Real world route planning must take into account a range of costs associated with your fleet of vehicles in order to accurately portray optimal solutions based on the specific characteristics of that fleet. Any system that only takes only distance or time into account (but not both) is not going to be able to calculate the best possible solutions because it is ignoring half of all your cost generators.
Consider a big truck that costs $2 per kilometer in fuel and wear and tear as well as $15 per hour in driver's salary. Now it's quite easy to imagine a scenario in which there is a highway ringing the city allowing the truck to travel much faster and get to the next stop much quicker. For argument's sake, let's assume the following:
- Route through town: Slow, but shorter distance. 15km, taking 1 hour.
- Route on highway around town: Fast, but longer distance. 40km, taking 30 minutes.
Calculating these costs using our above values is easy. We have:
- Route through town: 15km x $2 + 1 hour x $15 = $45.
- Route on highway around town: 40km x $2 + 1/2 hour x $15 = $87.5.
Clearly the highway around town is far more expensive in real terms. However, time only based route optimizations will always select the highway around town because it is faster (and therefore appears to be cheaper when only time based costs are considered). The converse argument is also true for optimizations that only consider distance costs.
Here's a quick summary of the three types of costs Optergon considers when optimizing routes:
- Fixed Cost: Any cost associated with actually using a vehicle in a solution. A good example might be rental vehicles that require an upfront booking fee before they can be used.
- Distance Cost: Per kilometer fuel costs, along with wear and tear, can all be thought of as distance related costs. The further your vehicles travel, the more often they need to be serviced and maintained.
- Time Cost: Employees (i.e. drivers, and other staff) have an hourly cost associated with their labor that must be taken into account.
Now, as it turns out, there will be occasions when other factors, such as time based constraints or delivery capacities come into play. In these instances a more expensive trip between two locations might be selected in order avoid situations that would drastically increase the overall cost of the entire solution. For the purposes of this article, however, we're going to focus solely on seeing how different costs lead to significantly different solutions without worrying about extraneous details.
Route Optimizations with Different Fixed Costs
There are any number of scenarios where it helps to use as few vehicles as possible in order to save money (as opposed to using as many vehicles as available in order to finish as early as possible). One example might be a basic minimum paid to drivers who are required to come into the depot - regardless of how long they drive for. Another might be payments for rental vehicles required to meet all your delivery/pickup obligations.
In both instances, you'd want to use fewer vehicles to avoid high fixed costs. Here's a sample schedule showing two vehicles with relatively high fixed costs:
The Red Pickup costs $40 to make use of and the White Pickup costs $50 to make use of. All other things being equal, with distance costs set to $1 per kilometer and time costs set to $15 per hour, if we are able to use only one vehicle then it should be the Red Pickup since this will save us $10.
Here's the solution (as expected):
This result seems fairly straightforward, but it leads to some pretty powerful solutions in more complex examples because it isn't simply saving you $10, it's also telling you how many vehicles you actually need to complete the schedule. This is useful when you are dealing with 50 vehicles and find that you actually only need 40. Instead of growing your fleet to meet demand it may be possible to shrink it.
Route Optimizations with Different Distance Costs
What if fixed costs weren't really a concern to you? Instead, you had one older vehicle that was slightly heavier on fuel and another newer one that cost slightly less to run. In that case, you might expect to see costs like this:
Here, the Red Pickup has a distance cost of $1.30, which is 30% more than the White Pickup. We'd expect that the White Pickup should do most, if not all, of the driving distance required because it is cheaper to run. Here's the solution:
So the White Pickup was used exclusively because it is cheaper to run. So far so good.
Route Optimizations with Different Time & Distance Costs
But what if the driver of the White Pickup is being paid more? Then we'd have a situation in which one vehicle was more expensive on time and the other more expensive in distance:
In this case it might be a bit harder for you to predict the outcome of the solution because each vehicle may be cheaper to run under different circumstances. In addition, the distance cost of the Red Pickup is 30% more, but the time cost of the White Pickup is a touch over 33% more. This might hint to you that, overall, the White Pickup might be slightly more expensive to run, depending on the ratio of distance to time the solution has.
Here's the result:
Is this a surprising result? It's easy to check what the cost would have been if the White Pickup was used by calculating $28.45 x $1 per hour + 2.51.11 x $20 per hour = $85.50. Using the Red Pickup saved us around $6 even though it is more expensive per kilometer.
How Differing Costs Affect Solutions
Let's assume that we have a limited amount of time to do all our deliveries and that our schedule will run from 9AM 'til 11AM. Just 2 hours in total. Far less than the 2:51 it takes a single vehicle to do all the stops.This means that both vehicles will have to be used in order to complete everything within the specified start and end time for the schedule. In this case, we have the following vehicle costs:
Since one vehicle cannot complete everything by itself we are going to get a solution using both vehicles. One is cheaper per kilometer and the other per hour so how will they be used to optimize for the lowest overall cost? Here's the solution:
This is a great result because it shows how the Red Pickup utilized its full quota of 2 hours (literally to the minute) because it is far cheaper on a per hour basis. The White Pickup on the other hand is far cheaper on a per kilometer basis so it ended up driving a longer distance even though it spent over 20 minutes less on the road overall.
While this example only involves 2 vehicles you can see how powerful the results can be when you take into account all the real world costs associated with your vehicles. What you can be sure of is that super lightweight and cheap vehicles will be utilized to the maximum benefit of your bottom line, while more expensive vehicles will be used far more sparingly and only when necessary in order to keep costs down even further.
Long story short. So long as you accurately capture the costs associated with using your vehicles (regardless of whether they are cheap or expensive to run, drive, and maintain), Optergon will ensure your overall costs are minimized.