Demonstration case 01 - production capacity
Synthetic production scenarioCan we accept the new order?
A manufacturer receives a request for an additional 100 units of P3, due by the end of week three. Total capacity appears sufficient, but one resource becomes the bottleneck. Should the order be accepted and under what conditions?
Synthetic demonstration based on a realistic business problem. It does not represent a project for a specific client.
View the analysis
What does the decision look like without a model?
If everything is added to week three, CNC-2 exceeds capacity.
The existing plan in week three already requires 67.4 h on CNC-2. The additional 100 units of P3 require another 22.0 h on the same resource.
At first glance this suggests one of four reactions:
- overtime
- moving other orders
- additional capacity
- rejecting the order
CNC-2 - Week 3111.8%
89.4 / 80 h9.4 h above available capacity
67.4 h+22.0 h=89.4 h
What does the model consider?
We do not only test whether the order fits the current schedule.
The model searches for a feasible production allocation across available periods while respecting the current plan, deadlines and the capacity of every resource.
Objective
Deliver the new order on time.
Constraints
Resource capacity, current plan, deadline and production process.
Variables
Additional P3 quantity produced in each week.
Priority
Find a feasible solution without unnecessary capacity expansion.
How is the problem formalised?
For each week, resource load is the sum of planned product quantities multiplied by their processing time on that resource. The extra P3 quantity may be split across weeks 1-3, while every weekly resource load must remain within capacity.
Existing plan
| Product | Week 1 | Week 2 | Week 3 | Week 4 |
|---|---|---|---|---|
| P1 | 120 | 140 | 130 | 120 |
| P2 | 100 | 110 | 120 | 100 |
| P3 | 90 | 100 | 110 | 100 |
| P4 | 80 | 90 | 100 | 90 |
Processing time per unit (h)
| Product | Laser | CNC-1 | CNC-2 | Welding | Assembly |
|---|---|---|---|---|---|
| P1 | 0.10 | 0.18 | 0.12 | 0.08 | 0.10 |
| P2 | 0.08 | 0.10 | 0.18 | 0.12 | 0.08 |
| P3 | 0.12 | 0.05 | 0.22 | 0.14 | 0.16 |
| P4 | 0.06 | 0.12 | 0.06 | 0.16 | 0.12 |
Weekly capacityLaser 80 hCNC-1 80 hCNC-2 80 hWelding 100 hAssembly 100 h
Before and after
The model uses spare capacity in the previous week.
One feasible demonstration solution is to produce 65 new P3 units in week two and the remaining 35 in week three.
111.8%
89.4 / 80 h97.9%
78.3 / 80 h93.9%
75.1 / 80 hDecision
The new order can be accepted.
The order can be accepted without new equipment and without overtime, but not if it is produced according to the original schedule.
Among the other analysed resources, the highest utilisation remains 69.1%, so CNC-2 remains the only relevant bottleneck in this scenario.Adding the order directly creates a 9.4 h overload.
The model finds an allocation that uses existing capacity reserve.
The 100-unit order fits without new equipment or overtime.
What-if / scenario analysis
What if conditions change?
The question is not only whether the current order can be accepted, but how much further the system can grow before capacity needs to change.
For +15% and +20%, the existing P1-P4 plan in the first three weeks is increased proportionally. The new order remains +100 P3 and must be completed by the end of week three. The existing weekly plan remains fixed while the new P3 quantity may be allocated across weeks 1-3.
Base scenario
65 units in week 2 and 35 in week 3. Peak CNC-2 utilisation is 97.9%.
Existing demand +15%
One balanced feasible allocation is 64 / 27 / 9 units across weeks 1-3. CNC-2 reaches about 99.5%, leaving only about 0.4 h of minimum weekly reserve.
Existing demand +20%
CNC-2 requires 248.08 h across the first three weeks while only 240 h is available. At least 8.08 h of total CNC-2 time is missing, or the schedule, capacity or operating method must change.
XAIOR - explaining the result
Why did the model make this recommendation?
The key factor is CNC-2.
The other resources have sufficient available capacity, but P3 requires the most processing time on CNC-2.
If all 100 new units are produced in week three, CNC-2 exceeds available capacity. Moving part of the production to week two uses spare capacity and removes the overload.
Scenario analysis also shows the robustness boundary: with 15% growth in existing demand, the solution is still feasible but with almost no operational reserve. At 20%, the same capacity is no longer sufficient.
From demo to a real problem
What if these were your data?
In a real engagement, P1-P4 would be your products, the resources would be your machines, lines, people or other constraints, and the synthetic values would be replaced with data from your ERP, spreadsheets or another system.
Can we accept the new order?
Where will the next bottleneck appear?
When does an extra shift or new equipment become justified?