Urged by the necessity to establish sustainable supply chains (SCs), this study focuses on exploring the closed-loop inventory routing problem (CIRP) for perishable food packed by multi-type returnable transport items (RTIs). The selling revenue of perishable food is dependent on food's remaining shelf life and the specific type of RTIs used for packaging. RTI selection decisions need to be jointly considered in the CIRP to weigh the potential benefits against associated costs. For this problem, we first develop an integer linear programme (ILP) to maximise the total profit of the holistic SC. Subsequently, we design a tailored kernel search (KS) matheuristic as an efficient solution. A real CIRP with multi-type RTIs for fresh strawberries is used to demonstrate the practicality of the ILP. For this case study, we perform extensive sensitivity analysis of the relevant parameters, extracting valuable managerial insights. Finally, experiments are conducted on 170 randomly generated instances. Computational results show that the proposed KS manages to achieve competitive solutions for instances with up to 10 retailers much more efficiently than CLPEX. For instances with up to 40 retailers, the KS algorithm significantly outperforms CPLEX in terms of solution quality, improving the obtained profit by 80.03% on average under the same computational time.