Which mobile tire jobs should a van take? Window and drive-time math
Short answer: pick the set and order of jobs whose combined margin, after the drive between them, is highest and that all fit their windows and get the van home on time. A van does one thing at a time, so a good job can be a bad choice if it displaces two better ones.
A worked queue
Ten requests, one van leaving at 08:00 and due back at 17:00, costing $35 an hour while driving or working and $0.70 a mile, driving 30 mph over roads 1.3 times the straight-line distance. Prices range from a $55 valve stem to a $620 four-tire truck job.
Taking calls in the order they came in fits 6 jobs and earns $308.45.
Biggest tickets first fits 3 jobs and earns $127.33: it takes the $620 truck job first, a long drive out with a 10:00 window, and that leaves room for only two more.
The best day runs 8 jobs, starting with the rush roadside spare swap, and earns $486.23 over 86.2 miles, home at 16:57. That is $177.77 more than the best simple rule.
The four-tire truck job is turned down in the best day, and would earn a place only at about $652.65, so the quote to give is that, not the $620 asked. The $55 valve stem 15 miles out loses money even as the only job and would need about $97.66.
What to feed it
Hourly cost: van payment, insurance, technician wages and benefits divided by hours actually worked, not hours paid.
Per-mile cost: fuel plus tires and maintenance per mile driven.
For each job, the window from the customer and the miles east and north from your depot.
Check any motor-club or fleet agreement first: some require you to answer certain calls, and a stranded or unsafe driver comes before any optimum.
Questions
How do I decide which mobile tire calls to take?
Compare whole days, not single calls: for a set of jobs in a given order, add what each pays after materials and on-site time, subtract the drive between them, and check every time window. The best day is the best such set and order. The picker finds it exactly for up to 14 jobs.
Is taking the biggest tickets first a good rule?
Not reliably. Big tickets often sit far from each other or in the same window, so the van drives and waits for them. On the worked queue it earns $127.33 against $486.23 for the best day.
What should a job pay to be worth a detour?
The picker prints, for each job it turns down, the price at which the best day would include it. That is the number to quote for a far or awkward call, or the number to give a fleet that asks for a discount.