Supply Chain Optimization vs Simulation
What It Solves, How It Works, Where It Stops

Network optimization answers one kind of question: given a fixed set of choices, what’s the best combination? Here’s the math behind it, the problem types it covers, and where a supply chain simulation has to take over.

What problem does it solve?

Optimization answers a specific class of question: given a fixed set of choices, what is the best combination? It isn’t “what would happen if I did X?” That’s simulation. Optimization searches the space of possible decisions and returns the one with the lowest cost, the highest service or the best tradeoff.

In supply chain network design, the choices are typically:

• Which facilities should be open?
• Which supplier should serve which customer?
• How much should flow on each lane?
• Which transport mode (truck, rail or ocean) on each lane?
• How much of each SKU should each plant make?

The optimizer evaluates millions of combinations against a single mathematical objective, usually “minimize total landed cost,” subject to constraints such as capacity, demand, service level and flow conservation. It returns one answer: the provably best decision under the model’s assumptions.

The math: mixed-integer programming

A network design optimization problem is expressed as three pieces.

1. Decision variables. What the solver is allowed to choose. There are two kinds:

• Continuous variables: how much to ship on a lane (x_ij units, 0 to ∞)
• Binary variables: whether to open a facility (y_i ∈ {0, 1})

The “mixed integer” in mixed-integer programming (MIP) comes from having both at once.

2. Objective function. What to minimize or maximize. For network design, it’s almost always total cost:

minimize  Σ produce_cost_i · q_i        (production at each site)
        + Σ transport_cost_ij · x_ij     (flow on each lane)
        + Σ operate_cost_i · y_i         (fixed cost of running each facility)
        + Σ inventory_cost_i · stock_i   (carrying cost, if modeled)

The total landed cost a business actually pays is the sum of these terms.

3. Constraints. What the solver must respect:

• Demand: every customer’s demand must be served, Σ_i x_ij = demand_j for each customer j.
• Capacity: facilities can’t exceed their throughput, Σ_j x_ij ≤ capacity_i · y_i.
• Flow conservation: whatever comes in must go out, so intermediate nodes can’t create or destroy product.
• Logic: a closed facility ships nothing, x_ij ≤ M · y_i (the “big-M” trick).
• Service: every customer must be within distance D of its assigned site, when that’s modeled.

The solver searches the decision space using branch-and-bound: try one combination, prune branches that can’t beat the current best, and repeat. With binary y_i variables the problem is NP-hard in general, but at the scale most companies actually run (tens to hundreds of facilities), commercial solvers handle it routinely.

The classic problem types

Every real network optimization is a variant of one of these.

Basic cost optimization. All facilities are open and fixed. The optimizer assigns lanes (which DC serves which customer) to minimize total transport and handling cost. The result is a customer-to-DC sourcing map. These are small problems, usually a few minutes of solve time.

Facility selection (the open/close problem). Add binary variables for which facilities are open, and a fixed operating cost for each open one. The optimizer chooses how many and which facilities while it assigns customers. This is the highest-value optimization most companies run, because footprint decisions are 5-to-10-year commitments. It’s a hard problem, and modern solvers still handle hundreds of candidates. Greenfield analysis is the fast first pass that often comes before it.

Flow constraints. Add must-flow or must-not-flow rules between specific sources and destinations. These are used when business rules override pure cost (for example, a SKU that by regulation can only ship from one country), or to test “what if we forced this routing?”

Sourcing optimization. The decision is which supplier or suppliers to use for each input. It adds time, lead-time variance, tariffs and in-transit holding cost to the decision. The Tariff demo in the Sandbox is a sourcing optimization: an Asia-Pacific supplier against a Mexico supplier across a grid of tariff rates. The tariff network redesign guide covers that case in full.

Multi-period optimization. Decisions over time. The solver chooses when to open or close, when to build inventory and how to phase capacity additions. Every variable gets a time index, so the problem grows with the number of periods.

Production-modeling optimization. Add a bill of materials: making finished good A consumes 2 units of raw material B. The solver routes raw materials, runs production and distributes finished goods, all in one combined MIP. The Coffee co-pack demo in the Sandbox has this shape, with 2 raw beans, 1 finished blend and 3 candidate plants.

Multi-objective optimization. Some questions don’t reduce to one number: cost vs service vs carbon vs risk. Multi-objective solvers either weight them into one combined objective (min α·cost + β·service_violations) or trace the Pareto frontier, the curve of best possible tradeoffs.

Optimization vs simulation: which to reach for

Optimization gives you the answer. Simulation tells you whether the answer survives reality. How supply chain simulation works covers the other half.

Known limitations of optimization

It’s important to understand the model’s gaps:

• Static. Optimization typically uses aggregate annual or monthly demand, averaged. Real demand has day-to-day variance the model doesn’t see.
• Costs assumed continuous. Real shipping costs step (full truckload vs less-than-truckload). MIPs can model this with piecewise functions, but most don’t.
• Service projections are optimistic. Optimization assumes capacity is fully usable. Real facilities have downtime, surge limits and human factors.
• No time-series visibility. “75% service rate” might mean always at 75%, or 100% for 270 days and 0% for 90. Optimization can’t tell the difference.

That’s why a well-run network design project uses both: optimize to find the candidate design, then simulate to check that it holds up under realistic variance.

Try it in the Sandbox

The Tariff and Coffee demos in the Sandbox Networks tier are real optimization runs against precomputed scenario inputs. The solver reads a network specification and returns the optimal sourcing, flow and facility decisions.

For a network model on your own data, including capacity, lane, freight and labor constraints, talk to us. Real network design runs in a desktop tool, so your data stays on your own machine.

Sources: archived enterprise network-optimization training projects (2013–2015): basic cost, facility selection, flow constraints, bill of materials, production modeling and multi-objective. Standard supply chain analytics methodology as taught in commercial tools and OR/SCM courses.