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Machine scheduling by column-and-row generation on the time-indexed formulation

We consider the general machine scheduling problem to minimize the scheduling cost. One of the most efficient approaches to solve this problem is to use time-indexed Integer Programming formulation. However, the size of this formulation is very big, and even solving its Linear Programming (LP) relaxation is very time consuming. In this work, we apply the column-and-row generation approach to solve the LP relaxation of the time-indexed formulation in significantly less amount of time.