An economic production lot size model for randomly imperfect production system with stock-dependent demand and rework

Abstract

This paper considers a single item, imperfect economic production lot-size (EPL) model with stock-dependent demand and partial rework. In real life EPL models, defective production commences from the out-of-control state, after the passage of some time from production commencement. Its occurrence is random after the lapse of certain time and imposed here through a chance constraint. The set-up cost is partly production dependent. Unit production cost is also production dependent and a part of it is taken as environment protection cost. Defective rate is also assumed to be random and production dependent. The model is formulated as an average cost minimisation problem subject to a chance constraint and solved using a nonlinear optimisation technique - generalised reduced gradient (GRG) method through LINGO 11.0. Several special cases are derived and more specifically, the present investigation the works of Sana (2010) and Khouja and Mehrez (1994). Numerical experiments are performed to illustrate the general and particular models. Some sensitivity analyses are presented against few model parameters.