Heuristic Algorithms for Single Batching Machine with Total Weighted Completion Time

The problem of n jobs to be processed on single batching machine with a capacity to minimize the total weighted completion time is discussed.An analysis and proof are given for the quality of optimal solution under some condition,based on which two heuristic algorithms are carried out,selecting jobs ordered by WSPT rule(WSPTS) and selecting jobs ordered by SPT rule(SPTS).To compare the proposed algorithms,heuristic dynamic programming based on WSPT and SPT respectively is carried out,and so does full batch algorithm.The experiment result shows that the heuristic WSPTS is the best one and the SPTS is the most stable one among all the algorithms.