Consignment stock theory with a fixed batch manufacturing process

This paper deals with stock control in a supply chain. The focus is on consignment stock (CS), an innovative collaborative relationship, which can create a win–win situation between the vendor and the buyer. Recently some analytical formulations have been proposed to optimise CS, and the present paper extends these models by considering a new critical factor: a fixed batch production process at the vendor's plant. This kind of production is typical if there are batch processing machines that can hold and simultaneously process a finite number of items, such as kilns for long heat treatment. Specifically, we consider a deterministic single-vendor single-buyer system. The buyer consumes a single product at a constant rate and is replenished by the vendor who produces in batches and incurs set-up costs. Each batch is dispatched to the buyer in a number of shipments, some of which may take place while production is still running. To minimise total operating costs (that is, manufacturing, replenishment and holding), two alternative production and shipment policies are proposed and analytically formulated as integer optimisation models. A step by step heuristic procedure to obtain the optimal solution is finally presented and demonstrated through numerical examples.