Job shop scheduling with alternative machines

In this paper the authors investigate the problem of minimizing the mean flow time in a general job shop type machining system with alternative machine tool routeings. An analytical formulation of the problem as a mixed integer programming is developed. An efficient algorithm based on this formulation is developed to solve the problem by decomposing it into subproblems that are easier to solve. The algorithm solves large problems in relatively short time. A second algorithm based on the SPT rule is developed and its performance is compared with the first algorithm. A greedy procedure is also developed for the case when a penalty cost is associated with adding alternative machines. Numerical examples are given to demonstrate the use of the above algorithms.