An inventory model for non-instantaneous deteriorating items with multivariate demand and backlogging under inflation

In this paper, a deterministic inventory model for non-instantaneous deteriorating items with price- and time-dependent demand with inflation is developed. The demand is continuous and differentiable function of price and time. Shortages are allowed and the unsatisfied demand is partially backlogged at a negative exponential rate with the waiting time. The objective is to find the optimal replenishment cycle such that present value of total profit is maximized, for any given selling price. We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model that can be easily implemented by practitioners. Comparisons of the present model with various cases are presented as the special case. Numerical examples are used to illustrate the theoretical results and the sensitivity analysis with respect to major parameters on the optimal solutions is also performed.