A multi-period inventory routing problem with procurement decisions: a case in China

The classical multi-period inventory routing problem (MIRP) combines inventory management and vehicle routing problems, attempting to maintain customer inventory levels via autonomous deliveries, with the assumption that stock-out never occurs at the supply side. While this is no more the truth when a common third-party logistics company operates a central warehouse for a group of small and medium sized retailing companies. Procurements have to be made to refill inventory at the central warehouse. This study thus extends the traditional MIRP by incorporating procurement decisions (MIRP-PD) and tries to minimize the total cost of procurement, inventory holding and transportation. To our knowledge, this paper is among the first to formally describe MIRP-PD and model it as a mixed integer linear program. A hybrid two-level heuristic is proposed to address large-scale instances. The upper level of the algorithm determines the visiting schedule while the lower level works out procurement and routing decisions accordingly. Components from tabu search and adaptive threshold acceptance are also embedded to help escape from local optima. Extensive numerical instances are generated from a real case in Chengdu (China), based on which the computational results reveal the effectiveness and efficiency of the proposed algorithm compared with the commercial solver CPLEX. The comparison between MIRP and MIRP-PD has demonstrated the cost advantage of incorporating procurement decisions into inventory and routing plans. Impacts on costs of key factors including delivery frequency and buffer size of stores have also been examined to provide managerial implications to practitioners.