An EPQ model with partial backorders considering two backordering costs

We propose an EPQ model with partial backorders considering linear and fixed backordering costs. Time intervals rather than ordering size and backordering level are used as decision variables to derive the closed-form optimal solution. Our approach analyzes different optimal inventory policies and decides whether shortage period should be scheduled. In addition, a critical backordering rate is derived to determine the feasible optimal solution. The numerical example is provided to illustrate the solution procedure.