The optimal production-run time for a stock-dependent imperfect production process

This paper develops an inventory model for a hypothesized volume flexible manufacturing system in which the production rate is stock-dependent and the system produces both perfect and imperfect quality items. The demand rate of perfect quality items is known and constant, whereas the demand rate of imperfect (non-conforming to specifications) quality items is a function of discount offered in the selling price. In this paper, we determine an optimal production-run time and the optimal discount that should be offered in the selling price to influence the sale of imperfect quality items produced by the manufacturing system. The considered model aims to maximize the net profit obtained through the sales of both perfect and imperfect quality items subject to certain constraints of the system. The solution procedure suggests the use of ‘Interior Penalty Function Method’ to solve the associated constrained maximization problem. Finally, a numerical example demonstrating the applicability of proposed model has been included.