What the from-to matrix delivers
The from-to matrix is the working instrument of material flow analysis. It answers how strongly the areas of a factory are connected to each other, and therefore which areas should be located close together in the layout.
Its value lies in completeness: while process descriptions emphasise the main flow, the matrix also exposes return flows, cross traffic, empty-container trips and storage detours. In factories that have grown over time, exactly these secondary flows often account for the largest share of the transport effort.
The matrix supplies volumes, the layout supplies distances. Only the product of both is a reliable key figure, and only that can be compared between variants.
Structure of the matrix
Rows are sources, columns are destinations. Each cell holds the transport volume from the source to the destination within the reference period; the diagonal stays empty, because transport inside an area is not considered. Row and column totals show how much an area sends and receives.
An example with five areas: goods receipt (GR), store (ST), machining (MA), assembly (AS) and shipping (SH). Figures in transport trips per week:
| from ↓ / to → | GR | ST | MA | AS | SH | Σ out |
|---|---|---|---|---|---|---|
| GR | — | 120 | 40 | 0 | 0 | 160 |
| ST | 0 | — | 180 | 240 | 0 | 420 |
| MA | 0 | 60 | — | 210 | 0 | 270 |
| AS | 0 | 30 | 0 | — | 150 | 180 |
| SH | 0 | 0 | 0 | 0 | — | 0 |
| Σ in | 0 | 210 | 220 | 450 | 150 | 1,030 |
Even without any calculation, something is visible: the store is involved in 630 of the 1,030 trips (420 outgoing, 210 incoming) and is therefore the most strongly connected area. Assembly receives the most with 450 trips. Both belong in the middle of the route network, not at its edge.
The figures in this example are freely chosen and only serve to illustrate the calculation.
Data sources and preparation
A from-to matrix is rarely surveyed from scratch; it is usually built from existing data:
- Routings and bills of material (ERP). The sequence of operations per article plus the production programme yields the volume flows between workplaces or areas.
- Stock movements and transport orders. Postings from warehouse management or a forklift control system already contain source, destination and often the trips themselves.
- Goods receipt and shipping data. Inbound and outbound volumes close the matrix at the plant boundary.
- Observation and interviews. For flows without a posting trail, such as empty containers, tools, rework or auxiliary materials, recording on site remains necessary. These flows are frequently underestimated in grown structures.
Preparation steps
- Fix the reference period and keep it identical for all sources: a year, a quarter or a typical week.
- Fix the level of aggregation. Which objects are rows and columns: functional areas, machine groups, individual workplaces? The yardstick is what can be moved in the layout.
- Establish the mapping. Assign every posting point, cost centre or machine number unambiguously to one area. This mapping table is the actual work package, because it decides the quality of the result.
- Convert volumes into trips (see the next section).
- Check plausibility. Mirror row and column totals against known figures: inbound deliveries, shipped volumes, forklift operating hours. Large deviations point to missing flows or wrong assignments.
From volumes to trips
The most common mistake in material flow analyses is the unit. The ERP delivers piece counts, weights or volumes, but what moves is the load carrier. The conversion is:
Trips = volume ÷ load carrier capacity × (1 ÷ fill rate), rounded up per transport movement
Three figures decide the result and are often missing from master data, so they have to be collected: the capacity of the load carrier, the realistic fill rate, and the batch size actually transported. Delivering in small quantities multiplies the number of trips at an unchanged annual volume.
If trips are additionally weighted by effort, weight or the required handling equipment enters as a factor: a crane move with a die is not equivalent to a pallet-truck trip. In that case an effort factor is added per relationship and disclosed in the report, because it materially affects the result.
Transport intensity and transport performance
Matrix and layout together produce two key figures:
- Transport intensity per relationship: transport volume × distance between source and destination. It evaluates a single source-destination relationship.
- Transport performance of the factory: the sum of all transport intensities within the reference period. This is the comparison figure between layout variants.
The distance metric matters
Which distance you use changes the result considerably. Three metrics are common:
- Straight line (Euclidean). Quick to calculate, systematically too short, because transport does not run through machines.
- Rectangular (Manhattan). A reasonable approximation for an orthogonal hall grid and the sensible choice when no route network is modelled.
- Actual route network. The shortest path along the real aisles, including detours around installations and one-way rules. The most accurate option, but it requires a maintained route network in the model.
Whichever metric you choose, it has to be identical for all variants. Comparing variants calculated with different metrics is the surest route to a wrong decision.
Worked example
Continuing the example above. Variant A corresponds to the as-is situation: the store sits along the hall wall next to goods receipt, machining at the opposite end. Distances come from the route network of each variant and are calculated rectangularly.
| Relationship | Trips/week | Distance A (m) | Intensity A | Distance B (m) | Intensity B |
|---|---|---|---|---|---|
| GR → ST | 120 | 30 | 3,600 | 25 | 3,000 |
| GR → MA | 40 | 55 | 2,200 | 60 | 2,400 |
| ST → MA | 180 | 25 | 4,500 | 20 | 3,600 |
| ST → AS | 240 | 45 | 10,800 | 25 | 6,000 |
| MA → ST | 60 | 25 | 1,500 | 20 | 1,200 |
| MA → AS | 210 | 70 | 14,700 | 50 | 10,500 |
| AS → ST | 30 | 45 | 1,350 | 25 | 750 |
| AS → SH | 150 | 35 | 5,250 | 35 | 5,250 |
| Total | 1,030 | — | 43,900 | — | 32,700 |
Unit of intensity: trips × metres per week. In variant B the store sits centrally between machining and assembly, and machining moves closer to assembly. The distance from goods receipt to machining becomes longer as a result (55 → 60 m), yet the total effort drops from 43,900 to 32,700 trip-metres per week, a drop of roughly 25 %.
That is the actual benefit of the calculation: a single relationship getting worse is noticed immediately, but it is weighed against the improvement of the strong relationships. Intuition would probably have moved machining closer to goods receipt and made the strongest relationship in the factory worse.
Interpreting the results
Check the concentration
Sort the relationships by intensity. In the example the two strongest relationships (ST → AS and MA → AS) account for 25,500 out of 43,900, almost 58 % of the transport effort across eight relationships. This concentration is typical: a few relationships determine the result, and exactly those belong close together in the layout.
Read the flow picture
Drawing the flows onto the layout with line width by intensity reveals three things a table hides: crossings (two strong flows intersect), return flows (material runs against the main direction) and detours (long lines between neighbouring areas). A Sankey diagram complements this for the decision paper, because it shows the proportions independently of the geometry.
Mind the direction
The matrix is directed. For arrangement decisions the sum of both directions usually counts; for sizing conveyors, one-way routes and empty-container loops the direction is essential. So only merge directions when you evaluate proximity, not before.
From result to layout
- Build a proximity ranking. Sort relationships by intensity; the top group determines which areas have to be adjacent.
- Design the ideal layout. Arrange areas without regard to the building so that the strong relationships become short. The intermediate step is described in Online layout planning.
- Work in the constraints. Column grid, cranes, floor loads, utility connections, immovable equipment, gates.
- Calculate the variants. Same matrix, same distance metric, different arrangement. Compare transport performance per variant.
- Cross-check with a second key figure. The flow-optimal variant is not automatically the space-efficient one. Floor space balance, share of traffic area and bottlenecks belong in the same decision paper.
In matflow these steps run in one model: the from-to matrix is imported from Excel or CSV, mapped to the areas in the layout and drawn as a flow picture; KPIs and variants come from the same status as the plan.
Common mistakes
- Volumes instead of trips. Piece counts without conversion via the load carrier distort the ranking in favour of small parts.
- Mixed reference periods. Annual volumes from the ERP and one week of observation in the same matrix do not produce comparable cells.
- Straight-line distances. They systematically underestimate effort and favour variants with diagonal relationships that cannot be driven in reality.
- Forgetting empty containers and rework. Return flows often use the same routes and double the load on individual relationships.
- Aggregating too finely. A matrix at article level produces thousands of relationships with tiny volumes and hides the few large ones.
- Reporting only the total. Without a ranking and a flow picture it is impossible to see why a variant is better. For an approval, the reasoning matters as much as the number.
- Looking at material flow only. Employee routes, maintenance access and information flows belong alongside. How this relates to value stream work is covered in Value stream design or material flow analysis?