Implementing a near-optimal solution for the multi-stage, multi-product capacitated lot-sizing problem by rolling out a cyclical production plan

This paper describes the implementation and operational results of a cyclical master production-scheduling model, steering the manufacturing process of a photographic film-producing company. The involved company has a number one or two selling position in the medical and graphical film market. In film production all items are produced within two stages. The first stage is process-oriented and produces a limited number of intermediate products. The second stage is flow-shop oriented and cuts and slices the intermediate products into a large number of end products. In its search for a global optimum, the company wanted to synchronise operations by establishing a common replenishment period as a co-ördination mechanism between the first and second production stage. The proposed cyclical model uses a level-by-level approach and solves the economic lot-scheduling problem (ELSP). The cyclical model proved to be very robust when aligning with dynamic demand, allowing a synchronisation of operations. Based on the resulting schedule stability management lowered the levels of safety stock, which resulted in significant savings. This paper compares the cyclical model with the mathematical optimum, generated by solving the corresponding capacitated lot-sizing problem (CLSP). The results prove the ability of the proposed method to achieve a near optimal solution. The cyclical model does not suffer from the NP hardness of the CLSP and is, therefore, able to solve large-scale models.