Community physiotherapy services that rely on home visits face a scheduling problem in which therapist no-show rates vary across patient groups and over time, so that nominal appointment allocation can produce unequal realised continuity of rehabilitation. the present analysis formulates the problem as a constrained multi-objective optimisation in which a scheduler maximises expected session completion and minimises the dispersion of completion rates across equity strata, subject to therapist capacity and travel-time constraints. Because no field data are available, the study is framed as a design and operating-characteristics evaluation: a before-after-control-impact estimator is characterised under a declared variance structure with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64, across cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points, with 2000 replications per design cell. The contribution is a formalisation that treats no-show variability as a constraint on equity rather than as noise to be averaged away, together with a design-level statement of what a community physiotherapy evaluation can and cannot detect at feasible cluster counts.
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Ferreira et al. (2026) studied this question.
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