A multiple-retailer replenishment model under VMI: Accounting for the retailer heterogeneity

- We model a single supplier - multiple retailer replenishment scenario under VMI.
- Our model outperforms the existing models for all levels of retailer heterogeneity.
- We introduce a measure for calculating the level of heterogeneity in a VMI system.
- We perform a numerical analysis to comment on suitability of the various policies.

Vendor managed inventory (VMI) is a well-established supply chain practice where the supplier is responsible for managing inventory at the retail point. In particular, the supplier takes care of when to order and how much to order on behalf of the retailer. This paper considers a single supplier - multiple retailer setting where the supplier takes inventory replenishment decisions for retailers such that the replenishment quantity for each retailer is within an upper bound that is mutually agreed upon in the VMI contract. We develop a nonlinear mixed-integer programming model to compute the optimal replenishment frequency and quantity for each of the retailer, such that the total system cost is minimized. A conceptual and numerical comparison is made with the existing models in the VMI literature. The proposed model is found to perform better for all levels of retailer heterogeneity, thereby establishing generalization among the class of models. We also propose an efficient heuristic for solving the proposed model by utilizing the concept of cycle ratio (setup cost/holding cost ∗ demand), thus reducing the computational time drastically. Lastly, through a numerical analysis, we find that the proposed model with integer ratio policy structure is more stable as compared to the existing alternative replenishment models.