Scheduling is resource allocation through time to implement a series of tasks. The allocation of resources over time to run a series of tasks, arise in different positions. In scheduling theory, resources usually referred as a machines and tasks referred as jobs.Some of the important objective of scheduling are efficient use of resources, quick response to demand and adaption of delivery dates with pre-specified due date. One of fields of scheduling is splitting job scheduling. Splitting jobs according to their structural characteristics can divided into two categories: continuous or discrete splitting jobs. In the first category it is possible to split jobs into any form and size but the second category consist of unit jobs and processing time of sub jubs is an integer multiple unit jobs processing time. Both mentioned categories are applicable in many industrial case and they can be discussed with their own unique characteristics. Splitting jobs is the same kind of interruption in job with a difference that splitting jobs can processed at the same time. In this research, minimizing total completion time in parallel machines scheduling problem with setup times and splitting jobs has been studied. According to studies, firstly some dominance rules were developed and used to propose mathematical models and branch and bound algorithms. According to the complexity of the problem, branch and bound algorithms and mathematical models need lots of time to achieve the optimal solution in medium size problems. Hence, in order to obtain good solutions for the size of the problems that optimal method cannot solve them in a reasonable time, a heuristic algorithm was presented that solves problem in two phases: create basic solution and improvement it. The computational results for minimizing total completion time in parallel machines scheduling problem with setup times and splitting jobs indicated that performance of the proposed branch and bound algorithm is better than the mathematical models and can solves problem with 27 unit jobs over 8 machines and 9 jobs in the time limit 3600 seconds. Heuristic algorithm also can solves problem whit average error less than 2.5% for instant of problems with 72 unit jobs over 8 machines and 9 jobs.
