A method is required to deal with earliest and latest penalties for each job in machine scheduling. Special types of jobs are costly and they must attract penalty in case they complete the operations earlier and also later than the specified due date. It is a custom to consider only the latest penalty (tardiness) in case it is delayed beyond the due date. Here it is assumed that the customer satisfaction affects the reputation of industry in case it delivers its products beyond the due dates. It is also equally important to see that the costly finished jobs are to be kept in inventory for minimum amount of time to reduce the inventory carrying costs to the extent it is possible. Hence it is felt equally important to add the earliest penalty to the latest penalty of all the jobs. Even though the costly jobs which are completed early may not affect the external environment, but it surely affects the financial aspect of the industry to some extent. By adding these two controversial terms in objective function it is possible to generate the schedule by using the lagrangian relaxation technique which optimizes the objective function. As the objective function consists of multi objectives as mentioned above, it is framed as a linear function rather than quadratic function.
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