Housing unit optimization literature exhibits two critical gaps that limit practical applicability under contemporary policy requirements. First, single-objective profit maximization provides no mechanism to quantify trade-offs between commercial returns and housing affordability Second, deterministic formulations ignore the cost volatility and demand uncertainty inherent in multi-year developments.
This study addresses both gaps through a novel multi-objective mixed-integer stochastic programming (MO-MISP) framework – representing the first application of integrated stochastic mixed-integer programming to housing unit allocation optimization. This methodological innovation explicitly models the profit-affordability trade-off frontier while incorporating scenario-based uncertainty quantification. This framework was applied to a residential project in Riyadh comprising 728 housing units of various types, including duplexes, townhouses and villas.
The validated MO-MISP model revealed asymmetric market sensitivity (boom: ±2.015% vs. baseline: ±0.126%), a 1.11:1 profit-affordability trade-off ratio, nonlinear diversification costs and land as the highest-value constraint (SAR 353.32/m2).
This research advances housing optimization methodology by integrating multi-objective trade-off analysis with stochastic robustness within a unified framework directly applicable to large-scale residential developments under Saudi Vision, 2030.
This study contributes a novel contextual adaptation and empirical validation of an integrated MO-MISP formulation for housing unit allocation under Saudi Vision, 2030. Their combined application to quantify the profit-affordability trade-off in residential development has not been previously undertaken.
