Assigning customer-dependent travel time limits to routes in a cold-chain inventory routing problem

Abstract

This study is activated by a real-world case of cold chain distribution in the Yangtze River Delta of China. Due to the uneven spatial distribution of customers, the customers close to the depot are distributed by self-owned vehicles (SOVs) with a short route time limit while the far customers are distributed by outsourced vehicles (OSVs) with a long route time limit. Although the divide-and-conquer heuristic procedure is practically used in the examined case, it fails to continuously optimize the solutions in timely manners. The examined cold chain distribution problem is an extension of inventory routing problems (IRPs) while the combination of SOVs and OSVs with different route time limits makes the present solution methods inapplicable. Compared with IRPs, the transportation cost and fuel cost of vehicle cold storage are considered simultaneously; the vehicle travel time limits are assigned depending on the distances from the depot to the visited customers. A formal mixed-integer linear program (MILP) and a descriptive model are developed. Considering the case and its dataset cannot be solved by a MILP solver, a genetic algorithm is developed for exploring good solutions using the descriptive model. The algorithmic tuning and operational parameters are investigated by demonstrative and sensitivity analyzing experiments. The examined case is general in cold chain distribution. The solution method can be extended to scheduling heterogeneous fleets for uneven spatially distributed customers.