Is it possible to solve the Multiple Depot Vehicle Scheduling Problem (MDVSP) in OR-tools?
The problem is detailed in this paper, but here is a brief summary.
We are given a set of depots and the number of available vehicles at each. We are given a set of timetabled trips, and we know the origin, destination, start time, end time, and a set of depots that can serve a given trip. While connecting two trips, that is assigning a vehicle to serve for two trips sequentially, there may be an unoccupied travel, so called a dead-head trip. There are also dead-heads while going from a depot to the first trip and returning from the last trip to a depot. The objective is to minimize the sum of all dead-head trip costs while ensuring each trip is served by exactly one vehicle and the number of vehicles used does not exceed the availability. (Other trips/links, i.e., occupied trips, must in any case need to be served/traversed; so, there is no need to include them in the objective).
Seems you want to take into account the arc cost only if vehicle is empty. (note: fixed typo)
AFAIK, there is no easy way to do it using OR-Tools. In C++ you may use the DimensionDependentDimension and returning the arc cost if a capacity dimension is zero, and zero otherwise...
Also I'm curious why you would like to only count dead-trip e.g. if the overall vehicle route is several time longer with very few dead-trip instead of a shorter route with few dead-trip why would you want to incentive the first one ?
e.g. a route of 100km with 1km dead-trip is two time better than a 50km route with 2km dead-trip...
For multiple depots please take a look at
vrp_starts_ends.py
For TimeWindows: vrp_time_windows.py
Did you take a look at the documentation ?
e.g. https://developers.google.com/optimization/routing/cvrp
using routing.NextVar(A).SetValues([A, B]) you can force the chain A->B
ref: https://github.com/google/or-tools/blob/49b6301e1e1e231d654d79b6032e79809868a70e/ortools/constraint_solver/routing.h#L1364-L1366
note: Solver won't have the possibility to use A->C->B even if is shorter than A->B->C or C->A->B (supposing TW allow both of them...)
I have a problem where I have several events that are occurring in a project, the events happen semi-concurrently, where they do not start at the same time but multiple can still be occurring at once.
Each event is a team of people working on a linear task, starting at the beginning and then working their way to the end. Their progress is based on a physical distance.
I essentially need to figure out each events start time in order for no teams to be at the same location, nor passing eachother, at any point.
I am trying to program this in MATLAB so that the output would be the start and end time for each event. The idea would be to optimize the total time taken for the project.
I am not sure where to begin with something like this so any advice would be greatly appreciated.
If I understand correct, you just want to optimize the "calendar" of events with limited resources (aka space/teams).
This kind of problems are those called NP and there is no "easy" way to search for the best solution.
You here have two options:
Greedy like algorithm: You will have your solution in a resonable time but it won't be the best one.
Brute force like algorithm: You will find the best solution but maybe not in the time you need it.
Usually if the amount of events is low you can go for 2nd option but if don't you may need to go for the first one.
No mather which one you choose first thing you will need to do is to compute if a solution is valid. What does this mean? It means to check for every event wheter if it collisions whith others in time, space and teams.
So lets imagine the problem of making the calendar on a University. There you have to think about:
Students
Teacher
Classroom
So for each event I have to check if another event have same students, teacher or classroom at the same time. First of all I will check the events that match in time with the actual event. Then I will compare the actual event with all the others.
Once you have this done you could just write a greedy algorithm that starts placing events on time just checking if it collides with some other.
I have project that I need to display a leaderboard of the top 20, and if the user not in the leaderboard they will appear in the 21st place with their current ranking.
Is there efficient way to this?
I am using Cloud Firestore as a database. I believe it was mistake to choose it instead of MongoDB but I am in the middle of the project so I must do it with Cloud Firestore.
The app will be use by 30K users. Is there any way to do it without getting all the 30k users?
this.authProvider.afs.collection('profiles', ref => ref.where('status', '==', 1)
.where('point', '>', 0)
.orderBy('point', 'desc').limit(20))
This is code I did to get the top 20 but what will be the best practice for getting current logged in user rank if they are not in the top 20?
Finding an arbitrary player's rank in leaderboard, in a manner that scales is a common hard problem with databases.
There are a few factors that will drive the solution you'll need to pick, such as:
Total Number players
Rate that individual players add scores
Rate that new scores are added (concurrent players * above)
Score range: Bounded or Unbounded
Score distribution (uniform, or are their 'hot scores')
Simplistic approach
The typical simplistic approach is to count all players with a higher score, eg SELECT count(id) FROM players WHERE score > {playerScore}.
This method works at low scale, but as your player base grows, it quickly becomes both slow and resource expensive (both in MongoDB and Cloud Firestore).
Cloud Firestore doesn't natively support count as it's a non-scalable operation. You'll need to implement it on the client-side by simply counting the returned documents. Alternatively, you could use Cloud Functions for Firebase to do the aggregation on the server-side to avoid the extra bandwidth of returning documents.
Periodic Update
Rather than giving them a live ranking, change it to only updating every so often, such as every hour. For example, if you look at Stack Overflow's rankings, they are only updated daily.
For this approach, you could schedule a function, or schedule App Engine if it takes longer than 540 seconds to run. The function would write out the player list as in a ladder collection with a new rank field populated with the players rank. When a player views the ladder now, you can easily get the top X + the players own rank in O(X) time.
Better yet, you could further optimize and explicitly write out the top X as a single document as well, so to retrieve the ladder you only need to read 2 documents, top-X & player, saving on money and making it faster.
This approach would really work for any number of players and any write rate since it's done out of band. You might need to adjust the frequency though as you grow depending on your willingness to pay. 30K players each hour would be $0.072 per hour($1.73 per day) unless you did optimizations (e.g, ignore all 0 score players since you know they are tied last).
Inverted Index
In this method, we'll create somewhat of an inverted index. This method works if there is a bounded score range that is significantly smaller want the number of players (e.g, 0-999 scores vs 30K players). It could also work for an unbounded score range where the number of unique scores was still significantly smaller than the number of players.
Using a separate collection called 'scores', you have a document for each individual score (non-existent if no-one has that score) with a field called player_count.
When a player gets a new total score, you'll do 1-2 writes in the scores collection. One write is to +1 to player_count for their new score and if it isn't their first time -1 to their old score. This approach works for both "Your latest score is your current score" and "Your highest score is your current score" style ladders.
Finding out a player's exact rank is as easy as something like SELECT sum(player_count)+1 FROM scores WHERE score > {playerScore}.
Since Cloud Firestore doesn't support sum(), you'd do the above but sum on the client side. The +1 is because the sum is the number of players above you, so adding 1 gives you that player's rank.
Using this approach, you'll need to read a maximum of 999 documents, averaging 500ish to get a players rank, although in practice this will be less if you delete scores that have zero players.
Write rate of new scores is important to understand as you'll only be able to update an individual score once every 2 seconds* on average, which for a perfectly distributed score range from 0-999 would mean 500 new scores/second**. You can increase this by using distributed counters for each score.
* Only 1 new score per 2 seconds since each score generates 2 writes
** Assuming average game time of 2 minute, 500 new scores/second could support 60000 concurrent players without distributed counters. If you're using a "Highest score is your current score" this will be much higher in practice.
Sharded N-ary Tree
This is by far the hardest approach, but could allow you to have both faster and real-time ranking positions for all players. It can be thought of as a read-optimized version of of the Inverted Index approach above, whereas the Inverted Index approach above is a write optimized version of this.
You can follow this related article for 'Fast and Reliable Ranking in Datastore' on a general approach that is applicable. For this approach, you'll want to have a bounded score (it's possible with unbounded, but will require changes from the below).
I wouldn't recommend this approach as you'll need to do distributed counters for the top level nodes for any ladder with semi-frequent updates, which would likely negate the read-time benefits.
Final thoughts
Depending on how often you display the leaderboard for players, you could combine approaches to optimize this a lot more.
Combining 'Inverted Index' with 'Periodic Update' at a shorter time frame can give you O(1) ranking access for all players.
As long as over all players the leaderboard is viewed > 4 times over the duration of the 'Periodic Update' you'll save money and have a faster leaderboard.
Essentially each period, say 5-15 minutes you read all documents from scores in descending order. Using this, keep a running total of players_count. Re-write each score into a new collection called scores_ranking with a new field players_above. This new field contains the running total excluding the current scores player_count.
To get a player's rank, all you need to do now is read the document of the player's score from score_ranking -> Their rank is players_above + 1.
One solution not mentioned here which I'm about to implement in my online game and may be usable in your use case, is to estimate the user's rank if they're not in any visible leaderboard because frankly the user isn't going to know (or care?) whether they're ranked 22,882nd or 22,838th.
If 20th place has a score of 250 points and there are 32,000 players total, then each point below 250 is worth on average 127 places, though you may want to use some sort of curve so as they move up a point toward bottom of the visible leaderboard they don't jump exactly 127 places each time - most of the jumps in rank should be closer to zero points.
It's up to you whether you want to identify this estimated ranking as an estimation or not, and you could add some a random salt to the number so it looks authentic:
// Real rank: 22,838
// Display to user:
player rank: ~22.8k // rounded
player rank: 22,882nd // rounded with random salt of 44
I'll be doing the latter.
Alternative perspective - NoSQL and document stores make this type of task overly complex. If you used Postgres this is pretty simple using a count function. Firebase is tempting because it's easy to get going with but use cases like this are when relational databases shine. Supabase is worth a look https://supabase.io/ similar to firebase so you can get going quickly with a backend but its opensource and built on Postgres so you get a relational database.
A solution that hasn't been mentioned by Dan is the use of security rules combined with Google Cloud Functions.
Create the highscore's map. Example:
highScores (top20)
Then:
Give the users write/read access to highScores.
Give the document/map highScores the smallest score in a property.
Let the users only write to highScores if his score > smallest score.
Create a write trigger in Google Cloud Functions that will activate when a new highScore is written. In that function, delete the smallest score.
This looks to me the easiest option. It is realtime as well.
You could do something with cloud storage. So manually have a file that has all the users' scores (in order), and then you just read that file and find the position of the score in that file.
Then to write to the file, you could set up a CRON job to periodically add all documents with a flag isWrittenToFile false, add them all to the file (and mark them as true). That way you won't eat up your writes. And reading a file every time the user wants to view their position is probably not that intensive. It could be done from a cloud function.
2022 Updated and Working Answer
To solve the problem of having a leaderboards with user and points, and to know your position in this leaderboards in an less problematic way, I have this solution:
1) You should create your Firestorage Document like this
In my case, I have a document perMission that has for each user a field, with the userId as property and the respective leaderboard points as value.
It will be easier to update the values inside my Javascript code.
For example, whenever an user completed a mission (update it's points):
import { doc, setDoc, increment } from "firebase/firestore";
const docRef = doc(db, 'leaderboards', 'perMission');
setDoc(docRef, { [userId]: increment(1) }, { merge: true });
The increment value can be as you want. In my case I run this code every time the user completes a mission, increasing the value.
2) To get the position inside the leaderboards
So here in your client side, to get your position, you have to order the values and then loop through them to get your position inside the leaderboards.
Here you can also use the object to get all the users and its respective points, ordered. But here I am not doing this, I am only interested in my position.
The code is commented explaining each block.
// Values coming from the database.
const leaderboards = {
userId1: 1,
userId2: 20,
userId3: 30,
userId4: 12,
userId5: 40,
userId6: 2
};
// Values coming from your user.
const myUser = "userId4";
const myPoints = leaderboards[myUser];
// Sort the values in decrescent mode.
const sortedLeaderboardsPoints = Object.values(leaderboards).sort(
(a, b) => b - a
);
// To get your specific position
const myPosition = sortedLeaderboardsPoints.reduce(
(previous, current, index) => {
if (myPoints === current) {
return index + 1 + previous;
}
return previous;
},
0
);
// Will print: [40, 30, 20, 12, 2, 1]
console.log(sortedLeaderboardsPoints);
// Will print: 4
console.log(myPosition);
You can now use your position, even if the array is super big, the logic is running in the client side. So be careful with that. You can also improve the client side code, to reduce the array, limit it, etc.
But be aware that you should do the rest of the code in your client side, and not Firebase side.
This answer is mainly to show you how to store and use the database in a "good way".
I have beeen constructing a model in Anylogic in the last weeks, and I am currently simulating the time a truck takes to deliver its products, so I used a delay for this in which different parameters are multiplied to several distributions. Is there any was I can keep track of the value of the distribution each time the process takes place. The following is in example:
normal(2, 8, 4.67, 1.96)*DropSize
The DropSize is my parameter, but I wish to know what value was generated for the normal distribution, and keep track of this.
Sure, several ways (as usual with AnyLogic :-) ). Here is one:
create a collection of type ArrayList:
Then, create a function that draws the random value, stores it in the collection and returns it as below:
Last, replace your code creating the random value with calling that function. Now, whenever you pull a value from the distribution, it is also stored in the collection.
cheers
It's common to see messages like "Installation will take 10 min aprox." , etc in desktop applications. So, I wonder how can I calculate an approximate of how much time a certain process will take. Off course I won't install anything but I want to update some internal data and depending on the user usage this might take some time.
Is this possible in a iPhone app? How Cocoa guys do this, would it be the same way in iPhone apps?
Thanks in advance.
UPDATE: I want to rewrite/edit some files on disk, most of the time these files are not the same size so I cannot use timers for the first iteration and calculate the rest from that.
Is there any API that helps on calculating this?
If you have some list of things to process, each "thing" - usually better to measure a group of 10 or so "things" - is a unit of work. Your goal is to see how long it takes to process a single group and report the estimated time to completion.
One way is to create an NSDate at the start of each group and a new one at the end (the top and bottom of your for loop) for each group. Multiply the difference in seconds by however many groups you have left (minus the one you just processed) and that should be a reasonable estimate of the time remaining.
Of course this gets more complicated if one "thing" takes a lot longer to process than another "thing" - the above approach assumes all things take the same amount of time. In this case, however, you may need to keep track of an average window (across the last n "things" or groups thereof).
A more detailed response would require more details about your model and what work you're performing.