Job Shop Sequencing Problem on Two Machines with Time Lag Constraints

The problem studied is that of two-machine job shop sequencing where some jobs are processed first on machine 1 and then on machine 2, while the remaining jobs are processed in the reverse order. The objective is to determine an ordered sequence which minimizes the total processing time, subject to some specified lag time constraints. A rule is given for determining two different sequences for the two machines which represent an optimal solution.