Optimizing used clothing sustainability through multi-algorithm MILP models for collection, sorting and recycling

Purpose Sustainable fashion and circular-economy policy have advanced considerably, yet the textile reverse-logistics (TRL) literature has given comparatively little attention to optimizing the three operational stages on which textile circularity depends collection, sorting and up/recycling – or to the cost structures that determine whether those stages are economically viable. This paper develops and solves a multi-objective mixed-integer linear programming (MILP) model that optimizes the three stages jointly rather than in isolation. Design/methodology/approach The model maximizes an attainment index crediting sorted and upgrading-weighted output against total collected supply and minimizes total TRL cost across collection, inventory, remanufacturing and inbound and outbound transport, with plant-activation fixed costs carried by binary variables. The two objectives are reconciled by a weighted, range-normalized scalarization whose weight is swept rather than fixed at a single value. Particle swarm optimization (PSO), a genetic algorithm (GA) and the parameter-free Jaya algorithm are benchmarked against the exact branch-and-bound optimum over ten independent seeds at two evaluation budgets. Every coefficient carries an explicit provenance label – reported, derived, modeled or unavailable – and coefficients requiring partner-firm records are declared unavailable rather than imputed. Findings In a destination-level application over 957.4 million kg of verified 2024 worn-textile trade, optimized allocation improves the model objective by between 10.0 and 21.8 percent depending on weighting but raises the Herfindahl concentration index from an observed 0.091 to between 0.118 and 0.130 even under a twenty percent per-destination cap. In a supplier-parameterized instance solved to proven optimality, the exact Pareto sweep locates a knee near w = 0.35 and shows the attainment index saturating at 157.2 against finite supply. Measured against that optimum, no metaheuristic seed recovers more than 68 percent of the attainable improvement: Jaya leads under a constrained budget (45.4 percent mean recovery against 37.6 for GA and 20.4 for PSO) and GA overtakes it only when the evaluation budget is roughly quadrupled. Research limitations/implications The solved instance uses six representative plants and a modeled grade structure, making it an allocation illustration rather than a facility-siting study; cost coefficients are labeled modeled throughout, and no empirical cost claim attaches to them. A partner-firm application under a data-use agreement remains the outstanding requirement. The divergent algorithm orderings obtained on two different instances support a reporting standard in which no comparative claim about stochastic optimizers rests on a single configuration or a single seed. Practical implications For the linear core of this problem, the exact solver dominates, so branch-and-bound is the tool of record, and the role of metaheuristics lies in nonlinear extensions where no exact benchmark exists. Reporting a transparent outcome vector rather than a single headline improvement percentage prevents optimization from appearing to deliver a free gain and makes the concentration cost visible to policy readers. Originality/value The paper contributes a fully specified and auditable MILP formulation that integrates collection, sorting and up/recycling in one model; an exact benchmark against which the three metaheuristics are measured; and an evidence-gating discipline under which every reported coefficient is labeled by provenance and no unavailable coefficient is silently imputed.