### Table I. Computation times in seconds for minimum cost and minimum makespan problems, using MILP, CP, and logic-based Benders methods. Each time represents the average of 5 instances. Computation was cut off after two hours (7200 seconds), and a + indicates that this occurred for at least one of the five problems.

2004

Cited by 15

### Table 1. Computation times in seconds for minimum cost and minimum makespan problems, using MILP, CP, and logic-based Benders methods. Each time represents the average of 5 instances. Computation was cut off after two hours (7200 seconds), and a + indicates that this occurred for at least one of the five problems.

2004

"... In PAGE 8: ... No precedence constraints were used, which tends to make the scheduling portion of the problem more difficult. Table1 displays computational results for 2, 3 and 4 facilities as the number of tasks increases. The CP solver is consistently faster than MILP, and in fact MILP is not shown for the makespan problems due to its relatively poor performance.... ..."

Cited by 15

### Table II. Computation times in seconds for minimum cost and minimum makespan problems, using MILP, CP, and logic-based Benders methods. Each time represents the average of 5 instances. Computation was cut off after two hours (7200 seconds), and a + indicates that this occurred for at least one of the five problems.

2004

Cited by 15

### Table 2-1: Logic-Based Formalisms

1997

"... In PAGE 18: ... Table2 -2: Logic-Based Formalisms Criteria OBJ Larch Temporal Model none none Automated Tools few some Reliability good good Proof System axiomatic axiomatic Industrial Strength some great Methods of Veri. theorem prov.... ..."

Cited by 2

### Table 2-1: Logic-Based Formalisms

1997

"... In PAGE 3: ... Table2 -2: Logic-Based Formalisms Criteria OBJ Larch Temporal Model none none Automated Tools few some Reliability good good Proof System axiomatic axiomatic Industrial Strength some great Methods of Veri. theorem proving theorem proving Concurrency interleaved interleaved Communication sync.... ..."

Cited by 1

### Table 2-2: Logic-Based Formalisms

1997

"... In PAGE 18: ... theorem proving theorem proving both both Concurrency none none norm exist none Communication none none norm exist none Reverse Eng. yes yes no no Table2 -1: Logic-Based Formalisms Criteria ITL DC TAM RTTL RTL Temporal Model sparse dense sparse sparse sparse Automated Tools few none none few none Reliability good good good good good Proof System axiomatic axiomatic axiomatic axiomatic axiomatic Industrial Strength great some great some some Methods of Veri. theorem prov.... ..."

Cited by 2

### Table 2-2: Logic-Based Formalisms

1997

"... In PAGE 3: ... both both Concurrency none none norm exist none Communication none none norm exist none Reverse Eng. yes yes no no Table2 -1: Logic-Based Formalisms Criteria ITL DC TAM RTTL Temporal Model sparse dense sparse sparse Automated Tools few none none few Reliability good good good good Proof System axiomatic axiomatic axiomatic axiomatic Industrial Strength great some great some Methods of Veri. theorem pv.... ..."

Cited by 1

### Table 1. Illustrating the e ect of logic-based optimizations.

1997

"... In PAGE 9: ... The \leader5 quot; system corresponds to the system used in the SPIN suite. Table1 gives the space and time gures for two di erent formulas, F1 being a least xed point formula stating that in every run of the system a leader is eventually elected, and F2 being a nested xed point formula stating that in every run of the system at most one leader is elected. In this table, for a system of given size, the rst line indicates the space and time gures with the naive encoding without any of the optimizations of the previous section, and the second line gives the corresponding gures with all the optimizations in place.... ..."

Cited by 2

### Table 1: Computation times in seconds for minimum cost and minimum makespan problems, using MILP, CP, and logic-based Benders methods. Each time represents the average of 5 instances. Computation was cut off after two hours (7200 seconds), and a + indicates that this occurred for at least one of the five problems. The test problems are cNjMmK, where N is the number of tasks, M the number of facilities, and K the problem number (K =1,...,5).

2004

"... In PAGE 22: ... Both result in substantially better performance. Table1 displays computational results for minimum cost and minimum makespan prob- lems on 2, 3 and 4 facilities. The CP solver is consistently faster than MILP on minimum cost problems.... ..."

Cited by 4