PROBLEMS OF THE HAULIER AND CARRIER.
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Finding the Approximate Answer to a Problem the Solution of which is Indeterminable.
IN my previous article I dealt with a very difficult problem--that of quoting for point-to-point deliveries within a large area. The conditions were such that the distance from one point to another might be anything from one mile to 50 miles, and there was the further complication that the start of the day and its finish would probably involve a long trip from the haulier's own headquarters to the depot where the first load was to be picked up and back again from that at which the last load was delivered. These details were given at length in the previous article, to which my readers should refer.
Trying to Find a Solution.
The contractor was asked to quote a price for any one of those possible deliveries, basing his quotation on the distance from point to point, the load in every case being 2 tons. In an endeavour to arrive at some sort of solution I described three possible days work, such as might happen under the conditions of the contract, and I dealt with two of them. The basis for calculation was a total of standing charges, establishment costs and profit amounting to 110 7s., and ninning costs, per mile, 4d.
In One of these examples I assumed a trip which involved a journey from headquarters to collection point of 20 miles, from collection to delivery 40 miles and return to headquarters 36 miles, total 96 miles for this one trip.
another I took as an example a day during which deliveries were made between depots three miles apart and distant from headquarters approximately 12 miles. I showed that five trips were possible in the day, the total. mileage being 54.
Then I took an example more likely to be of the kind generally experienced, starting with a run of three miles to the first depot and then from depot to depot collecting and delivering in accordance with the accompanying figure (Fig. 4), which appeared in the last article as Fig. 2, and is here reproduced for convenience.
Now, it is (pate easy to calculate costs and fair charges in the first and second cases. They come to £3 13s. 8th for the 40-mile trip and 11s. 9d. each for the three-mile one. The assessment of these costs and charges for the other example is anything but easy. It is obviously, for example, no use trying to adduceanything directly from the length of the trip. Forty miles at 13 13s. 8d. is approximately is. 10th a mile; three miles at us. 9d. is 3s. 11d, a mile. The trouble is
0th.
3 mls. .30 mit., • • 13 6
Tchal firre c,tapied 8 hourt
(Above Fig. 4) The example of a day's, run with a van which, as Fig 2, accompanied S.T.R.'s article in the previous Issue of "The Commercial Motor." In the course of an 8hour journey, the distance of 72 miles was covered, six depots being visited. (Right, Fig..5) A diagram showing the relation between the length of the trip and the number of trips which can be run in the course of a day.
70 mks —
that the dead mileage is so. difficult to assess. It is not as though there was a regular distance from home to the starting point each day, nor are the trips always from one depot to another and back again. In this particular example the dead mileage is 34, the useful mileage 38. In the first case there were 56 useless miles to add on to a 40-mile trip and these were en-: tireiy covered in travelling to and from headquarters to depot. In the second case only 15 out of 54 miles were load-carrying ones. It is clear, therefore, that in endeavouring to find a formula for assessing these charges some provision must be made for this feature , of the contract.
Number of Trips per Day.
One way of getting over the difficulty is to take an average length for the run out to work in the morning and back at night and then to reckon the value of each trip on the basis of the number of trips of that length which could be made per day. I have shown that it is quite possible for one 40-mile run to be a day's work. It is not likely, within the area specified, that more than one run of this length could be managed inside a day, even if one of the termini happened to be comparatively near to headquarters. On the other hand, whilst five trips of three miles each have occupied 311...1.111 day it might be possible in the 1111111 case of a couple of depots of that distance apart to dosix, or even seven, if they
rclose to the centre of the city. happen to be Five, therefore, 111111111111111 may be taken quite reasonably NE.111111111 as the, average
number of three EMMEN mile trips which
could be run in a
day.
EMMENNow, I have
set out a dia 1111111111111111 gram which is re produced as the
/ 2 a ,5" 0 Fig. 5 of these
articles. Along the baseline I have set out the number of trips per day and, vertically, the number of miles per trip. For 40 miles I have assumed one trip per day and for three miles five trips. I have marked these points on the diagram as shown and joined them by a straight line. According to that line, two 30-mile trips could be covered in a day. Three of 20 miles and four of about 12 miles. From this we might draw up a schedule somewhat upon these lines :— For trips of anything up to five miles, assume five per clay; from five miles to 15 miles, four trips per day ; from 15 miles to 25 miles, three per day; from 25 miles to 35 miles, two per day. For anything above 35 miles, one trip per day may be assumed.
Then we must assume an average out-and-home trip to the starting point and back again from the finishing
No. of trips per day.
point. I am taking that average to be 12 miles each way, or 24 in all, and in order to calculate a price for a trip of any specific length, I shall take £2 a day as a regular charge. Add, to that double the mileage calculated by the maximum number of trips of the stated length, plus 24 miles for the out-and-home journey, the cost of the mileage being calculated at 44. a mile as already stated.
Now, I will apply this method to the two cases already taken and then try it out on the third example. , The first was a 40-mile trip, of which we have agreed that one per day is the maximum. Double the 40 is SO miles, add 24 for out and home and we get 104 miles, which, at 4d. per mile, is 34s. 8d. Add 34s. 8d. to £2 and the total is £3 14s. 8c1., which is very close to what we got in the previous calculation.
Let us now consider the second case of three-mile trips, five per day, which gives us 30 miles, plus 24 equals 54. Fifty-four at 4d. is 18s. Add to 12, that gives us £2 18s. Divide that by five trips and we get 11s. 7d., whieh again is very close to what we got
before -certainly as near as is possible by any approximate calculation.
We must now apply the same rule to be able to quote
for the three trips embodied in the example which is illustrated on the previous page, namely, one iof six miles, one of two miles and one of 30 mites. Six-mile trips go four to the day, and the cost works out as above —I need not give it in detail again here—at 168. each. Two-mile trips go five to the day and the cost is lie. each. Thirty-mile trips are two per day and the price for each is 34s.
I showed at the close of the previous article that, during a whole week, it is actually possible to do six of these six-mile trips and five each of the others. The total revenue would, therefore, be £4 16s. from the .sixmile trips, 12 15s. from the two-mile trips and £8 10s. from the others. The total revenue is thus £16 Is.
We may now calculate the cost to the haulier of this particular week's work, assuming that he carries on according to this diagram throughout the week and can thus determine a profit he would make if he were to charge on this basis.
Re covers 72 miles a day for five days. which is 360, and on the Saturday he travels 18 miles 378 miles. The running cost at 44. a mile is £6 6.9.; six hours' standing charges are £5 7s., and the total is £11 13s., so that his profit is 14 Sc. S.T.R.