The classical literature of inventory management focuses on optimizing an inventory system with complete knowledge of its parameters: we know in advance the demands, or the distribution they will be drawn from. Many efforts have been put into characterizing the optimal ordering policies, and providing efficient algorithms to find them. See e.g. the Economic Order Quantity model [

The credibility theory was introduced by B. Liu as a new way to describe the fuzzy uncertainty. The credibility measure is the fundamental notion of the credibility theory. Recently, L.Yang and K. Iwamura extended the credibility measure by defining the parametric measure $m_{\lambda}$ ($\lambda$ is a real parameter in the interval $[0,1]$ and for $\lambda= 1/2$ we obtain as a particular case the notion of credibility measure). By using the $m_{\lambda}$-measure, we studied in this paper a risk neutral multi-item inventory problem. Our construction generalizes the credibilistic inventory model developed by Y. Li and Y. Liu in 2019. In our model, the components of demand vector are fuzzy variables and the maximization problem is formulated by using the notion of $m_{\lambda}$-expected value. We shall prove a general formula for the solution of optimization problem, from which we obtained effective formulas for computing the optimal solutions in the particular cases where the demands are trapezoidal and triangular fuzzy numbers. For $\lambda=1/2$ we obtain as a particular case the computation formulas of the optimal solutions of the credibilistic inventory problem of Li and Liu. These computation formulas are applied for some $m_{\lambda}$-models obtained from numerical data.

We study multi-product inventory control problems where a manager makes sequential replenishment decisions based on partial historical information in order to minimize its cumulative losses. Our motivation is to consider general demands, losses and dynamics to go beyond standard models which usually rely on newsvendor-type losses, fixed dynamics, and unrealistic i.i.d. demand assumptions. We propose MaxCOSD, an online algorithm that has provable guarantees even for problems with non-i.i.d. demands and stateful dynamics, including for instance perishability. We consider what we call non-degeneracy assumptions on the demand process, and argue that they are necessary to allow learning.

A new tech trend has emerged at the world's largest retailer, as Walmart brings on board thousands of robots in nearly 5,000 of its 11,348 stores. According to CNN Business, these robots will be scrubbing floors, scanning boxes, unloading trucks and tracking shelf inventory at mostly domestic U.S. locations. Robots will replace lower-level jobs--serving in janitorial functions as well as performing basic inventory work--in order to manage rising costs. A new robot unloader has already been used on the docks in hundreds of stores, pulling boxes from delivery trucks while automatically scanning and sorting merchandise. The unloader will be deployed at over 1,100 retail locations in the near future.