This paper addresses the problem of scheduling production to meet Just-in-Time requirement in a Flow Shop where jobs are to be completed withingiven due windows rather than single due dates. This problem has been proven to be NP-Complete in the strong sense and shown to be intractable as the number of jobs-andmachines combination increase. Consequently, a Forward Shift Search (FSS) algorithm is developed to solve large problem instances. To assess the performance of FSS, a benchmark of 1200 test problem were solved and compared with solution obtained by an exiting algorithm in the literature. FSS performs better in terms of quality of solution and computational time. Also, FSS obtained a relative deviation index of 4% when compared with a optimal solution obtained by a commercial solver within 600 seconds of computational time. Therefore, FSS can be deployed to obtain good approximation schedule for large scale production where desired error tolerance is not more than 0.004.

Keywords : Early/Tardy, Forward-Shift,Flow Shop, Heuristics, Just-In-Time