Optimal promise time for customer orders in imperfect discrete production systems with earliness and lateness penalties

Discrete production systems are very common in industry. This paper studies the case where the system may generate imperfect units and rework is performed immediately before starting a new unit. These systems have not received enough attention in the existing literature. We consider make-to-order imperfect discrete production systems where the manufacturer quotes the customer a promise time for delivering the ordered quantity. This is a very realistic problem that arises often in practice. The random occurrence of imperfect units results in a huge number of possible outcomes. This difficulty is resolved by defining new quantities, and success times, which are possible points of time where an imperfect unit could be generated. These quantities are used efficiently to compute the probability of having a given number of perfect units in a given time, which in turn is used in determining the optimal promise time that minimises the costs associated with late and early production of the demand. This paper examines three cases: imperfect rework, perfect rework, and non-reworkable/scrapped units. It is expected that this work will generate interest in this type of production system.