un model which is given in Section 2.3 of Article 3 (Tseng et al., 2004) for solving the permutation flowshop makespan minimization problem, is based on the decision variable defining the start (begin) time of the job in a sequence position on a machine. Assume that there is a unit independent (detached) setup time before processing a job on a machine, and the objective to be minimized is the total tardiness, not the meakespan. Defining additional parameters and decision variables, transform the Wilson's model into a model, which is based on the decision variable defining the completion time of the job in a sequence position on's machine. 2. Consider the example problem, which is given in Section 4.2 of Article 4 (Santos and Roa 2007). Suppose that the stages in the example problem have been swapped. That is, machines 1 and 2 of Stage 2 becomes machines 1 and 2 of Stage 1, and machines 1, 2 and 3 of Stage 1 becomes machines 1, 2 and 3 of Stage 2 in the new example problem. Then, the optimal schedule obtained by solving the MILP model given in Section 4.1 is as: Stage 1 Machine 1: Job 2- Job 1 Machine 2: Job 4 Job 3 Stage 2 Machine 1: Job 2 Machine 2: Job 4 - Job 3 Machine 3: Job 1 (a) Draw the Gantt chart of the optimal schedule. (b) Using the optimal schedule, determine the values of all decision variables, and write each constraint explicitly. (e) When you compare the optimal schedules of the example problem given in the article and example described above, what do you observe? the CUSTUCI e Calpe pluuie, wil is givell lll Seul 4.2 U ALLIC 4 Ju duk 2007). Suppose that the stages in the example problem have been swapped. That is, machines 1 and 2 of Stage 2 becomes machines 1 and 2 of Stage 1, and machines 1, 2 and 3 of Stage 1 becomes machines 1, 2 and 3 of Stage 2 in the new example problem. Then, the optimal schedule obtained by solving the MILP model given in Section 4.1 is as: Stage 1 Machine 1: Job 2 - Job Machine 2: Job 4 - Job 3 Stage 2 Machine 1: Job 2 Machine 2: Job 4 - Job 3 Machine 3: Job 1 (a) Draw the Gantt chart of the optimal schedule. (b) Using the optimal schedule, determine the values of all decision variables, and write cach constraint explicitly. (c) When you compare the optimal schedules of the example problem given in the article and the new example described above, what do you observe? un model which is given in Section 2.3 of Article 3 (Tseng et al., 2004) for solving the permutation flowshop makespan minimization problem, is based on the decision variable defining the start (begin) time of the job in a sequence position on a machine. Assume that there is a unit independent (detached) setup time before processing a job on a machine, and the objective to be minimized is the total tardiness, not the meakespan. Defining additional parameters and decision variables, transform the Wilson's model into a model, which is based on the decision variable defining the completion time of the job in a sequence position on's machine. 2. Consider the example problem, which is given in Section 4.2 of Article 4 (Santos and Roa 2007). Suppose that the stages in the example problem have been swapped. That is, machines 1 and 2 of Stage 2 becomes machines 1 and 2 of Stage 1, and machines 1, 2 and 3 of Stage 1 becomes machines 1, 2 and 3 of Stage 2 in the new example problem. Then, the optimal schedule obtained by solving the MILP model given in Section 4.1 is as: Stage 1 Machine 1: Job 2- Job 1 Machine 2: Job 4 Job 3 Stage 2 Machine 1: Job 2 Machine 2: Job 4 - Job 3 Machine 3: Job 1 (a) Draw the Gantt chart of the optimal schedule. (b) Using the optimal schedule, determine the values of all decision variables, and write each constraint explicitly. (e) When you compare the optimal schedules of the example problem given in the article and example described above, what do you observe? the CUSTUCI e Calpe pluuie, wil is givell lll Seul 4.2 U ALLIC 4 Ju duk 2007). Suppose that the stages in the example problem have been swapped. That is, machines 1 and 2 of Stage 2 becomes machines 1 and 2 of Stage 1, and machines 1, 2 and 3 of Stage 1 becomes machines 1, 2 and 3 of Stage 2 in the new example problem. Then, the optimal schedule obtained by solving the MILP model given in Section 4.1 is as: Stage 1 Machine 1: Job 2 - Job Machine 2: Job 4 - Job 3 Stage 2 Machine 1: Job 2 Machine 2: Job 4 - Job 3 Machine 3: Job 1 (a) Draw the Gantt chart of the optimal schedule. (b) Using the optimal schedule, determine the values of all decision variables, and write cach constraint explicitly. (c) When you compare the optimal schedules of the example problem given in the article and the new example described above, what do you observe