Integer Batch Scheduling Problems for a Single-Machine to Minimize Total Actual Flow Time

This research addresses a batch scheduling model for a single-machine under a Just-In-Time (JIT) production system that produces discrete parts. The objective is to minimize the total actual flow time, defined as the time when parts are flowing on the shop floor from its arrival time to their common delivery time. The decision variables are the number of batches, integer batch sizes, and the sequence of the resulting batches. The problem is solved based on the Lagrange Relaxation method. The optimality test of the proposed algorithm is done by comparing the result of the proposed algorithm with the Integer Composition method. The result of numerical experiments demonstrates that the proposed algorithm is very efficient to solve the problems.