Vendor-managed inventory for joint replenishment planning in the integrated qualitative supply chains: generalised benders decomposition under separability approach

Vendor managed inventory (VMI) is a well-established supply chain (SC) practice where the supplier is responsible for managing the inventory level at the retail point. In this paper, we engage the VMI in a multi-product integrated qualitative supply chain in order to make the best joint replenishment policy. Accordingly, a screening process classifies the products into good and defective products. This process imposes the reworking cost, the disposal cost, the holding cost, and the screening cost on the model. A penalty mechanism will penalise the supplier, if the replenishment quantity exceeds the certain upper bound agreed upon the VMI contract. The model comes with some real stochastic constraints. The mathematical formulation of the model is stochastic, Mix Integer Nonlinear Programming (MINLP), and hard to solve. In this regards, Generalised Benders Decomposition (GBD) under separability approach is employed for optimising the decision variables, including the number of shipments and shipment quantities. The results of numerical analyses showed an excellent performance of the provided method with respect to the optimality criteria like number of taken iterations, optimality error, infeasibility, and complementarity.