### Table 6: Symmetric TSPs with Time Windows (Vehicle Routing)

in Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study

"... In PAGE 19: ...caling factor used was 2.2. Increasing the scaling factor does not affect the time-window structure in terms of overlaps, but may decrease the number of precedence constraints and thereby require a larger K. Table6 shows the results of these problems, having an average size of 51 cities. Optimal solutions were found in every case with K = 12, but for many, optimality could not be guaranteed with K less than 14.... ..."

### Table 6: Symmetric TSPs with Time Windows (Vehicle Routing)

in Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study

"... In PAGE 19: ...caling factor used was 2.2. Increasing the scaling factor does not a ect the time-window structure in terms of overlaps, but may decrease the number of precedence constraints and thereby require a larger K. Table6 shows the results of these problems, having an average size of 51 cities. Optimal solutions were found in every case with K = 12, but for many, optimality could not be guaranteed with K less than 14.... ..."

### Table 5: Symmetric TSPs with Time Windows (Vehicle Routing)

in Linear Time Dynamic-Programming Algorithms for New Classes of Restricted TSPs: A Computational Study

"... In PAGE 18: ... (1995) could guarantee the optimality of a solution even if their solution was optimal. The entry for Required K in Table5 indicates what value of K would be needed for a guarantee of optimality. As can be seen from Table 5, our algorithm solved 14 of these problems with a guarantee of optimality.... In PAGE 18: ... The entry for Required K in Table 5 indicates what value of K would be needed for a guarantee of optimality. As can be seen from Table5 , our algorithm solved 14 of these problems with a guarantee of optimality. Of these 14, Potvin et al.... In PAGE 18: ...1699.69 was verified to be optimal for rc201.3-.4 with K = 14 and q = 18 in 107.77 seconds Since all of the problems in Table5 are quite small (average size of 28 cities), we generated... ..."

### Table 5: Symmetric TSPs with Time Windows (Vehicle Routing)

"... In PAGE 18: ... (1995) could guarantee the optimality of a solution even if their solution was optimal. The entry for \Required K quot; in Table5 indicates what value of K would be needed for a guarantee of optimality. As can be seen from Table 5, our algorithm solved 14 of these problems with a guarantee of optimality.... In PAGE 18: ... The entry for \Required K quot; in Table 5 indicates what value of K would be needed for a guarantee of optimality. As can be seen from Table5 , our algorithm solved 14 of these problems with a guarantee of optimality. Of these 14, Potvin et al.... In PAGE 18: ...1699.69 was veri ed to be optimal for rc201.3-.4 with K = 14 and q = 18 in 107.77 seconds Since all of the problems in Table5 are quite small (average size of 28 cities), we generated... ..."

### TABLE I Data for a small single-vehicle routing problem with time windows.

### Table 2: Constructing Precedence Constraints from Time Windows

"... In PAGE 13: ... The initial ordering can be generated, for instance, by sorting the time windows by their midpoint. Table2 shows an example of this, along with the constants k(i) derived from this ordering. To keep things simple we take all tji to be zero.... ..."

### Table 2: Constructing Precedence Constraints from Time Windows

"... In PAGE 13: ... The initial ordering can be generated, for instance, by sorting the time windows by their midpoint. Table2 shows an example of this, along with the constants k(i) derived from this ordering. To keep things simple we take all tji to be zero.... ..."