Inventory drift and instability in order-up-to replenishment policies
Abstract
Production and inventory control (PIC) systems often comprise of two feedback loops. One is for maintaining inventory levels and the other is to constrain Work in Progress (WIP or “orders placed but not yet received”) levels. The inclusion of the WIP feedback loop is highly desirable because it allows a superior dynamic response to be obtained compared to a PIC system with only a single inventory feedback loop. In particular it is a big step towards enabling high customer service levels coupled with high stock turnover. However it comes at an additional financial cost. This is because extra information has to be included in the production ordering decision and the production lead-time needs to be accurately estimated. It is known that if the production lead-time is inaccurately estimated then there will be a steady-state error in the actual inventory level. The associated WIP calculation (which is used in the vast majority of academic OR and inventory management literature) is based on measuring and accumulating the difference between production orders and production completions after the “actual” production lead-time. This “actual” WIP level is then compared to a target WIP that is based on our “perception” of the production lead-time. It is this difference between “actual” and “perceived” production lead-time that causes the inventory error to occur. Consequently serious negative implications for either customer service levels (i.e. availability, fill rates) or inventory-holding costs may arise. We propose a solution to this problem by calculating the WIP levels used in the control algorithm in a slightly different manner. In this new method, WIP levels are based on our “perceived” production lead-time. This “perceived” WIP is then compared to our target “perceived” WIP level and because the comparison is based solely on a “perceived” production lead-time, the inventory drift problem is completely eliminated. Of course, if our perceived production lead-time was correct, then there is no difference between the established and the proposed WIP calculation methods. We have investigated this new method with simulation, z-transforms and stability and bifurcation analyses. We show via simulation that the proposed method also achieves the desired result when the lead-time changes over time for the case when the lead-time change is noticed (and the Order-Up-To (OUT) system settings updated) and when it is not noticed. The implications of this research are potentially far-reaching. It creates a whole new range of OUT system structures suitable for use in an uncertain world. These are robust and help ensure tight control despite variation in mean production lead-times.