An integrated vendor–buyer cooperative model under stochastic supply lead-time

This paper presents a single-vendor, single-buyer integrated inventory model. We relax the assumption of deterministic lead-time in the hitherto existing joint economic lot sizing (JELS) models and analyze the problem where the buyer lead-time is a stochastic variable. Moreover, we consider the situation in which shortage is allowed. The vendor produces the product in batches and periodically delivers final goods at a fixed lot size to the customer, who has a constant demand rate. The proposed model, based on the integrated expected total relevant costs of both buyer and vendor finds out optimal values of reorder point, order quantity, and number of shipments, using a solution procedure. Numerical examples are also used to analyze the savings in joint total cost over individually derived policies.