Exact Heuristic by Reallocation Paradigm

Step 1

• Input the total number of part types P.
• Input the total number of machines M.
• For p = 1 to P , input o_p,

                 For 0 = 1 to p_p.

                 For m = 1 to M,

Input the value of t_copm, T_copm ∀ o corresponds to m.

Step 2

For p = 1 to P, evaluate a_p by using Eq. (5).

Step 3

Arrange part type p, here p = 1 to P in decreasing order of the contribution a_p and generate the part type sequence.

Step 4

For p = 1 to P, input the value of I_p from part type sequence.

Step 5

Input t_aopm, T _aopm, for m = 1 to M .

Step 6

Determine ET_mp, ES_mp for m = 1 to M.

ET_mp is the necessary machining time requirement on machine "m" before the allocation of any necessary operation of part type.

ES_mp is the necessary tool slot needs on machine "m" before the allocation of any necessary operation of the part type.

Step 7

Initialize I_p = 1.

Step 8

Find A S_qp, the set of operation allocation of part type "p", for q = 1 to q_max.

Step 9

Find ERM_m*, ERT_m*, ATM_m*, ATS_m*.

where  ERM * = ET mp - ET (Oomp)

ERT_m*   = ES_mp - ES (O_om^p)

ATM_m*= t_aopm - taopm (O _om  ^p)

ATS_m*= T_aopm -  Taopm (O_om^p).

Step 10

Initialize q = 1.

Step 11

Determine t_ropm, T _ropm corresponding to.

Step 12

Evaluate PI (AS^p_q ) by using Eq. (4).

Step 13

If q < q_max, then q = q + 1, go to Step 11, Else go to Step 14.

Step 14

If for , where q = q to q_max, PI = ∝ (infinity),

then p∈P UTSC. Therefore reject the part because of tool slot constraints, I_p = I_p + 1,

Go to Step 8.

Else go to Step 15.

Step 15

Select  which has maximum PI ( ) value. Allocate operation on machines like per the ( )set of operation allocation.

Step 16

Update t_aopm, T_aopm, ET_mp, and E S_mp after allocation of part type "p". [Set t_ropmto t_aopm, T _ropmto T _aopm, ES_mp to ES_mp' , ES_mp to ES_mp' ]

Step 17

If I_p < I_p, increase I_p by 1 and go to step 8, Else go to step 18.

Step 18

Determine system Unbalance "SU" and part throughput "TH".

SU =  t_ropm and TH =  b_p, where p ∉ PU_TSC and PU_NSU.

P U_TSC = Set of part types unassigned because of tool slot constraints.

P U_NSU = Set of part types unassigned because of negative system unbalance.

Step 19

If SU is -ve , then go for reallocation, else output the ultimate SU and TH.

Step 20 : Reallocation

For p = 1 to P, where p ∉ P U_TSC and P U_NSU, do the following:

(a) Add TPT_p to SU and SU *.

(b) Select the minimum positive value of SU * and obtain the corresponding Throughput TH* and go to step C. If SU is till negative, then add TPT_p to SU and obtain SU**. Select the minimum +ve value of SU**and find out the corresponding TH** and go to step C.

(c) Drop off the part type "p" from the set of assigned part types. This part type is rejected because of negative system unbalance.

(d) Add equivalent machining time and tool slots of the part type "p" to the respective machines. Go to step G.

(e) Discard the part type p and p* from the set of pool of assigned part types (because of part types).

(f) Add equivalent machining time and tool slots of the allocate operations of the part type p and p* to m respective machines. Go to step G.

(g) Allocate part type p where p ε PUTSC and get SU & TH .

(h) If SU is -ve for all part types of P U_TSC, drop off these part types and get the final SU and TH.