This paper addresses the problem of scheduling a set of jobs with a common due data on a single machine. The objective is to minimize the sum of the earliness and tardiness of jobs subject to $T_{max}{le}{Delta};for{Delta}{ge}0$. Properties for the $MAD/T_{max}$ problem are found and the problem is shown to be NP-complete in the ordinary sense. According to the range of Δ, the problem can be solved in polynomial time. Also, some special cases where an optimal schedule is found in polynomial time are discussed.