Investigation of an additional part to optimal schedule

The pair‐wise comparison technique has been applied to many algorithms for solving complicated scheduling problems. The optimality gap between the pair‐wise comparison technique and mathematical programming model is mainly due to deterioration in performance when optimal pairs of different sub‐schedules are linked together to form a complete schedule. This paper investigates the effect of adding a part prior to the part‐pair in a 2‐part‐2‐machine optimal sub‐schedule. The conditions in which interchange of part‐pair sequence is required in order to minimise or maintain the makespan when a part is added are analysed mathematically, and the results are reported.