A research on multiple-period inventory routing problems with stable demand

De Bi Tsao*, Ahmad Rusdiansyah

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Multiple-Period IRP(MPIRP) is an extended model of the IRP (Inventory Routing Problem). It can be defined as an integrated decision-making problem of inventory replenishment scheduling (time and quantity) and delivery scheduling (time and route). Once an inventory replenishment schedule is determined, the delivery scheduling problem is solved utilizing VRP approaches. The problem is that independent inventory scheduling and independent delivery scheduling generally have contradicting solutions for delivery time. Hence, an increase in transportation cost may decrease inventory cost, and vice versa. In this paper, to cope with this contradiction, we construct an integrated inventory and delivery scheduling model, and develop an algorithm that minimizes total costs including inventory cost and transportation cost in a given planning horizon. We included a constant interval restriction of delivery on the delivery scheduling problem associated with the solution for the independent inventory scheduling problem, so to easily derive an approximate solution for the general MPIRP. Several alternative delivery-day combinations, which we call delivery patterns that contribute to the same inventory cost, were generated for each retailer under the assumption of stable demand, and the best combination of delivery patterns for retailers that minimizes transportation cost was determined using the proposed algorithm, The proposed model outperformed the existing MPIRP model in terms of total cost, reducing the total cost more than 10% in average.

Original languageEnglish
Pages (from-to)12-18
Number of pages7
JournalJournal of Japan Industrial Management Association
Issue number1
Publication statusPublished - 2005
Externally publishedYes


  • Delivery
  • IRP
  • Inventory
  • Scheduling
  • TSP
  • VRP


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