We present a decomposition heuristic for a large class of job shop scheduling problems. This heuristic utilizes information from the linear programming formulation of the associated optimal timing problem to solve subproblems, can be used for any objective function whose associated optimal timing problem can be expressed as a linear program (LP), and is particularly effective for objectives that include a component that is a function of individual operation completion times. Using the proposed heuristic framework, we address job shop scheduling problems with a variety of objectives where intermediate holding costs need to be explicitly considered. In computational testing, we demonstrate the performance of our proposed solution approach.
Bulbul, K. and Kaminsky, P. (2013). "A Linear Programming-Based General Method for Job Shop Scheduling." Journal of Scheduling, 16(2):161-183. doi: 10.1007/s10951-012-0270-4