of different processing routes without recirculation. The jobs on each machine should be ordered to minimize the makespan. • Job set and machine set: 𝐽 = {1, 2, … , |𝐽|} and 𝑀 = {1, 2} • Processing time of 𝑘th (𝑘 ∈ {1, 2})) operation of job 𝑗 ∈ 𝐽: 𝑝!4 • Processing route of job 𝑗 ∈ 𝐽: 𝜇! = 𝜇!# , 𝜇!$ ∈ { 1, 2 , 2, 1 } • Job sequence on machine 𝑚 ∈ 𝑀: 𝜋- = (𝜋-# , 𝜋-$ , … , 𝜋- " ) • Starting time of operation (𝑗, 𝑘): 𝑆!4 • Completion time of operation (𝑗, 𝑘): 𝐶!4 • Makespan: 𝐶%&' = max !,4 ∈"×{#,$} 𝐶!4 Two-Machine Job Shop Scheduling Problem