An advertising-inclusive production lot size model under continuous discount pricing

This article deals with the interaction of a deterministic production lot size inventory model with uniform replenishment rate and differential pricing conditions. We present a method for arriving at a production lot size formula, which takes into account the effect of varying marketing conditions on demand and the possibility of defective items in the production process. Additionally, based upon the previous studies, different model formulations are introduced to deal with the issue of defective items. The profile maximization problem for this model is derived for two quantity discount cases: hyperbolic-decreasing and linear-decreasing. A numerical example along with sensitivity analysis is provided to illustrate the results derived. Furthermore, an easy-to-use computer algorithm is developed to determine the optimal values of production lot-size and profit.