So if we consider all possible starting times for each job we end up with this big matrix where we have divided the columns referring to each job. The red columns refer to the red job and each column is a possible schedule. The blue is the second job and each column is a possible schedule. So the first job lasts three units of time, and these are its three corresponding ones. The second lasts two units of time and the third one four units of time. We call the column jp the pattern p of job j. Then we introduce a variable x_jp with value 1 if the pattern p of task j is employed, 0 otherwise. Then we have to impose that at least one pattern be taken because the job must be processed. So, we need another matrix which takes care of this assignment constraint. Let's call the first matrix A, the second one B, then the constraints say that Ax is less or equal to 1, so that there is no overlapping in time of the jobs and Bx is equal to 1 meaning that each job is processed at a certain time. The variables must be 0,1. Then if we attach a cost to each pattern we may minimise the cost over all possible patterns. However, the problem here is integral and we relax it as before.