Random sales price-sensitive stochastic demand

Purpose This research work introduces an imperfect production system where the demand is assumed to be stochastic and it is influenced by random selling price. The shift time from an “in-control” state to an “out-of-control” state is exponentially distributed. The accumulated inventory contains both perfect and defective items which are all sold with a free repair warranty (FRW) offer. Complete back ordering of shortages are taken into account. The purpose of this paper is to determine the optimal selling price and hence the optimal production lot size such that the expected profit is maximized. Design/methodology/approach The general model is discussed separately for both types of uniformly distributed selling price-sensitive demand pattern: additive type and multiplicative type. Numerical examples and graphical representations of the optimal solutions are provided to illustrate the models. Findings This paper helps the manager to manage future situations and it may be considered as a base work for the researchers to work in this direction. Research limitations/implications The main limitation of this model is to consider a single item for a single channel system. There are many correlated issues that need to be further investigated. The future study in this direction may include the consideration of multi-items, diverse demand pattern with different types of price distributions. Originality/value In the production inventory literature, plenty of articles are available considering imperfect production but none of them have considered selling price-sensitive stochastic demand where the sales price is random in character under an FRW offer.