Synchronization of replenishment decisions for the multi stage economic lot delivery and scheduling problem

The challenging problem of jointly sequencing multiple items at the manufacturer facility, deciding on the delivery policy of end-items to the downstream retailers, as well as the replenishment strategy of raw materials from upstream suppliers is tackled in this paper. The objective is to develop the production and shipping schedule such that the chain-wide total setup, holding and ordering costs are minimized while satisfying end customers´ demand. The manufacturer adopts the common rotation cycle policy in which all the end-items are produced sequentially on a single facility within that cycle. A mixed-integer nonlinear programming formulation that adopts the integer multiplier of the cycle time policy is developed. Through the use of differential calculus, an interval that brackets the optimal value of the cycle time is identified followed by a greedy search algorithm within that interval. A numerical example that illustrates the efficiency of the proposed solution algorithm is also presented.