Lot sizing with perishable items

We address the uncapacitated lot sizing problem for a perishable item that has a deterministic and fixed lifetime. In the first part of the study, we assume that the demand is also deterministic. We conduct a polyhedral analysis and derive valid inequalities to strengthen the LP relaxation. We develop a separation algorithm for the valid inequalities and propose a branch and cut algorithm to solve the problem. We conduct a computational study to test the effiectiveness of the valid inequalities. In the second part, we study the multistage stochastic version of the problem where the demand is uncertain. We use the valid inequalities we found for the deterministic problem to strengthen the LP relaxation of the stochastic problem and test their effiectiveness. As the size of the stochastic model grows exponentially in the number of periods, we also implement a decomposition method based on scenario grouping to obtain lower and upper bounds.