A production model and maintenance planning model for the process industry



12

Figure 3: Inventories and backorders for the basic scenario

Basic scenario

Scenario 1

Scenario 2

Scenario 3

Setup costs

sij=1,000 for all i,j

sij=3,000 for all j
s
ij=1,000 for i=2,...,5,
j=1,2________________

sij=1,000 for all i,j

sij=1,000 for all i,j

Capacity

Capj=336 for all j

Capj=336 for all j

Cap1=336

Cap2=168

Capj=336 for all j

Backorder costs

li=1,000 for all i

li=1,000 for all i

li=1,000 for all i

l1=3,000

li=1,000 for i=2,...,5

Table 6: Summary of the four scenarios

Job sequence

Objective value ($)

Scenario 1

Line 1: 1 2 3 1 2 M 2 2 1 1

Line 2: 4 4 5 5 3 M 4 5 3 5

285,620

Scenario 2

Line 1: 4 4 5 1 M 5 2 1 1 4

Line 2: 4 3 3 1 3 3 M 5 4 5

443,960

Scenario 3

Line 1: 1 2 3 5 M 2 2 1 1 5

Line 2: 4 4 1 5 2 M 3 4 3 5

334,270

Table 7: Results of three scenarios

All three scenarios validated the working of the model. It is important to note that, while the
basic scenario was solved optimally, the other three scenarios were not. Instead, good feasible
solutions were obtained using a special branching strategy in the Branch and Bound procedure,
because of the computation time involved. This branching method and the important issue of
computational efficiency, is elaborated on next.

6. Branching Strategy and Performance of the Model



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