A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints

This paper develops a mathematical model for a single period multi-product manufacturing system of stochastically imperfect items with continuous stochastic demand under budget and shortage constraints. After calculating expected profit in general form in terms of density functions of the demand and percentage of imperfectness, particular expressions for those density functions are considered. Here the constraints are of three types: (i) both are stochastic, (ii) one stochastic and other one imprecise (fuzzy) and (iii) both imprecise. The stochastic constraints have been represented by chance constraints and fuzzy constraints in the form of possibility/necessity constraints. Stochastic and fuzzy constraints are transformed to equivalent deterministic ones using ‘here and now’ approach and fuzzy relations respectively. The deterministic problems are solved using a non-linear optimization technique-Generalized Reduced Gradient Method. The model is illustrated through numerical examples. Sensitivity analyses on profit functions due to different permitted ‘aspiration’ and ‘confidence’ levels are presented.