Optimal Inventory Level Control and Replenishment Plan for Retailers

Chih Kang Lin, Shangyao Yan, Fei Yen Hsiao

Research output: Contribution to journalArticlepeer-review


In vendor managed inventory (VMI) operations, it is necessary for both the suppliers and the customers to reach an agreement on the maximal and minimal inventory level. In practice, in VMI, inventory levels are decided manually by planning personnel, based on their experience and past operating records. From a system optimization point of view, the determination of the upper and lower inventory levels in storage areas is complicated, necessitating analysis of many factors. Consequently, it may not be possible to obtain the best planning results, to determine and maintain the optimum levels of inventory. In this study, we utilize network flow techniques to build a replenishment model to deal with the upper-and-lower inventory level control problem, with the objective of minimizing the total cost in short-term operations, subject to inventory level control and other operating constraints. The model is formulated as an integer network flow problem with side constraints and is characterized as NP-hard in terms of optimization. To efficiently and effectively solve the large-scale problems that occur in the real world, a solution algorithm is also developed. Finally, numerical tests are conducted using real data from a major retail company in northern Taiwan. The results demonstrate the usefulness of the proposed model and solution algorithm for replenishment planning in actual practice.

Original languageEnglish
Pages (from-to)57-83
Number of pages27
JournalNetworks and Spatial Economics
Issue number1
StatePublished - Mar 2021


  • Network flow
  • Replenishment planning
  • Solution algorithm
  • Upper-and-lower inventory level
  • Vendor managed inventory


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