Guide
Read the Answer
After the solver runs, the Results screen shows the recommended plan, the limits that shaped it, and how the answer changes across scenarios. This page explains every part of the output.
Recommended decision
The headline is the objective value — the best achievable throughput, lowest achievable cost, or minimum resource usage given your constraints. Below it, you'll see the flow values for every edge: how much moves through each path in the optimal plan.
If you're running a multi-period plan, each period gets its own flow breakdown, and you'll see how the recommendation evolves over time with demand growth and ramp rates.
Active limits
Active limits (binding constraints) are the constraints that are fully used up in the optimal solution. They have zero slack — there's no room left.
In this example, yield is binding (holding back throughput), line 3 capacity is almost binding (91% used), and budget has slack — money isn't the bottleneck.
Bottlenecks
A bottleneck is the constraint that limits your objective the most. SSPLAX identifies bottlenecks using two methods:
The constraint with the highest shadow price is the one where relaxation pays off the most. If yield's shadow price is 250 units/% and budget's is 0.3 units/$, yield is the bottleneck.
SSPLAX tightens each constraint by a small percentage and re-solves. The constraint that causes the largest drop (or first infeasibility) under stress has the highest pressure score.
The tornado chart on the Bottlenecks tab ranks all constraints by impact, combining both approaches into a normalized pressure score.
Marginal value
The shadow price (also called marginal value or dual value) tells you exactly how much the objective improves per unit of constraint relaxation.
Select a constraint from the tradeoff dropdown to see its shadow price, the range over which that shadow price is valid, and a tradeoff curve showing how the objective changes as you relax the constraint from tight to loose.
Shadow prices are only valid within a range. Beyond that range, a different constraint becomes binding and the shadow price changes. SSPLAX shows you this validity range so you don't overextend the interpretation.
Available headroom
For non-binding constraints, the slack value tells you how much room is left. A constraint with 20% slack can tighten by 20% before it becomes binding.
Headroom matters for robustness: if a constraint has very little slack, small real-world variations could make it binding and change the optimal plan. The stochastic feasibility analysis quantifies this risk.
Infeasible results
When no plan can satisfy all constraints simultaneously, the solver returns an infeasible status. This means your constraints contradict each other — there's no possible operating point.
SSPLAX then computes the minimum relaxation: ranked single-limit relaxations that could restore feasibility. Each option shows one constraint, how far it would need to move, and in which direction.
This tells you exactly which assumptions need to change for the plan to work — and by how much.
What changed from baseline?
When you adjust constraints and re-solve, the Compare tab shows a side-by-side diff between your current scenario and the baseline. You'll see:
- -Which constraint values changed and by how much
- -The objective delta (how much better or worse)
- -Flow shifts: which paths gained or lost volume
- -Binding constraint changes: which limits became active or relaxed
For more on running scenarios, see Decision Workflow.