Sensitivity of multi-product two-stage economic lotsizing models and their dependency on change-over and product cost ratio’s

This study considers the production and inventory management problem of a two-stage semiprocess production system. In case both production stages are physically connected it is obvious that materials are forced to flow. The economic lotsize depends on the holding cost of the endproduct and the combined change-over cost of both production stages. On the other hand this 'flow shop' is forced to produce at the speed of the slowest stage. The benefit of this approach is the low amount of Work In Process inventory. When on the other hand, the involved stages are physically disconnected, a stock of intermediates acts as a decoupling point. Typically for the semi-process industry are high change-over costs for the process oriented first stage, which results in large lotsize differences for the different production stages. Using the stock of intermediates as a decoupling point avoids the complexity of synchronising operations but is an additional reason to augment the intermediate stock position. The disadvantage of this model is the high amount of Work-In-Process inventory. This paper proposes the 'synchronised planning model' realising a global optimum instead of the combination of two locally optimised settings. The mathematical model proves (for a two-stage single-product setting) that the optimal two-stage production frequency corresponds with the single EOQ solution for the first stage. A sensitivity study reveals, within these two-stage lotsizing models, the economical cost dependency on product and change-over cost ratio‟s. The purpose of this paper is to understand under which conditions the „joined setup‟ or the „two-stage individual eoq model‟ remain close to the optimal model. Numerical examples prove that the conclusions about the optimal settings remain valid when extending the model to a two-stage multi-product setting. The research reveals that two-stage individually optimized EOQ lotsizing should only be used when the end-product stage has a high added value and small change-over costs, compared to the first stage. Physically connected operations should be used when the endproduct stage has a small added value and low change-over costs, or high added value and large change-over costs compared to the first production stage. The paper concludes with suggesting a practical common cycle approach to tackle a two-stage multi-product production and inventory management problem. The common cycle approach brings the benefit of a repetitive and predictable production schedule.