Step 3 found our box car (Rutland 197; an ordinary PS-1 40' all-steel car) on the B&M in Nashua, New Hampshire, empty after delivering a load of scrap paper from Rockford Illinois.
For step 4, R 197 failed to find a load in Nashua and returned empty via the service route to the last interchange point (Worcester Massachusetts, on the NH). The distance travelled was 58 miles, all on the B&M, and the car was empty.
Competition for Loads and Car Selection:
New Hampshire is a net importer of commodities that travel primarily by box car. Roughly 24 empty box cars compete for every 10 outgoing loads. To generate this step I experimented with a simplified version of the AAR car selection rules I am calling "EasyAAR" (because the actual AAR car selection process is beyond my current capability to develop an algorithm that can be automated; I'm taking a first baby step here).
I generated 10 loads using the 1% waybill survey state-to-state distribution from New Hampshire as the probability density function. Then I generated 24 empty cars using a modified Gilbert-Nelson distribution (with 30% B&M cars) as the probability density function. Then I stepped through each load and assigned an empty car such that the destination state was in the empty car's AAR Home District. I worked on the cars in the order of those with the least number of states in their home district to most. At the end, with 24 cars from which to choose, I quite easily found a solution where every load could put an empty car in its home district. Of course the solution I found isn't unique, and there are a couple of differences from the actual AAR car selection process, but this is a much easier algorithm to tackle and it works quite well for situations where there are more empties than loads.
Here are the inputs and the solution I found using EasyAAR:
| Empty Car | Marking | Page | Item | Load | Term. State | Car Selection | |
| 1 | BM | 192 | 41 | 1 | Illinois | IC | |
| 2 | BM | 192 | 35 | 2 | Kansas | ATSF | |
| 3 | NYC | 113 | 33 | 3 | Kentucky | L&N | |
| 4 | UP | 424 | 42 | 4 | Maryland | Seaboard | |
| 5 | ATSF | 488 | 4 | 5 | Michigan | B&O | |
| 6 | BM | 192 | 37 | 6 | Michigan | ERIE | |
| 7 | BM | 192 | 36 | 7 | New Hampshire | BM | |
| 8 | BM | 192 | 24 | 8 | New York | NYC | |
| 9 | BM | 192 | 24 | 9 | Texas | ATSF | |
| 10 | Southern | 12 | 41 | 10 | Virginia | Southern | |
| 11 | SP | 440 | 11 | ||||
| 12 | L&N | 40 | 1 | ||||
| 13 | R | 103 | 1 | ||||
| 14 | Seaboard | 8 | 53 | ||||
| 15 | BM | 192 | 41 | ||||
| 16 | IC | 334 | 47 | ||||
| 17 | BM | 192 | 24 | ||||
| 18 | BM | 192 | 36 | ||||
| 19 | BM | 192 | 41 | ||||
| 20 | ATSF | 484 | 6 | ||||
| 21 | B&O | 151 | 67 | ||||
| 22 | BM | 192 | 34 | ||||
| 23 | BM | 192 | 41 | ||||
| 24 | ERIE | 176 | 63 |
Page and Item numbers refer to the January 1958 edition of the ORER. Our car (Rutland 197) is highlighted in green. The cars highlighted in yellow are the ones that were selected from the list of 24 empties; the match to the load is shown in the last column. Note that the Rutland car was not selected by the algorithm, and thus was returned empty via its service route to the last interchange point.
Charles Hostetler
Goshen, Ind.