One of the most common and successful approaches for integrated supply chain management (SCM) is vendor-managed inventory (VMI). In VMI, a vendor takes control decisions retailers. To establish long-run relationship between retailer, it necessary to consider two impactful factors: vendors retailers' reliability, optimal selection For this purpose, redundancy allocation problem (RAP), as an effe...

Background: The classical mathematical formulation of the vendor-managed inventory (VMI) model assumes an infinite planning horizon, and consequently, solution derived ignored impact first cycle. is associated with another implicit assumption that input parameters remain static indefinitely. Methods: This paper develops two models for VMI a joint economic lot-sizing (JELS) policy. Each consider...