1. INTRODUCTION
Title of the article is “Minimizing the sum of earliness/tardiness in multi-machine scheduling: a mixed integer programming approach”, and which at first defines the ET systems briefly. An early or late delivery will affect cost directly and objective of the ET problem fits perfectly. Assumptions in this problem are;
• Due date assignments; being JIT is important to have maximum benefit from the sold product.
• Penalty costs for being early or late; both situations cause penalty costs from warehouse or customer.
• Sequence dependencies; machines setups are important in some cases and also the precedence may be required.
• Machines; single or multiple machine systems are designed and N jobs are assigned to M machines. Moreover expectation is to reduce penalty costs by assigning in the right sequence.
The author constructed a model by considering the above definitions and made a first draft, provided in the appendix 1. The objective function is about reducing the sum of earliness and tardiness costs with respect to the times of being early or tardy. First constraint claims the equality of the due date in terms of the time including the completion, earliness, tardiness, which restricts the values of being tardy or early because the due dates are appointed. Second constraint is a determination factor in binary system where if Z11 equals to 1 that job is held on machine 1 otherwise 0. Third and fourth constraints define the relation between precedence of jobs over the machines. Moreover this also helps to assign machines. Last constraint of the first draft ensures that the completion time of a job i is far enough after that of job j to include the processing time and setup time for job i. this model has much 1 and 0 variables which increase the solving time of the LP. To become more efficient, author considered to improve the model by adding or