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How heuristic software can save millions on transport costs

How heuristic software can save millions on transport costs

Any company that incurs transport related costs stands to benefit from ensuring their vehicles do their pickups and deliveries as efficiently as possible – both in terms of time and distance. And, while there are solutions out there that can help optimise routes, many businesses rely on a combination of human skill and software to ensure they are operating efficiently.

Humans, oddly enough, are actually very good at coming up with reasonable solutions to route optimization problems. We rely on “common sense” to ensure we don’t end up sending vehicles all the way across town because we intrinsically understand this isn’t efficient. Computers don’t have this built-in understanding of efficiency so they are quite bad at solving this type of problem.

Before we begin, however, let’s quickly define what we mean by “this type of problem”.

Multiple Traveling Salesman Problem

Imagine you have a bunch of salesman who have to visit a bunch of stops. What’s the most efficient way for them to visit all the stops? This is known as the multiple travelling salesman problem (mTSP). The mTSP is pretty famous in mathematics because it falls into a category of problem known as NP-Hard (Non-deterministic Polynomial Hard). One of the defining features of these types of problems is that it is not possible to know the solution unless you test every possibility.

Unfortunately, the number of possibilities in a very modest type of route optimization can quickly spiral out of control. Let’s consider a delivery company that has to make 60 stops with a single vehicle. To test every possibility, we would start by picking a point (initially we have 60 possibilities), then another (59 possibilities), and another (58 possibilities), and so on until we had stopped everywhere.

The number of permutations can be given by a function on your calculator called “bang” – it’s denoted by an exclamation mark. Since we have 60 stops, our equation for the number of permutations is given by:

60! = 60 x 59 x 58 x … x 3 x 2 x 1 = 8.32 x 1081

That’s a really big number. To put it into perspective, there are approximately 1080 hydrogen atoms in the entire universe. So in all the stars and planets and dust and gas in our solar system, in our galaxy, in the Andromeda galaxy, in our local cluster, in the entire super structure of all that exists, there are less hydrogen atoms than permutations in this seemingly simple problem. That’s why computers struggle with vehicle routing problems.

Optimizing routes

So humans are pretty good at working on this type of problem because we are able to take “common sense” shortcuts that end up giving us a pretty reasonable solution. The problem is that at some point even we become overwhelmed and simply can’t take into account all the factors required from modern businesses.

Imagine you had the task of creating a schedule for 10 vehicles, with 300 stops, over the course of a week, having to keep in mind that each stop is either a pickup or delivery (with a certain capacity – you can’t overload the vehicles), each location takes a certain amount of time, as does the trips between the stops, but your vehicles only run from 9am to 5pm, so there are time limits as well as capacity limitations.

Vehicles have different running costs – large trucks consume more fuel than lighter ones, but can carry more – they might also require drivers with specialized licenses who have a higher hourly rate. So you need to try and work out whether it is better to send a small vehicle a longer distance (bearing in mind that it can only visit a limited number of stops before its load capacity is reached), or send the larger vehicle because it also has capacity to deliver to other nearby stops.

But, each delivery takes time so the person creating the schedule also needs to ensure that the truck’s route doesn’t leave it miles away from the depot at 4:58pm – meaning that the driver ends up being furious that he or she will get home late. Vehicles also come with a built in range before they have to refuel, so you can’t assume they can drive indefinitely without building in time for refueling stops and driver breaks.

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What happens when some deliveries can only be made at certain times? If several locations require deliveries at the same time, the scheduler has to ensure that all the vehicles are delivering to those locations at the right time while still keeping the overall costs to a minimum.

Human optimizations

In the scenario above, the amount of work a human would have to perform is pretty daunting. Companies pay very smart people to generate their schedules ahead of time. It’s hard, specialized work that costs a lot of money.

But, to demonstrate how a human might approach this problem, let’s consider the following set of locations with two depots, each with a vehicle that has an operating time limit and a range limit (i.e. it may only travel 150Km per day). These limits, in the real-world, would depend on the unique resources and limitations of your own operation. But for now, here’s what we have:

70point-2vehicles

    Intuitively, we know that (unless there is a specific reason) sending the vehicle from the depot in south east (the orange marker towards the right of the map) to locations in the north west (top left of the map), near the second depot, is probably not going to be the most efficient way to do things. We might decide that it is a good idea to simply divide up the points roughly equally like this:

    70point-2vehicles-red-line

      From there it is up to us to try create the most efficient individual routes for each vehicle in order to produce the solution. I actually gave it a bash. It’s really not easy. Here’s what I came up (full disclosure, I had to get some help) shown in Google Earth:

      70point-2vehicles-googleearth

        Not bad, right? There are a couple of cross-overs in each tour, but this is because London is full of one-way streets and is crisscrossed with rivers that mean vehicles have to find nearby bridges, which can affect the course of their optimal routes.

        But there’s a problem. Neither of these vehicles’ tours come in at less than 150Km – one came in at 151.1Km and the other at 150.4Km. You might think I’m being pedantic but, for big operations that rely on efficiency, small differences have a habit of working their way up the chain to become big problems.

        Simply put, I couldn’t do it. From my perspective, this problem cannot be solved. Maybe people with a lot more experience and time on their hands can give it a go and see if it is possible. But, all is not lost. There are software applications that offer route optimizations available. I used one of these to try and improve on my solution.

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        Computer optimizations

        Because of the massive complexity involved in trying to calculate reasonable solutions, mathematicians and programmers have become pretty sneaky in the way they approach things. They abandoned traditional programming techniques and began to use heuristic algorithms, which can produce pretty good solutions in a reasonable amount of time. A heuristic algorithm can look for solutions among many possibilities, but not necessarily guarantee it finds the best one.

        One example of a heuristic algorithms is called the Ant Colony Optimization (ACO), which mimics the way an ant colony forages for food. Initially ants head out in all directions. If an ant finds a food source it runs back to the nest leaving a trail of pheromones. When the next wave of ants set out, some are influenced by the weak pheromone trail and follow it. If they too come across the same source of food, they rush back to the nest, leaving a stronger trail of pheromones that influences the following waves of ants more and more, until eventually the ants make a nice straight line between the nest and their food source.

        By taking sensible shortcuts, implementing a few heuristic algorithms, and making a few assumptions here and there, computer scientists can create a system than can outperform even the best humans. I applied one of these to my problem and came up with this result:

        70point-2vehicles-computer-googleearth

          This is a better solution than I could manage, but it still broke the distance constraints of one of the vehicles – by less than 1Km. The other vehicle made it with a few hundred meters to spare.

          Ok, so we’re getting better. But this is a pretty simple problem. There aren’t delivery time windows, there aren’t vehicle and location constraints – i.e. does the vehicle need to have cold chain facilities, or be able to transport liquid volumes – or any of a myriad other potential stumbling blocks that might crop up in the real world.

          I did manage to run this particular problem on an enterprise system – to see if it is in fact possible.

          Enterprise optimizations

          There are significant differences in the quality of the solution between lightweight programs that use shortcuts (like basing cost calculations only on distance, or only on time) and built in assumptions (i.e. using human “common sense” to divide the map into areas each vehicle will deliver to), and ones that throw significant computing resources at complex real-world problems to produce unbeatable quality optimizations that genuinely produce significant savings on fuel, time, and costs.

          Instead of considering only distance or only time costs, enterprise systems must consider and measure both – just as both are factors in real world optimizations. A delivery truck might require two operators (i.e. a driver and an assistant to help unload) who work on hourly wages. This can have an impact on whether the system routes the vehicle via a shorter, but slower route, or a longer (but faster) one.

          Systems that only optimize the time taken, or the distance travelled, will never be able to get this fundamental balance of costs right because they only ever consider one or the other. Programs that use “common sense” shortcuts will also, by definition, miss out on potential solutions that aren’t intuitive to our minds – and there are many, many, many (uncountably many) of these.

          To generate our enterprise solution, I utilized Optergon, which is in use in over 60 countries around the world and integrates with transport, tracking and logistics companies via an API service. What makes Optergon interesting is that it doesn’t make use of so-called common sense shortcuts. Instead it relies on a combination of heuristic algorithms, including the ACO (mentioned earlier) and simulated annealing.

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          Simulated annealing mimics the process of tempering steel, in which the metal is heated to get the atoms jiggling about with weaker bonds. The steel is then hammered forcing the atoms into a closer, more densely packed array as it cools. This process is repeated until the steel’s atoms are packed as tightly as possible.

          But cutting-edge algorithms and a system that teaches itself as it goes aren’t enough to tackle enterprise level problems on their own.

          Because of some curious features of the mTSP it is virtually impossible to avoid situations in which a solution “looks” great, but isn’t close to what the actual best solution looks like. This is what’s known as a “local minimum”, and is a tricky problem to overcome because you don’t know ahead of time whether the system has found a genuinely good solution, or a local minimum.

          In order to get around this, Optergon had to implement a massively parallel architecture that allows it to work on the same problem, and specific aspects of the problem, at the same time across hundreds of different processes. Sharing tidbits of information and gleaning new insight at every step of the way, Optergon’s individual processes make use of existing and proprietary heuristics to teach the overall system how to generate an unbeatable solution

          With all this in mind, our current problem turns out to be possible. Here’s the solution:

          70point-2vehicles-enterprise

            Solution courtesy of 3DTracking, integrated with the Optergon route optimization API

            In this solution, each vehicle arrives back at the depot within the bounds of the constraints set – one vehicle made it in 148.3Km, and the other in 147.9Km. Pretty tight, but valid.

            So why am I going on about the difference between a few kilometres? Well, for a start, you wouldn’t want a system that generates a magnificently cost effective solution that requires your vehicles to travel 2000 miles on a single tank of gas, carrying 30 tonnes of cargo that it doesn’t have capacity for, arriving at locations at the wrong time, and so on.

            An enterprise solution must produce the most cost effective solution possible within the real-world bounds dictated by the business. Which brings me to my next point…

            Not only did this optimization reduce our costs, it also showed us something we didn’t know before – whether or not it was actually possible to successfully visit all the locations within the given restraints. This makes a system like Optergon useful for determining whether or not it’s even possible to attempt certain things.

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            A good example of where this is useful might be when transport companies quote for business. If they are able to run accurate optimizations on transport contracts before delivering a quote they can be much more accurate and competitive because they know exactly what is possible, and how much it will cost them.

            Comparing costs

            So, apart from the fact that two out of three solutions weren’t valid, what were the differences in cost? Bearing in mind that it is more important to produce a solution that is valid (i.e. possible within the constraints of the business) than a cheaper one that is not. It’s important to compare the distance and times provided by each solution as the cost is essentially an arbitrary reflection of these two components – for the sake of making the math a bit easier, I set the time and distance cost of $5 per hour and $5 per km respectively.

            Real businesses would need to input values that reflected their operation accurately in order to derive the correct costs – although, since the costs are the same for all three optimizations, we can also look at the percentage difference in costs to determine how much better one solution is over another.

            Human solution (with help) – Invalid

            Unit 1 (North west depot)

            • Distance: 151.1Km
            • Time: 35191 seconds
            • Cost: $824.41

            Unit 2 (South east depot)

            • Distance: 150.4Km
            • Time: 32480 seconds
            • Cost: $817.17

            Overall cost: $1641.58

            Computer solution – Invalid

            Unit 1 (North west depot)

            • Distance: 150.9Km
            • Time: 33856 seconds
            • Cost: $821.65

            Unit 2 (South east depot)

            • Distance: 149.8Km
            • Time: 34046 seconds
            • Cost: $816.63

            Overall cost: $1638.28

            Enterprise solution – Valid

            Unit 1 (North west depot)

            • Distance: 148.3Km
            • Time: 33142 seconds
            • Cost: $807.85

            Unit 2 (South east depot)

            • Distance: 147.9Km
            • Time: 34464 seconds
            • Cost: $807.50

            Overall cost: $1615.35

            In essence, the enterprise solution provided by Opteron produced a valid result that was in the region of 1.5% – 2% better than a human (with help), and a human using routing software. Although, this is a very simple problem and that gap would widen up quickly as more and more vehicles and stops were added – but 60 points was more than enough for me. For a company doing a few hundred locations a day, the improvements might be nearer to 10%, or 15%, depending on how good their existing optimizations are.

            Ok, so a couple of percent might not sounds like much. But, anyone who works in a logistics company and knows how much transport costs are would jump at the chance to shave entire percentage points off their costs. This might equate to millions of dollars being saved every year for even moderate sized organizations.

            Don’t forget about the fact that better route optimizations mean less distance travelled, which not only saves on fuel but also on labor and vehicle wear-and-tear costs. And fuel costs are only ever going to go up in the long run (assuming the global economy recovers at some point) so saving on fuel will become more and more of a financial imperative as time goes by.

            And, let’s not forget about the fact that if companies are travelling up to 10% less, then 10% less carbon is being pumped into the atmosphere. Not using enterprise route optimization is not only wasteful in terms of cost, it’s unnecessarily bad for the environment. Additionally, if you know ahead of time what the optimal way to perform your pickups and deliveries are, it means you also know how to pack the vehicles. Obviously, packing the vehicle is important because you don’t want to arrive at the first stop and have to unpack the entire truck to get at the first item to be delivered.

            If you know how to pack the trucks, you also now how to stock the warehouse so that the packers can operate as efficiently as possible, working quickly because everything they need is warehoused in a convenient location. In this way, having enterprise level route optimizations not only saves on transport but can also serve to maximize the efficiency of your operation up and down the chain, from the warehouse to delivery.

            Featured photo credit: Daniel Gimbert via flickr.com

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            Last Updated on February 15, 2019

            7 Tools to Help Keep Track of Goals and Habits Effectively

            7 Tools to Help Keep Track of Goals and Habits Effectively

            Now that 2011 is well underway and most people have fallen off the bandwagon when it comes to their New Year’s resolutions (myself included), it’s a good time to step back and take an honest look at our habits and the goals that we want to achieve.

            Something that I have learned over the past few years is that if you track something, be it your eating habits, exercise, writing time, work time, etc. you become aware of the reality of the situation. This is why most diet gurus tell you to track what you eat for a week so you have an awareness of the of how you really eat before you start your diet and exercise regimen.

            Tracking daily habits and progress towards goals is another way to see reality and create a way for you clearly review what you have accomplished over a set period of time. Tracking helps motivate you too; if I can make a change in my life and do it once a day for a period of time it makes me more apt to keep doing it.

            So, if you have some goals and habits in mind that need tracked, all you need is a tracking tool. Today we’ll look at 7 different tools to help you keep track of your habits and goals.

            Joe’s Goals

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              Joe’s Goals is a web-based tool that allows users to track their habits and goals in an easy to use interface. Users can add as many goals/habits as they want and also check multiple times per day for those “extra productive days”. Something that is unique about Joe’s Goals is the way that you can keep track of negative habits such as eating out, smoking, etc. This can help you visualize the good things that you are doing as well as the negative things that you are doing in your life.

              Joe’s Goals is free with a subscription version giving you no ads and the “latest version” for $12 a year.

              Daytum

                Daytum

                is an in depth way of counting things that you do during the day and then presenting them to you in many different reports and groups. With Daytum you can add several different items to different custom categories such as work, school, home, etc. to keep track of your habits in each focus area of your life.

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                Daytum is extremely in depth and there are a ton of settings for users to tweak. There is a free version that is pretty standard, but if you want more features and unlimited items and categories you’ll need Daytum Plus which is $4 a month.

                Excel or Numbers

                  If you are the spreadsheet number cruncher type and the thought of using someone else’s idea of how you should track your habits turns you off, then creating your own Excel/Numbers/Google spreadsheet is the way to go. Not only do you have pretty much limitless ways to view, enter, and manipulate your goal and habit data, but you have complete control over your stuff and can make it private.

                  What’s nice about spreadsheets is you can create reports and can customize your views in any way you see fit. Also, by using Dropbox, you can keep your tracker sheets anywhere you have a connection.

                  Evernote

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                    I must admit, I am an Evernote junky, mostly because this tool is so ubiquitous. There are several ways you can implement habit/goal tracking with Evernote. You won’t be able to get nifty reports and graphs and such, but you will be able to access your goal tracking anywhere your are, be it iPhone, Android, Mac, PC, or web. With Evernote you pretty much have no excuse for not entering your daily habit and goal information as it is available anywhere.

                    Evernote is free with a premium version available.

                    Access or Bento

                      If you like the idea of creating your own tracker via Excel or Numbers, you may be compelled to get even more creative with database tools like Access for Windows or Bento for Mac. These tools allow you to set up relational databases and even give you the option of setting up custom interfaces to interact with your data. Access is pretty powerful for personal database applications, and using it with other MS products, you can come up with some pretty awesome, in depth analysis and tracking of your habits and goals.

                      Bento is extremely powerful and user friendly. Also with Bento you can get the iPhone and iPad app to keep your data anywhere you go.

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                      You can check out Access and the Office Suite here and Bento here.

                      Analog Bonus: Pen and Paper

                      All these digital tools are pretty nifty and have all sorts of bells and whistles, but there are some people out there that still swear by a notebook and pen. Just like using spreadsheets or personal databases, pen and paper gives you ultimate freedom and control when it comes to your set up. It also doesn’t lock you into anyone else’s idea of just how you should track your habits.

                      Conclusion

                      I can’t necessarily recommend which tool is the best for tracking your personal habits and goals, as all of them have their quirks. What I can do however (yes, it’s a bit of a cop-out) is tell you that the tool to use is whatever works best for you. I personally keep track of my daily habits and personal goals with a combo Evernote for input and then a Google spreadsheet for long-term tracking.

                      What this all comes down to is not how or what tool you use, but finding what you are comfortable with and then getting busy with creating lasting habits and accomplishing short- and long-term goals.

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