated. For computed the system imbalance, both over employed and under employed times are considered. The given conditions and assumptions must be satisfied for the formulation of the underlying problem.

(a)   Any type of machine cannot perform more than one operation of the task or job at a time.

(b)   Any type of job that is selected for processing upon a specific machine must finish all its operations upon a specific machine before considering the next task or job in sequence for that machine.

(c)    Any exact operation of any job doesn't necessitate more than one machine.

(d)   Processing needs of the jobs are identified in advance.

(e)   Duplication and Sharing of tools is not considered.

(f)     Loading or unloading and transportation time is negligible.

Notations

Indices

j = index of job; 1 ≤ j ≤ J.;

m = index of machine; 1 ≤ m ≤ M;

Parameters

S = selected jobs.

R_NSU = job rejected because of negative system imbalance.

R_TSC = job rejected because of tool slot constraint.

SU = system imbalance;

TH = throughput;

H = planning horizon;

SU_max = maximum system imbalance (= M × H);

O_j = set of operations for the job j;

M_jo = set of machines for performing o^th operation of the job j;

bsz_j = batch size of the job j;

 MT^o_m = over employed time on machine m;

 MT^H_m = under employed time on machine m;

 MT^a_job = time available on machine m for performing oth operation of job j;

 MT^r′_job = time required by machine m for performing oth operation of job j;

 MT^r′′_job  = time remaining on machine m after performing oth operation of job j;

 MS^a _job = tool slot available on machine m for performing oth operation of job j;

 MS^r′' _job   = tool slot required by machine m for performing oth operation of job j;