Aggregate Constrained Inventory Systems with Independent Multi-Product Demand

In many practical problems inventory managers are confronted with aggregate constraints that are the result of warehouse space limitations, available workforce, maximum investments or a demanded client service level. We analyze and optimize this multi-product inventory problem with independent demand and one or multiple aggregate constraints. For demand we consider discrete distributions, Poisson and compound Poisson, but also the approximating continuous normal distribution. We analyze and quantify the performance criteria errors of the classic one-item inventory equations when applying the approximating normal distribution. The considered performance criteria are: average inventory, average backorders, average order frequency, fill rate service level and order-line service level. An exact formula is created for the order-line service level. We introduce error-reducing functions for each of the performance criteria. We create closed formed approximations for the standard normal first and second order loss functions and also for their inverse functions. We develop three methods for optimizing these multi-item inventory problems with aggregate constraint(s). Through the use of two practical cases we show the significant potential of multi-item system approach.

Steven De Schrijver
  • El-Houssaine Aghezzaf Hendrik Vanmaele
May 26, 2012, 1:40 p.m.
Research group