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This study proposes a mathematical formulation and solution approach for a novel extension of the location-routeing problem (LRP), namely line-haul feeder LRP (LFLRP), where large vehicles (trucks) are synchronised with small vehicles (motorcycles) throughout delivery process. Customers are visited by site-dependent vehicles such that those not accessible by trucks must be served by motorcycles. The LFLRP is formulated as a mixed-integer linear programming model, and two efficient heuristic algorithms called EHA and Enhanced-EHA are developed to solve the problem. Experimental results show that the proposed algorithms can provide near-optimal solutions for 18 randomly generated small-scale LFLRP test instances and best-known solutions for 12 out of 19 large-scale standard LRP test instances in reasonable computation time. A cost-benefit analysis also indicates that the LFLRP model can considerably reduce total costs compared to equivalent standard LRP formulations. To provide managerial insights, a case study and sensitivity analysis of key parameters are conducted.

Line-haul feeder location-routeing problem: mathematical model and heuristic algorithm