An integrated production inventory model with raw material replenishment considerations in a three layer supply chain

Most of the existing research has focused on a two stage single-vendor single-buyer supply chain. However, in reality, supply chain networks are more complex and involve more than just a vendor and a buyer. This paper deals with the joint economic lot sizing problem (JELP) in the context of a three stage supply chain consisting of a single supplier, single manufacturer and multi-retailers. The objective is to specify the timings and quantities of inbound and outbound logistics for all parties involved such that the chain-wide total ordering, setup, raw material and finished product inventory holding costs are minimized. In developing the model, the cycle time at each stage is set to be an integer multiple of that for the adjacent downstream stage. To bear a better resemblance to practice, shipments from a particular lot are allowed to take place during production and not after producing the whole lot. We employ derivative-free methods to derive a near closed form solution for the developed model. A numerical example is presented for illustrative purposes and a comparison to models established in the literature is also provided.