Lot sizing and job shop scheduling with compressible process times: A cut and branch approach

This paper studies simultaneous lot sizing and scheduling problem in a job shop environment over a finite number of periods. The machines are flexible such that the production manager is able to change their working speeds. Also, the production schedule of the items over machines should be in consistence with technological precedence relationships. The problem is formulated as an integer linear program. Then, a number of valid inequalities are developed based on the problem structures. The proposed valid inequalities are added to the problem formulation in a “cut and branch” manner to accelerate the search process by common solvers. Finally, performance of the valid inequalities is investigated with CPLEX 12.2 on a set of randomly-generated test data.