A City-Scale Activity Scheduler That Reproduces the Swiss Microcensus on an Open-Source Stack

A continuous-time MILP framework built with SBB at EPFL, calibrated on 10,110 real microcensus schedules and run end-to-end on a 46,970-schedule synthetic Lausanne population — without a single rule-based patch

Travel-demand forecasting depends on simulating what real people actually do during the day, when they work, when they shop, when they have lunch, not just how many cars are on the road. Most operational models cheat on the temporal layer with rule-based heuristics, and lose all the realism the moment something disruptive happens.

We worked with SBB and EPFL to build a proper optimization model for the time dimension. A mixed-integer program decides each person's full daily schedule jointly, calibrated on real Swiss microcensus data. The result is a city-scale simulation whose activity profiles match the empirical observations without any heuristic patching.

46,970

Lausanne synthetic-population schedules simulated end-to-end

10,110

real Swiss microcensus schedules used to calibrate the framework

Open-source

runs on SCIP / OR-Tools — zero commercial-solver license cost

STRC 2021

peer-reviewed, SBB × EPFL co-authorship, Innosuisse-funded

The challenge

Traditional activity-based travel models simulate decisions sequentially, what to do, then when, then where, then how, which makes them blind to trade-offs. Two activities competing for the same hour? Forty thousand people trying to commute and shop at the same time? Sequential models guess; they don't optimize.

SBB needed a framework realistic enough to feed traffic assignment in MATSim, fast enough to simulate full daily schedules for an entire city, and flexible enough to absorb major behavioral shifts like the rise in working from home.

Our approach

We turned the temporal layer into a real optimization problem: each person's start times, durations, and activity sequence are decided jointly by a mixed-integer linear program with utility parameters estimated from data. Non-temporal choices (where, what, how) stay in SBB's existing discrete-choice models, feeding the optimizer as fixed inputs.

We deployed it on the open-source SCIP solver via OR-Tools so the operational pipeline doesn't need a commercial license, and validated against the Swiss microcensus on the full-time-worker subpopulation of Lausanne.

The outcome

Deliverable: a calibrated, validated activity-based scheduling framework that resolves time conflicts in daily schedules through a utility-maximising MILP, built on the open-source SCIP / OR-Tools stack (zero commercial-solver license cost). Published at STRC 2021 in co-authorship with SBB and EPFL, as part of the Innosuisse-funded SBB × EPFL travel-demand modelling collaboration (Project 2155006680).

On a 46,970-schedule synthetic Lausanne population, the simulated activity profiles reproduce every empirical signature of the Swiss microcensus, morning work peak, lunch dip, evening leisure window, multi-tour structure, without a single rule-based patch. The framework calibrates 64 behavioral parameters on 10,110 real microcensus schedules and reaches ρ̄² = 0.165.

Technical deep dive

The model behind the result.

The model

Each individual i has a fixed set of activities A_i to perform within a 24-hour budget ξ. The MILP picks the start time x_a, duration τ_a, travel time tt_a to the next activity, and a binary sequence indicator z_{ab} (= 1 if a is immediately followed by b). The objective is the total schedule utility, a sum of penalties for deviating from desired start times and durations, plus a travel-time disutility.

U_{i} = a \in A_{i} \sum U_{timing} (x_{a}) + a \in S_{i} \sum U_{duration} (τ_{a}) + O \in {P_{i}, H_{i}} \sum U_{duration} (a \in O \sum τ_{a}) + a \in A_{i} ∖ {dusk} \sum β^{travel} t t_{a} .

Schedule utility. Secondary activities are penalized individually; primary and home activities share a duration budget across the day.

U_{timing} (x_{a}) = β_{a}^{early} max (0, x_{a}^{*} - x_{a}) + β_{a}^{late} max (0, x_{a} - x_{a}^{*}) .

Piecewise-linear timing penalty around the desired start time x_a*. Asymmetric, being early can hurt more or less than being late.

U_{duration} (τ_{a}) = β_{a}^{short} max (0, τ_{a}^{*} - τ_{a}) + β_{a}^{long} max (0, τ_{a} - τ_{a}^{*}) .

Mirror penalty around the desired duration τ_a*. Estimated from microcensus data via maximum likelihood.

(z_{ab} - 1) ξ \leq x_{a} + τ_{a} + z_{ab} t t_{a} - x_{b} \leq (1 - z_{ab}) ξ \forall a, b \in A_{i} .

Big-M sequence consistency. When z_{ab} = 1, this collapses to the equality x_b = x_a + τ_a + tt_a; otherwise the bounds are inactive.

a, b \in A_{i} \sum (τ_{a} + z_{ab} t t_{a}) = ξ, b \neq = a \sum z_{ab} = 1, b \neq = a \sum z_{ba} = 1 \forall a \in A_{i} ∖ {dawn, dusk} .

Time budget fills the 24-hour day exactly. Each activity (except dawn/dusk endpoints) has exactly one predecessor and one successor.

The flexibility parameters β^early, β^late, β^short, β^long are unknown per activity type. We estimate them by maximum likelihood: for every observed schedule in the microcensus, we build a competitive choice set, score every alternative with the utility above, and fit the parameters that make the observed schedule most likely under a logit choice model. The parameters then drop into the same MILP at simulation time.

Benchmark

Estimated flexibility parameters for selected activity clusters (significant at the 5% level).

Activity / cluster	β^early	β^late	β^short	β^long
work : morning start	−0.615	−0.436	-	-
work : afternoon start	−0.406	0	-	-
work : daily duration budget	-	-	−0.022	0
leisure : lunch (sub-tour)	−1.610	−0.821	−7.550	−1.360
leisure : evening secondary tour	−0.076	0	−3.060	−0.692
shopping : in a secondary tour	−0.239	−0.486	−5.910	−0.721
home : after work	−0.073	−0.596	-	-
home : daily duration budget	-	-	0	−0.354

Negative numbers are penalties (loss of utility per hour of deviation). Lunch is the most rigid activity, both for being off-time and for missing the desired duration. Morning work has a stiff start time; afternoon work is much more flexible. The home-late penalty (β^late = −0.596) captures the well-documented preference to be home by early evening. Sample size 10,110 cleaned full-time-worker schedules, ρ̄² = 0.165, log-likelihood improved from −57,295.58 to −47,847.37 over 64 parameters.

From the record

Figure 1 from the report: the two streams of the framework. The top row calibrates flexibility parameters from microcensus schedules; the bottom row uses those parameters to simulate schedules for the synthetic population.

Figure 4 from the report: simulated activity profiles (left) versus observed microcensus profiles (right) for the full-time-worker subpopulation. The morning work peak, lunch dip, evening leisure ramp, and home dominance reproduce without rule-based patching.

Figure 5 from the report: 2D start-time × duration heatmaps for work and leisure activities, model versus microcensus. The bimodal work pattern (morning-only vs morning-and-afternoon split) and the lunch-leisure spike at 12:00 are captured by the optimization alone.

Techniques

Continuous-time activity-based scheduling
Mixed-integer linear programming via OR-Tools / SCIP
Maximum-likelihood estimation of utility parameters
Choice-set generation (likely + random alternatives)
Coupling MILP optimization with sequential discrete-choice models

Stack

Python
OR-Tools
SCIP
Biogeme
Ray (parallel execution)
MATSim integration

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