Inventory Management

Inventory Management tries to optimize the ordering of stocks and safety stocks along the supply chain, aiming to minimize holding and backorder costs while fulfilling the typically uncertain demand of customers. We develop methods for the measurement and control of inventory system performance under uncertainty. The research focuses on robust policies for integrated forecasting and replenishment under non-stationary conditions. Applications are the distribution of safety stocks in supply networks in the process industries, spare parts distribution, and reorder policies in retailing.

Spare parts:
For almost all technical products there exist spare parts which have to be provided until long after the end of production of the particular product (think of product warranty). Often it is not known whether units of the original product are still in someone‘s use and if therefore spare parts should still be provided or not. In such a case, the questions are how many spare parts to keep, whether to keep spare parts at all or alternatively to follow different strategies like, e.g., remanufacturing.

Newsvendor:
The Newsvendor is one of the most famous problems in inventory management. Imagine, you want to sell newspapers tomorrow and you can decide only at the beginning of the day, how many newspapers you buy in order to sell them later. After having bought a certain number, there are three scenarios: 1) (unlikely) There are exactly as many customers as you have newspapers on stock. 2) There are more customers than you had newspapers (you lose profit by not having enough newspapers). 3) There are less customers than newspapers (you lose some money for buying but not selling them). Luckily, there exists an analytic solution on how many newspapers you should buy in the first place, depending on some assumptions and inputs like, e.g., procurement price. The logic behind the newsvendor problem can be found in lots of other applications.

Data-driven inventory control:
In inventory control, we usually face a lot of uncertainty, e.g. customer demand, stochastic lead times or price changes. For modeling these uncertainties often parametric stochastic distributions are used. However, the more direct way would be to use data directly and hence the original non-parametric distribution. Data-driven inventory control accomplishes this, see, e.g., the data-driven newsvendor.

Safety stocks:
Wherever you face uncertainty, you tend to search for an insurance against this uncertainty. In inventory management, this insurance are safety stocks. But caution: Does your insurance premium stand in relation to the risk? Too much safety stock might cause high holding costs. Therefore, one reasonable idea is to relate the amount of safety stock to a certain service level that should be accomplished.