This paper is concerned with an n jobs one machine Job shop scheduling problems in which all jobs have a common due date and unequal penalties occur when a job is completed before or after due date. The objective is to determine an optimal sequence and the corresponding common due date that yield the global minimum value of a penalty function Then a sequence that minimize the penalty function globally is a V-shaped sequence Using the idea of linear equations and a LGP(Linear Goal Programming), this paper shows that LGP and MAD(Mean Absolute Deviation) are equivalent problems. Therefore an efficient algorithm that is developed for MAD problem holds for LGP problem and vice-versa. A numerical example to account for the algorithm is provided.