A single-supplier, multi-buyer, multi-product VMI production-inventory system under partial backordering

Abstract

The vendor managed inventory (VMI) is an efficient coordination policy in supply chain management, in which supplier is responsible to manage inventory at the buyer and decides on replenishment policies. This paper presents a VMI model for a supply chain problem with a single supplier, multi-buyer and multi-product, via a production-inventory system in which shortage is allowed and partially backordered. In order to take into account the concern about environmental issues, the total green house gas emission is also considered as a green constraint. The aim is to find the appropriate values of production quantity and the maximum shortage level for all products of all buyers in such a way that the total cost of supply chain is minimized under VMI. The problem is formulated as a non-linear programming model and then a decomposition based analytical approach is proposed to solve it optimally. At the end, a numerical example is discussed to illustrate the proposed approach.