A manufacturer-buyers integrated inventory model with generic distribution of lead times to deliver equal and/or unequal batch sizes

Although lead time variation is common in practice, integrated single-manufacturer multi-buyer model considering this factor is unavailable in the extant literature. This article considers generic distribution of lead times of delivering equal and/or unequal batch (sub-lot) sizes of a lot in developing a synchronised integrated single-manufacturer multi-buyer model. The batch sizes are assumed to be in geometric series. The variables considered in the model are the smallest batch size, total number of batches and number of unequal batch sizes delivered from the manufacturer to buyers. The smallest batch sizes delivered to the buyers are bounded below by 1 and above by the capacity of the transport vehicle. The minimal total cost solution technique to the model is derived by the method of differentiation. Significant minimal total cost reductions by the synchronised flow is illustrated through solutions to some numerical example problems. Sensitivity analyses on increasing costs of transportation, shortage, inventory and increasing mean lead times upon the optimal solution have been performed.