SCHEDULES: FUNDAMENTALS, EXAMPLES, AND IMPLEMENTATION
4. ILLUSTRATING THE MPS PROCESS COMPLEXITY
performance indicators - like those just mentioned - how can the system define a good schedule? Imagine, for instance, that just for one period, ten different SKUs need to be scheduled to one of four possible - but different - production lines and that, depending on the line chosen, different changeover times can incur? What if these lines have different processing rates? What if some products cannot be scheduled simultaneously because the use same tools, pallets or fixtures? What if some products should be scheduled only after others? Consider in this scenario that even with these four lines, the shop floor cannot yet manufacture all the requirements - which products should the system schedule first? Expand these questions to a scenario with three hundred different SKUs, forty production lines, and a planning horizon with fifteen time buckets - what do you do? How many different solutions can exist? Based on importance weights, can a system find the best (optimal) solution - a solution that maximizes profits?
These are just some of the dilemmas involved in the master scheduling process that an MPS information system must consider - especially if some optimization is desired. One of the following sections mentions some techniques that can be used in an master production scheduling system - focusing and exemplifying on the use of two artificial intelligence techniques: genetic algorithms (GA) and simulated annealing (SA).
4. ILLUSTRATING THE MPS PROCESS
the production lines is by itself a complex problem that will not be considered in this illustration.) Hence, production capacity is related only to production lines hours, more specifically, to the quantity of available and used hours per period.
The usage rate (parts/hour) is described in Table 7-2.
Therefore, products A, B, C can be made at any resource (at different speeds) but product D can only be made at L2 and L3, at 10 and 15 parts per hour, respectively.
As said above, regular capacity is eight hours per day, however, the MPS can use overtime. In this illustration, up to 1.6 extra hour can be used per day (8 hours a week), and, during the monthly periods, overtime can be up to 40 hours - that is, overtime is limited to a maximum of 20% of regular capacity.
Following the heuristic, Table 7-3 shows the ideal case, where, if capacity is widely available, the Total MPS equals Net Requirements (initial step of the heuristic).
Following the heuristic's logic described at Figure 7-4:
1. Time bucket: t=l, meaning Week 2;
2. Product selection. Product D has more restriction since it can be made only at L2 and L3; whereas the other products can be made at any resource. Hence/? = D, andp(r) = D(600).
3. Resource selection. Lines L2 and L3 do not have any "exact spare capacity left in ^." On the contrary, both have all of their capacity (40h) available in t, L3 is chosen since it is the fastest one.
4. Pre-assigning D to L3 would consume 40 hours (600/15).
5. Since L3 has enough capacity to make D(600), then the pre-assignment is confirmed.
The process repeats, since product B is still left. However, since there is no resource with available capacity left, B(600) will not scheduled in t. Part of B's gross requirements can be postponed to the next time bucket, however, in this illustration, backlogging is not allowed. The process continues for the remaining periods. The final results are shown in Table 7- 4.
In Week 3, B's net requirements are 1200, which can be made by LI or L2. Because the rate is 20 units/hour for either line, and 40 hours is the maximum regular capacity available per line, one could schedule only one line, in which case, 800 (40x20) units could be made. All of the requirements would be met, but there would be ending inventory below safety stock; or another 20 h of the other production line could be used. This would result in requirements not met for the other two products.
Calculate net requirements and initialize variables (optimal solution would have Total MPS identical to Net Requirements).
Define time bucket (^ = r + 1)
Product selection. Choose product (p) with more restrictions, i.e., the one with the least number of resources that can make it.
Resource selection. Pick the resource (r) with an "exact" spare capacity in t, which can fit production of/? "perfectly." If no resource has exact spare capacity
window left, choose the resource with largest available capacity in /. If a tie occurs, choose the fastest one.
Pre-assign the quantity q ofp [p(q)] to r. (q is the net requirement of/?)
Does r have available capacity sufficient to make the whole quantity ofp{q)l
Is there another resource r to m2k.Qp(q) - preferably completely? (If more
than one is available, choose the fastest.)
p(q) can be made at r but there might be demand (requirements) not met, in case no resource has enough capacity to make q.
Assign/? tor.
Have all products been analyzed?
Have all time buckets been considered?
Redo the logic above for inventory building (build inventory during low demand periods to be used at high demand periods), if needed.
Reinitiate to cover all planning horizon
Figure 7-4. An MPS creation heuristic
Table 7-2. Usage rate matrix for the example scenario LI L2 L3
A 15 20 25 B 20 20 25 C 15 30 20 D - 10 15
Table 7-3. Item-table-
On-hand Initial inventory Gross requirements Standard lot size Safety inventory (SI) Net requirements
MPS Li
U
u
Total Requirements met Requirements not met Service level Average service level in the period
Ending inventory Average inventory in the period
Total avg inventory in the period
Below safety inventory Below SI in the period
Ideal case: Total MPS = Net Requirements (first 2 weeks only)
Week 2 A
100 100 400 200 400 800
800 400 0 1
B 300 300 400 200 500 600
600 400 0 1
c
250 250 500 200 400 800
800 500 0 1
D 350 350 500 200 300 600
• ' / ''-'„'
600 500 0 1 1
500 300
500 400
550 400
450 400 1500
0 0 0 0
0
Week 3 1 A
500 600 200 400 600
" ":' ^ ;
600 600 0 1
B
500 650 200 500 800
' '>"' ^ . ' ' / ' . '
800 650 0 1
c
550 650 200 400 600
'^^, \
600 650 0 1
D 1
450 600 200 300 600
600 600 0 1 1
500 500
650 575
500 525
450 450 2050
0 0 0 0
0
The process repeats:
6. Product selection. Since all products left can be made at any resource, A is randomly chosen: A(800).
7. Resource selection. Any resource can make A. L3 is the fastest but has no spare capacity. L2 is chosen then.
8. Pre-assigning A to L2 would consume 40 hours (800/20).
9. Since L2 has enough capacity to make A(800), then the pre-assignment is confirmed.
The process repeats:
lO.Product selection. Either B or C can be picked. Since the net requirements of C are the largest, that is chosen: C(800).
11. Resource selection. LI is the only resource left with available capacity.
12.Pre-assigning C(800) to LI would consume 53.33 hours (800/15).
Maximum overtime is 8 hours making up to 48 hours of maximum available capacity. (Requirements not met will occur even if overtime is used).
13. Since there is no other resource left, C(800) is assigned to LI - over time (8 h) will be considered but there will still be 80 units fi'om net requirements that will not be met.
Table 7-4. Final results
On-hand Initial inventory Gross requirements
Standard lot size Safety inventory (SI)
Net requirements
MPS Li L2
U
Total Requirements met Requirements not met
Service level Average service level in the period
Ending inventory Average inventory in the period
Total avg inventory in the period
Below safety inventory
Below SI in the period
using the MPS creation heuristic (the
Week 2 A
100 100 400 200 400 800
800
800 400 0 1
B
300 300 400 200 500 600
0 300 100 0,75
c
250 250 500 200 400 800 720
720 500 0 1
D
350 350 500 200 300 600
600 600 500 0 1
i"1
w 3
48 40 40
0,94
500 300
0 150
470 360
450 400
1210
0 500 0 0 500
first 2 weeks)
Week 3 A
500 600 200 400 600
300
300 600 0 1
B
0 650 200 500 1200
650
650 650 0 1
c
470 650 200 400 600 600
600 650 0 1
D
450 600 200 300 600
600 600 600 0 1
a. 1
40 47,5
40
1,00
200 350
0 0
420 445
450 450
1245
200 500 0 0 700
From the results presented in Table 7-4, one can also see that overtime is used in all periods but the last, being mostly adopted in Week 4 and Month 2.
Although this heuristic does not include any optimization principle, the reader can rapidly begin to see the complexity in an MPS process, especially if the production scenario contains a large number of products, periods and resources. The real difficulty in this MPS creation heuristic is, therefore, located at three main points of the logic: at the product and resource selection and at the inventory building.