S. Lawrence: "Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (Supplement)", Graduate School of Industrial Administration, Carnegie-Mellon University (1984).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Kan [14] proved this problem to be NP Hard. One classic 10x10 job shop problem formulated by Muth and Thompson in 1963 was not solved until 1989 by Carlier and Pinson [6] Recently however, heuristics have been very successful in solving many of the early benchmark problems. Several authors [1,2,7,8,11,18,19,22] established additional benchmark problems as the heuristic approaches improved. A listing of 159 of these benchmark problems is located on J. Beasley s OR Library website (http: mscmga.ms.ic.ac.uk info.html) Authors commonly use a subset of these 159 benchmark problems for testing their job ....

Lawrence S., (1984). Supplement to, "Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques," Tech. Rep., GSIA, Carnegie Mellon University.

....fuzzy numbers to represent fuzzy durations. He used simulated annealing (SA) as an optimization technique and the optimization criterion was to minimize the fuzzy makespan. To test the approach, he fuzzified the FT 6x6 problem [8] and other famous problems such as La11, La12, La13, and La14 [9]. The produced solutions are flexible, since they are able to cope with all possible durations within the specified range. Ghrayeb [14] presented a genetic algorithm approach to optimizing fuzzy JSSPs, in which imprecise processing times are modeled as triangular fuzzy numbers. This approach ....

Lawrence, S., 1984, "Resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques," Carnegie Mellon University, Tech. Rep., Pittsburg, PA,

....the diagram, where a non robust solution searching scheme will result in a graph more to the right . The problems used in the experiments are all standard benchmark problems. The sizes and minimum makespans for the different problems can be seen in table 1. The problems prefixed by la are from [8] and the problem ft10 is from [5] All of the problems can be downloaded from the ORLibrary at http: www.ms.ic.ac.uk info.html. 5.1 Evidence of robustness To show the existence of robust solutions and answer the questions raised in section 3 we conduct the experiments described above in the ....

S. Lawrence. Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (Supplement). Graduate School of Industrial Administration, Carnegie-Mellon University, 1984.

....in the coevolutionary GA, when evaluating F (x, s) for a given schedule x # PX and breakdown s # PS , the breakdown time is rounded up to the time just before the end of processing of the current operation, or to Tmax . 5 Experiments The scheduling problem instances prefixed by la are from [Law84] and the problems prefixed by ft are from [FT63] For each scheduling problem a breakdown set was created. This was done by inspecting a number of nearoptimal schedules and selecting machines and times for each problem in such a way that parts of the schedules that would always be (near) critical ....

S. Lawrence. Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (Supplement) . Graduate School of Industrial Administration, Carnegie-Mellon University, 1984.

....930 2472 LA38 15 Theta 15 1196 1196 1196 1202 1198 41985 LA40 15 Theta 15 1222 1234 1233 1238 1237 31644 Table 1. Results on solved problems using a single processor. The problems LA38 and LA40 are believed to be the most challenging instances among the benchmarks introduced by S. Lawrence [7]. We started with these two problems and the smaller instance FT10 from [8] We used the hyperbolic cooling schedule where the parameter settings were taken from [10] In Tab. 1 we provide our results of consecutive runs using a single processor. The stated makespan was computed within an average ....

Lawrence, S., Resource Constrained Project Scheduling: An Experimental Investigation of Heuristic Scheduling Techniques (Supplement), Technical report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1984.

....0 5 10 15 20 1200 1400 1600 1800 2000 2200 2400 LA40 Figure 5: The maximum number of longest paths for instances of size 15 Theta 15. In Figure 5 8a, statistics of the maximum number of longest paths are given. For this experiment we have chosen the smaller instance FT10 [14] LA38 and LA40 [11], two of the four instances YN [24] and two of the instances SWV [19] The instances were selected such that for one problem we could improve the upper bound and for the other we could not exactly reach the upper bound. 0 5 10 15 20 25 30 35 40 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 YN1 ....

S. Lawrence. Resource Constrained Project Scheduling: An Experimental Investigation of Heuristic Scheduling Techniques (Supplement). Technical Report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1984.

....Some results obtained from 5 classical test problems are shown in Table 1. Those problems, as well as a lot of other benchmark O.R. problems, are collected in [30] FT6 has been designed by Fisher and Thompson [29] and La11 La14 (5 machines, 20 tasks of 5 operations) are taken from Lawrence [31]. For each problem with crisp values, ten sets of fuzzy durations where generated with a range of fuzziness equal to 30 . Those problems were optimized by Simulated Annealing and the minimum, the mean and the maximum of the ten defuzzified optimal makespan are given in Table 1. Name Crisp Obj. ....

S. Lawrence, "Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques," tech. rep., Carnegie-Mellon University, 1984.

....from J.E. Beasley s OR Library, from the le jobshop1.txt. Since the comparative characteristics were quite similar across all the job shop scheduling benchmarks we tried, we have just selected a few typical ones to present here. The sched orb instances are attributed to [2] and the sched la to [7]. The second problem set is Fibonacci programs and goals. b std is the standard (na ve) formulation, with the two recursive calls last. b utvpe is a slightly reordered formulation such that all the equations are UTVPE (after initial ground substitution) at the time they are passed to the ....

S. Lawrence. Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (supplement). Technical report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1984.

....[12] and has proven to be very difficult even for relatively small instances. An instance with 10 jobs and 10 machines posed in a 1963 book by Muth Thompson [10] remained unsolved until Carlier Pinson [7] finally solved it in 1986, and there is a 20 job and 10 machine instance of Lawrence [15] that remains unsolved despite a great amount of effort that has been devoted to improving optimization codes for this problem. The most effective optimization techniques to date have been branch andbound algorithms based on the disjunctive graph model for the job shop scheduling problem. The ....

S. Lawrence. Resource Constrained Project Scheduling: an Experimental Investigation of Heuristic Scheduling Techniques (Supplement). Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA, 1984.

....years. The most famous instance is a 10 10 problem of Fisher Thompson [MT63] that was left unsolved until 1989 when it was solved by Carlier Pinson [CP89] Classical benchmarks include problems randomly generated by Adams, Balas Zawak in 1988 [ABZ88] Applegate Cook in 1990 [AC91] and by Lawrence in 1984 [La84] Of the 40 problems published by Lawrence, one is still unsolved (a 20 10 referred to as LA29) The typical size of these benchmarks ranges from 10 5 to 30 10. 2.2 The branch and bound scheme with time windows Branch and bound algorithms have, however, undergone much study, and the ....

.... instance is a 10 10 problem of Fisher Thompson [MT63] that was left unsolved until 1989 when it was solved by Carlier Pinson [CP89] Classical benchmarks include problems randomly generated by Adams, Balas Zawak in 1988 [ABZ88] Applegate Cook in 1990 [AC91] and by Lawrence in 1984 [La84] Of the 40 problems published by Lawrence, one is still unsolved (a 20 10 referred to as LA29) The typical size of these benchmarks ranges from 10 5 to 30 10. 2.2 The branch and bound scheme with time windows Branch and bound algorithms have, however, undergone much study, and the method ....

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S. Lawrence. Resource Constrained Project Scheduling: an Experimental Investigation of Heuristic Scheduling Techniques. GSIA, Carnegie Mellon University 1984 29

....are poor up to now. 8 Computational results The computational merits of job shop scheduling algorithms have often been measured by their performance on the notorious 10 Theta 10 instance FT10 of Fisher and Thompson [29] Applegate and Cook [4] found that several instances of Lawrence [47] (LA21, LA24, LA25, LA27, LA29, LA38, LA40) pose a more difficult computational challenge. We have included the available computational results for these instances and, in addition, for two relatively easy instances (LA2, LA19) and for all remaining 15 Theta 15 instances of Lawrence (LA36, LA37, ....

S. Lawrence, 1984. Resource Constrained Project Scheduling: an Experimental Investigation of Heuristic Scheduling Techniques (Supplement), Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, Pennsylvania.

....all the other heuristics (p 0.0001) with significantly fewer heuristic commitments (p 0. 001, tested with a boot strap, two sample t test (Cohen, 1995) SumHeight finds signifiSource Problem (lower upper bound) Adams et al. 1988) abz5(1234) abz6(943) Fisher and Thompson, 1963) ft10(930) (Lawrence, 1984) la02(655) la19(842) la20(902) la21(1046) la24(935) la25(977) la27(1235) la29(1130 1153) la36(1268) la37(1397) la38(1196) la39(1233) la40(1222) Applegate and Cook, 1991) orb01(1059) orb02(888) orb03(1005) orb04(1005) orb05(887) Table 1: Test Problems cantly better ....

Lawrence, S. (1984). Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (Supplement). PhD thesis, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania.

....instances are very di#cult. Thus, we will use these instances to test the local search approach, too. In detail, we considered the following problems: job shop instances: These instances result from a reduction of jobshop benchmark instances from Fisher and Thompson [1963] FT1, FT2) and from Lawrence [1984]. The dimensions of the original jobshop instances (n denotes the number of jobs and m the number of machines) and of the reduced instances are given in Table 1. Open Shop m n n Job Shop m n n (orig. red. orig. red. tai01 tai10 4 4 34 FT1 6 6 74 tai11 tai20 5 5 52 FT2 ....

S. Lawrence [1984] Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques, GSIA, Carnegie Mellon University.

.... 66.01 9.14 28.8 LDS with k=4 35.04 104.68 19.04 52.06 3.86 18.49 LDS with k=2 51.12 116.71 40.24 72.12 11.29 32.47 DDS with k=4 63.98 112.88 16.34 36.72 2.21 21.4 IDFS 51.77 58.46 29.45 32.07 12.37 13.95 3. 3 A bigger example : la36 la36 is a medium jobshop (15 15) from [5]. For solving these problems, a time limit of 500 s was set on the resolution of these problems. LA36 (15 15) Strategy 1 agent 2 agents 4 agents DFS 500 500 500 500 231.07 246.71 BFS 500 500 500 500 500 500 BFS with tuning 500 500 500 500 100.37 210.79 LDS with ....

S Lawrence. Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques. Carnegie-Mellon University, Pennsylvania, 1984. supplement.

....statement for the NP completeness proof in Garey and Johnson [20] allows jobs to have fewer than m operations and only stipulates that no two adjacent operations of a job use the same machine. For ease of representation, though, many job shop benchmarks have m operations per job, one per machine [33, 47]. CHAPTER 4. EXPERIMENTAL RESULTS 77 of choice points, the tree is not necessarily of uniform depth. The order in which variables are instantiated and values assigned can have a dramatic effect on the size of the search trees and efficacy of the search algorithms. For our experiments, we have ....

....schedule length each time to slightly less than the length of the last schedule found. At any point in time, the algorithm s best schedule is the basis for computing e t . The job shop scheduling benchmark that we used consisted of thirteen problems taken from the Operations Research literature [33, 47, 49]. 4 The problems varied in size from 10 Theta 10 to 15 Theta 15 or 20 Theta 10 jobs and machines. Although the depths of the search trees varied, most were in the range of 100 to 800 choice points. 4.4 Comparison with AI Techniques Figure 4.1 shows the performance of the basic nonsystematic ....

S. Lawrence. Resource constrained project scheduling: an experimental investigation of heuristic scheduling. Technical Report Working paper GSIA, CarnegieMellon University, 1984. BIBLIOGRAPHY 158

....from MT10 [Fisher and Thompson 1963] a notoriously difficult 10 job 10 machine JSSP instance. Given sufficient search time, RS achieves results superior to or competitive with TS in 12 of 13 problems, the exception being FJS model p1p2p3 (851 vs. 849) The Table 2 problems are based on LA24 [Lawrence 1984], a 10 machine 15 job problem. Again, the self tuning RS yields superior or competitive solutions in 10 out of 12 cases. RS performance for FJS p1p2 (941 vs. 924) and FRJS c1 (959 vs. 919) is noticeably worse. Table 3 shows results for problems based on LA40 [Lawrence 1984] a 15 machine 15 job ....

....are based on LA24 [Lawrence 1984] a 10 machine 15 job problem. Again, the self tuning RS yields superior or competitive solutions in 10 out of 12 cases. RS performance for FJS p1p2 (941 vs. 924) and FRJS c1 (959 vs. 919) is noticeably worse. Table 3 shows results for problems based on LA40 [Lawrence 1984], a 15 machine 15 job problem. Out of 12 problems, 9 RS solutions are superior or competitive, with two problems, FJS c1c2 (1137 vs. 1136) and FRJS p1p2 (1157 vs. 1156) being close . One problem, FJS p1p1p1 (1242 vs. 1213) is much worse. Trac i ng o f t he prob l ems exh i b i t i ng i n f er i ....

LAWRENCE, S. 1984. Resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques. Graduate School of Industrial Administration, Carnegie-Mellon University.

....[1] to simulated annealing [7] have been tried. The most famous instance is a 10 Theta 10 submitted by Fisher Thompson in 1963 [5] and that resisted many attempts before being solved by Carlier Pinson in 1989 [3] Today, some other famous 20 Theta 10 instances published by Lawrence in 1984 [4] still remain open. Branch bound with domain reduction The method that we propose is based on a classical branch and bound scheme, where domains are associated to tasks. When a maximal makespan is fixed, a domain [t; t] can be associated to each task t, with the meaning that t time(t) t Gamma ....

S. Lawrence. Resource Constrained Project Scheduling: an Experimental Investigation of Heuristic Scheduling Techniques GSIA, Carnegie Mellon University, 1984

....optimality. There is a O(mn 2 ) time requirement to compute the makespan. The termination criterion is inadequate because even if optimality is achieved the process continues searching and the computational requirement is very high. Even though hard problems such as LA 21, 27, 29, 38 (Lawrence 1984); ABZ 7, 8, 9 (Adams et al. 1988) are not attempted the authors have solved FT 10 (Fisher and Thompson 1963) which is a well known hard instance. Until this point we have described systems based on the Hopfield network. However there are many scheduling systems which incorporate the back error ....

....parameters as that of the dispatch rule outputs. 30 10 PROBLEM As the computational effort required for large instances of P G is excessive an exhaustive search method becomes impractical for the creation of training examples. Therefore benchmark instances proposed in the P G literature (Lawrence 1984, Adams et al. 1988, Taillard 1993) have been used as training data. JAIN AND MEERAN JOB SHOP SCHEDULING USING NEURAL NETWORKS page (22) A two layer network is again used, with 300 nodes to input the processing times arising from 10 processes on every job and 300 input nodes to feed the ....

LAWRENCE, S., 1984, Resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques. Supplement, Graduate School of Industrial Administration, Carnegie-Mellon University, Pennsylvania, USA.

....this is not the case (919 vs 913) Increasing the nonimproving moves limit to 5000 affords some improvement (919 is reduced to 914) In each case, we note that increasing flexibility is associated with increasing preferential selection of routing moves. Table 2 presents flexible results for LA24 [Lawrence 1984], a 10 machine 15 job problem for which we obtained a classical makespan of 939. LA24 is machine time bounded; our best classical solution had one critical path and one machine with a predominant number of critical operations. In this case, repeated replication of the maximum time machine yields ....

....based on number of critical operations rather than processing time is noncompetitive (926 vs 924) unless the nonimproving moves limit is tuned (reducing 926 to 909) Again, we note an increase in the selection of routing moves with increasing flexibility. Table 3 presents flexible results for LA40 [Lawrence 1984], a 15 machine 15 job problem for which we obtained a classical makespan of 1226. LA40 is machine time bounded; our best classical solution had one critical path which forks and later rejoins itself, and one machine clearly identifiable as having the largest number of critical operations. Search ....

LAWRENCE, S. 1984. Resource constrained project scheduling: An experimental investigation of heuristic scheduling techniques. Graduate School of Industrial Administration, Carnegie-Mellon University.

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S. Lawrence: "Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (Supplement)", Graduate School of Industrial Administration, Carnegie-Mellon University (1984).

No context found.

S. Lawrence: "Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (Supplement)", Graduate School of Industrial Administration, Carnegie-Mellon University (1984).

No context found.

S. Lawrence, "Resource constrained project Scheduling : An Experimental Investigation of Heuristic Scheduling Techniques (supplement)", Graduate School of Industrial Administration, .Carnegie Mellon University, 1982.

No context found.

S. Lawrence. Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques (supplement). Technical report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1984.

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S. Lawrence, Resource constrained project scheduling: an experimental investigation of heuristic scheduling techniques-(supplement), Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, 1984.

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S. Lawrence. Resource Constrained Project Scheduling: An Experimental Investigation of Heuristic Scheduling Techniques (Supplement). Technical report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1984.

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