Simultaneous selection factories, assignment products to factories, lot-sizing and scheduling in distributed permutation flow shop

The simultaneous selection factory's problem has been recently proposed as a generalisation in distributed permutation flow shop setting. In this paper, a new generalisation of simultaneous lot-sizing and scheduling decisions in permutation flow shop problem to the distributed permutation flow shop has been studied. Under this generalisation, it is not necessary to use all existing factories and each product cannot be produced in more than one factory. An exact formulation of the problem provided as a mixed integer program. In order to solve the problem, a heuristic procedure has been developed. To test the accuracy of heuristic, a lower bound is developed and compared against the optimal solution.