Replenishment Decision Making with Permissible Shortage, Repairable Nonconforming Products and Random Equipment Failure

Abstract: This study is concerned with replenishment decision making with repairable nonconforming products, backordering and random equipment failure during production uptime. In real world manufacturing systems, due to different factors generation of nonconforming items and unexpected machine breakdown are inevitable. Also, in certain business environments various situations between vendor and buyer, the backordering of shortage stocks sometimes is permissible with extra cost involved. This study incorporates backlogging, random breakdown and rework into a production system, with the objective of determination of the optimal replenishment lot size and optimal level of backordering that minimizes the long-run average system costs. Mathematical modeling along with the renewal reward theorem is employed for deriving system cost function. Hessian matrix equations are used to prove its convexity. Research result can be directly adopted by practitioners in the production planning and control field to assist them in making their own robust production replenishment decision.