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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 March 30, 2020

            10 Best Calendar Apps to Stay on Track in 2020

            10 Best Calendar Apps to Stay on Track in 2020

            The success of our day is largely dependent on the quality of our planning. Not to miss out anything in their to-dos, some people prefer to make a list of upcoming tasks in a notebook, while others have long started using digital technology solutions.

            Calendar applications are some of the main tools that are worth using to organize our life and plan your time carefully.

            Many people have switched to specific tools; however, there are still some who do not use calendars on a daily basis. They may find some applications uncomfortable to use, non-functional, or expensive.

            In this article, we are going to check out the best calendars apps to help you stay organized.

            1. Cal Calendar

              Cal Calendar has recently appeared on the market of mobile applications (Android, iOS). It is the brainchild of the development team of Any.do that features impressive functionality and well-thought-out design.

              The application comes with many great features, including support for Exchange and Google Calendar, widgets, voice recording, and many more.

              Cal Calendar has direct integration with Any.Do To-Do List, which gives you a unique tandem of two applications.

              Apart from its extended functionality, Cal Calendar is easy to use. The creation of events is very simple and fast.

              What is more, depending on the name of the event, the application automatically adds contacts and geolocation data to the entry description. You can even import your lists and entries from Any.do.

              Cal Calendar is a great option for any type of user. It is very convenient and doesn’t overcomplicate the mode of display.

              Another good thing is that this tool is available for free, so you can use it without spending a dime for the software.

              Available for iOS and Android

              2. Google Calendar

                Google Calendar is the official calendar for Android devices that has been tested out by many users around the globe. If you are right now trying to get away from it, consider changing your mind.

                Since this application is installed on most Android devices by default, many users think that there is nothing special in this program. They are wrong.

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                Google has been updating its calendar for quite a few years, and now it comes in Material Design with advanced event features, direct integration into other Google services (for example, supports reminders and Google Now), and comes with Exchange support.

                The program is super easy and will not cost a dime for you. It is a good thing, right?

                Available for iOS and Android

                3. Jorte Calendar

                  Jorte Calendar is one of the most popular calendar applications in the Google Play store.

                  The program features a wide range of configuration options, with many design alternatives. You can adjust display mode to your needs and view calendar entries sorted by month, week, or day (by hours). It is convenient for quickly picking the desired date, using task bars, and setting reminders.

                  Apart from its ordinary information storing function, this application can be a special cloud service, Jorte Cloud, allowing you to synchronize calendars, schedules, and task lists on multiple devices. The application also supports data importing from Google Calendar.

                  For those paying attention to the program design, there is also Jorte Store, where you can buy styles and icons to personalize the calendar. This feature makes Jorte is one of the brightest calendar applications.

                  A basic version of the app is free of charge, so if you do not want to spend money on a calendar application, it is a good option.

                  Available for iOS and Android

                  4. Business Calendar

                    Business Calendar is geared towards people who use their calendar for work purposes and business task planning. It offers different modes with wide configuration capabilities.

                    The application gives a default view mode by months, and events can be marked in different colors. Display modes/ sorting can be adjusted to your needs (by month, day, year, or events).

                    You can also set a multi-day viewing mode to see how things look for the next few days. Scrolling up and down moves you by month, and if you check a few days, they will be shown in a more detailed form.

                    The day display mode offers hourly scheduling, and the schedule mode provides a detailed schedule for a single event.

                    Business Calendar is a great tool for planning/ scheduling cases, tasks, and events. There is a support for recurring events, which can be set up in just a few clicks.

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                    Having purchased software, you can use it to import and export other calendars, delete, copy, or move several events at the same time.

                    Android Business Calendar application may seem somewhat chaotic, but it works fine and is easy to work with if you play with it for a while.

                    A full version of the application is available for $4.99, but you can also find a free version for the app test drive.

                    Available for Android

                    5. Calendar

                      Calendar is a relatively new app. It works as a web app and for both iOS and Android devices. It is an intelligent app that learns your contacts, schedule and tasks. It also helps you schedule and arrange meetings according to your available time slots.

                      A good thing about Calendar is that it allows you to sync up with other calendars you use such as Apple Calendar and Google Calendar. And so you can manage all the calendars you have in one place.

                      Calendar also gives you analytics of your meetings, giving you a clear picture on how you can improve your time management.

                      Available for Desktop, and iOS

                      6. aCalendar

                        aCalendar opens our collection of top 10 calendar applications available on the market today. With its appealing design, easy navigation, and great functionality, it is one of the most popular calendar apps in our list.

                        Some of extra functions include color schemes for each case type (48 colors to choose from), different types of demonstrations, different widgets, moon phases, and much more.

                        Taking into account it functionality, aCalendar is a reliable calendar application that has an easy-to-navigate interface with three display options. Scrolling from side to side allows you to switch between the display modes of the month, week and day.

                        When scrolling down and up, you are moving through the calendar at intervals in accordance with the selected display mode.

                        Apart from its time planning feature, aCalendar synchronizes photos from contact lists or social networks to remind you about birthdays, anniversaries, or any other special dates.

                        The program also supports data transfer through NFC and full-screen widgets, which eases your work with any data.

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                        The program is available for free, but you can also get even more features if you buy the extended version of software for $4.99.

                        Available for Android

                        7. DigiCal Calendar

                          DigiCal Calendar is very similar to Cal Calendar in the fact that the application focuses on design more than on its functionality. However, this doesn’t mean that the application doesn’t serve the purpose.

                          With this calendar application, you can synchronize all your calendars and view them in different ways.

                          Along with the basic functions, this program comes with support for Google Calendar, Outlook, and includes some unique and interesting features. You can match keywords to the image or set up a dark theme.

                          The app can even show you the weather forecast for three days. There are many other features that deserve the attention of people who really like to use calendar applications.

                          Available for Android

                          8. SolCalendar

                            SolCalendar can be called a universal application. It claims to be an all-in-one digital solution having a basic calendar functionality combined with some other advanced features, such as weather forecast for a specific day.

                            The application supports Google Calendar, as well as tasks, widgets, lunar calendar and even Foursquare.

                            Those searching for a calendar application to cover just everything in its functionality, SolCalendar is a program to consider. There are a lot of interesting things in this application; the program does an excellent job working in “all-in-one” mode.

                            Test SolCalendar – the application is available for free. You can test it out without purchasing the service.

                            Available for Android

                            9. Today Calendar

                              Today Calendar is one of the most hip and edgy calendars in our list. The solution was one of the first ones that really embraced Material Design and remains one of the few that adhere to the neat style.

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                              The calendar application offers bold colors, simple controls, and great functionality. This is not as heavy an application as many others; it will not eat all the memory of your device.

                              If you are not searching for something complicated and over-functional, Today Calendar is what you need. You can always test the application before paying for it – the program is available for free.

                              Available for Android

                              10. Calendar Widget: Month

                                Sometimes people do not need a heap of calendar applications. They would prefer to have one efficient calendar widget.

                                Calendar Widget: Month perfectly fills this niche and meets all the needs of a modern user. It has some features of an ordinary calendar, but the real great thing about this software is that it has 80 or more themes in its library.

                                The design of the application is great; the themes are perfectly tuned. There are options for almost any theme of your smartphone. The only drawback is the fact that the widget memory is not too large, and you should be ready for it.

                                This simple calendar widget was created in the image and semblance of widgets from Yahoo. The widget window displays one calendar month with the ability to go to the previous and move to the next one.

                                If you need a simple and affordable calendar to plan your tasks and affairs for one month, this widget is ideal for you. Calendar Widget: Month is so simple that it does not even have Google Calendar support.

                                At the moment, it does not have the function of connecting any third-party calendars and services. Developers allow the possibility of introducing support for Google service as an addition to the widget, if users request to have this opportunity.

                                Available for Android

                                Our Verdict

                                Searching for the right application to manage your various calendars and plan your busy day can sometimes turn into a streak of obstacles.

                                Most of us need flexible applications that can be easily used to manage our tough schedule. The application should have all necessary time planning functions and be intuitive.

                                Stylish design and limitless compatibility also matter. It is not always easy to find such a program.

                                The above digital calendar solutions fall under the category “worth” of being used. They are modern, multifunctional, easy, and easy. Pick the one you like!

                                More Productivity Apps for Better Time Management

                                Featured photo credit: Unsplash via unsplash.com

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