Common replenishment cycle with mixed batch shipment policy for a single-vendor multi-buyer integrated system

This study addresses a single-vendor multi-buyer integrated system with a common replenishment cycle and a mixed batch shipment policy. The objective is to determine the common replenishment cycle, number of shipments and the structure of the mixed batch shipment which minimises the integrated total cost per unit time. The isolation model is constructed first, and then the isolation model is integrated into the integration model. The minimum total cost model is transformed into a maximum replenishment cycle model to optimise the structure of the mixed batch shipment. Moreover, two new concepts are introduced, namely domination curve and critical replenishment cycle. A new method, the replenishment cycle division method, is then developed to derive the optimal solutions to the subject problem. Examples are presented to illustrate the procedures involved in the replenishment cycle division method. [Received 2 February 2011; Accepted 13 September 2012]