This article contributes to distribution system literature on three inter-linked aspects viz. formulation of a novel integrated low-carbon/green distribution system for the demand side of a Supply Chain (SC) with a single product and multiple consumers, i.e. drop-off points, a novel and robust solution approach through a Design of Experiment (DoE)-guided Multiple-Objective Particle Swarm Optimisation (MOPSO) optimiser and exhaustive analysis of the solutions (i.e. prioritisation, ranking and scenario analysis). The total costs, CO2 emission and the traversed distances of the vehicles during transportation are optimised. The optimisation model for the strategic decision-making is formulated by effectively integrating the 0–1 mixed-integer programming with a green constraint based on Analytic Hierarchy Process. Due to the computationally NP-hard characteristic of the model, a systematic and technically robust DoE-guided solution approach is designed using a commercial solver – modeFRONTIER®. DoE guides the solution through the MOPSO optimiser in order to eliminate the un-realistic set of feasible and optimal solution sets. A popular multi-attribute decision-making approach, TOPSIS, evaluates the solutions found from the Pareto optimal solution space of the solver. Finally, decision-makers’ preferences are analysed for monitoring the changes in the controlling parameters with respect to the changes in the decisions. A scenario analysis of the events by considering alternative possible outcomes is also conducted. It is found that the implemented methodology successfully routes the vehicles with optimal costs and low-carbon emission thus contributing to greening the environment on the demand side of a SC network.