A discrete‐in‐time inventory model with deterioration and backlog

A new inventory control system with a constant rate of customer demand is studied. Any physical inventory experiences a constant rate of deterioration and any unsatisfied demand is completely backlogged. Time is treated as a discrete variable, whereas a practical point of view is taken into account by allowing the time at which the physical inventory level goes to zero to be a non‐integer. A closed‐form equation is derived to compute the optimal solution, while no closed‐form solution was presented in literature. This greatly reduces the computational efforts and makes sensitivity analysis possible. Some very useful insights are provided into sensitivity analysis.