The economic lot-size scheduling problem with equally sized batch shipment policy and stochastic demands

This study investigates economic lot-size scheduling problem (ELSP) comprising stochastic demand and equally sized batch shipment policy in a one-supplier multi-buyer integrated inventory model. All buyers have agreed on a joint replenishment policy with a common replenishment cycle (CRC). Equally sized batch shipment scheduling policy for each product in one CRC is applied to the whole system. The objective is to determine the optimal common replenishment cycle and the numbers of batch-shipment for each product, all of which minimises the integrated total cost. Moreover, a new concept is introduced; namely, critical replenishment cycle. The replenishment cycle division (RCD) and recursive tightening (RT) methods are then developed to obtain the optimal solutions to the subject problem. Two theorems are verified to ensure that the solution of ELSP involving equally sized batch shipment and stochastic demand model with the CRC policy obtained by the RCD and RT methods reaches the global optimum. An example is presented to illustrate the procedures involved in the RCD and RT methods. [Received 5 March 2013; Revised 25 September 2013; Revised 3 December 2013; Accepted 11 December 2013]