Optimal Run Time for EMQ Model with Backordering, Failure-In- Rework and Breakdown Happening in Stock-Piling Time

This study examines the optimal run time for the economic manufacturing quantity (EMQ) model with failure-in-work, backlogging, and random breakdown happening in stock-piling time. A recent article by Chiu and Chiu [Mathematical modeling for production system with backlogging and failure in repair, Journal of Scientific & Industrial Research, 65 (2006) 499-506] investigated optimal lot-size for EMQ model with backordering and failure-in-rework. By incorporating random machine breakdown-another inevitable reliability factor into their model, this research examines its effects on the optimal run time and on the long-run average costs. Mathematical modeling and cost analysis are employed and the renewal reward theorem is used to cope with variable cycle length. Convexity of the expected productioninventory cost function is proved. An optimal replenishment policy that minimizes overall costs is derived for such an unreliable system. Numerical example is provided to show its practical usage. Managers in the field can adopt this run time decision to establish their own robust production plan accordingly. Key-Words: Manufacturing, Run time, Breakdown, Failure-in-rework, Backorder