Deteriorating inventory model with quadratically time varying demand and partial backlogging

[EN] In this paper, a deterministic inventory model is developed for instantaneous deteriorating items in which shortages are allowed and partially backlogged. Deterioration rate is constant, demand rate is quadratic function of time and holding cost is linear function of time, backlogging rate is variable and depends on the length of the next replenishment. The model is solved analytically by minimizing the total inventory cost. This inventory model can also use as an inventory model for linear as well as constant demand rate by very small change in the incremental factor of the quadratic function. Numerical examples are provided to illustrate the solution and application of the model.