So We Have Cc (i) + a = Cnn + C 5 Computational Results

15 Acknowledgement We wish to thank two anonymous referees for their helpful comments. Single machine scheduling with dynamic arrivals: Decomposition results and a forward algorithm. 14 (columns 4{6). In column 2, maxit is the maximum number of neighborhood searches allowed. Column 4 lists the iteration when the observed best total completion time was found. The number of times the aspiration criterion was satissed is given in column 5. Column 6 lists the total number of moves that were declared tabu. Table 4 summarizes the performance of FCFS, SAJF and TS for three job sequences taken from the job data generated in simulation model 2 of Table 1. Column 2 gives the best solution found by TS. When n = 10 we have veriied that this is also the optimal value. The next two pairs of columns (3-4 and 5-6) list the average completion times for FCFS and SAJF and the ratios FCFS=TS and SAJF=TS, respectively. These ratios show that, at least for these examples, the worst-case analysis of Theorems 2 and 3 may be overly pessimistic for the average case. n maxit tabusize itr. best # Asp. In this paper, we applied the theory of on-line algorithms to the scheduling problem 1jr j j P C j , and studied the c-competitiveness of two on-line algorithms|FCFS and SAJF. Furthermore, we proved that there is no on-line algorithm with constant competitive ratio for this problem. We also presented some computational results that illustrated the dominance of SAJF and the overly pessimistic nature of the c-competitiveness worst-case results. As for the direction of future research, we are currently working on algorithms with look-ahead allowed. We are interested in applying the theory of c-competitiveness to other job scheduling problems. We would also like to generalize the algorithms for 1jr j j P C j to Pjr j j P C j and Rjr j j P C j in the multi-machine environment. 13 INTENSIFY the search by choosing a previously unselected member of a recorded set of best solutions to restart the improvement phase (retaining memory to choose a new successor), or by choosing a member of the best solutions uncovered but not yet visited. Repeat step 2. DIVERSIFY the search by driving it to explore new regions. This may be done with either a frequency based memory that favors the inclusion of rarely incorporated attributes, or a recency based memory that may …