Optimizing profit for pricing and advertisement sensitive demand under unreliable production system

Abstract

ABSTRACT This article deals with an imperfect economic production quantity (EPQ) model with an unreliable production system where the customers' demand depends on both selling price and advertisement. During the long run production process the machinery system goes into ‘out-of-control’ state after a random time τ and after that the system produces both perfect and imperfect quality items together. The imperfect or defective quality items are reworked to get it back as the perfect ones at a cost just after the regular production run time. The production process of imperfect quality items depends on the reliability of the machinery system where the failure rate may be variable. Here, we consider that the random time variable τ follows the two parameters ‘Weibull distribution’. The objective of this article is to maximize the expected average profit function of the unreliable system with respect to ordering lot size, selling price and frequency of advertisement. We use the incomplete gamma function to formulate the expected average profit function. The model is validated by numerical examples and sensitivity analysis is provided to illustrate the model.