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# Linear Programming - Science topic

Explore the latest questions and answers in Linear Programming, and find Linear Programming experts.

Questions related to Linear Programming

Can MATLAB solve large-scale linear programming problems? such as pathway toward carbon-neutral of power sector.

Please can anybody help me with my final year project?

I'm working on an assortment optimization problem in retail (Food industry), and i have a big transactional data . i have to chose only 4000 products from a set of 15000 product in a way to maximize the total revenue. I'm supposed to use an operational research approach , and the only thing that cross my mind is to use the MILP(mixed integer linear programming).

I dont have any constraint about the shelf space or the stock restriction, can i use a knapsack approach in this case ?

also i want to know if I can use multi label classification to determine the probability that a client might buy a product from a specified category?

thank you in advance for your answers.

Optimization is a statistical technique and done by using linear programming. it is being used in farming systems.

Where is the Jade due to the throwing out of a brick and a paving stone?

A brand new conception of preferable probability and its evaluation were created, the book was entitled "Probability - based multi - objective optimization for material selection", and published by Springer, which opens a new way for multi-objective orthogonal experimental design, uniform experimental design, respose surface design, and robust design, discretization treatment and sequential optimization, etc.

It aims to provide a rational approch without personal or other subjective coefficients, which is available at https://link.springer.com/book/9789811933509,

DOI: 10.1007/978-981-19-3351-6.

Best regards.

Yours

M. Zheng

I have used intlinprog in my code for solving integer linear programming problems and mixed integer linear programming problems. What is the complexity of intlinprog in terms of the number of constraints and variables?

Hi, I'm Anne Christina here 3rd year financial Mathematics student in UMT conducting my final year project entitle "Linear Programming in constructing feed formulation of Giant Gourami (Osphronemus Goramy) in Malaysia". For that I'm researching for the data on the feed ingredients needed for gourami and in detail on the nutrient content of amino acids. Hope my question will be answered by the person in this field. Thank you in advance.

**In my data envelopment analysis (DEA) model, I have 3 outputs, namely (i) No. of Sponsored Projects, (ii) No. of Consultancies and (iii) Total Revenue generated from Sponsored Projects and Consultancies. My DMUs are different universities. It is clear that the third output is the overlapping factor as the revenue is generated due to the sponsored projects and consultancies. If I choose only the third output, the problem is that I cannot take into account the social benefits from a university because it is possible that a university undertakes many projects and consultancies (i.e. indicators of social benefits) while generating less revenue. Again, if I take the first two outputs, then I miss the part of revenue generation because all the projects and consultancies may not generate same revenue. Should I consider the first two outputs or the third output or all the three outputs in my model?**

How many methods we have for multi-criteria Classification (sorting) problems? Could you please name them?

As I understood we have some methods in the below approaches:

1. Multi-Attribute decision making (ELECTRE-TRI, FlowSort, Promethee IV)

2. Multi-objective decision making

3. Goal programming

4. Linear programming (Integer programming)

5. Supervised methods (UTADIS/Decision tree)

6- Clustering (K-means/K-medoids/2steps/c-means)

Could you please name some more methods which can be applied for multi-criteria classification problems?

Thank you in advance.

Need to know about the softwares available for linear programming.

In the file that I attached below there is a line upon the theta(1) coefficient and another one exactly below C(9). In addition, what is this number below C(9)? There is no description

How can I get a MATLAB code for solving multi objective transportation problem and traveling sales man problem?

Consider a linear program of the form

min <c,x>: Ax <= b.

Suppose that b depends on a parameter y, such that b(y) is concave. Then the value of the LP is convex in this parameter y. This is easy to prove via duality and should be widely known. However, I do not find an appropriate reference. The only case I have found is when b is linear, this is treated in a recent book of Dantzig and Thapa. Could anyone help with a reference for the general concave case?

I am working on a 33 bus distribution network and I am trying yo maximise the number of critical loads restored and am using Dist flow for my power flow studies which I incorporated as one of the constraints but i cant seem to get the constraints formulated correctly in MATLAB

I want to learn MARKAL and TIMES energy modelling software. May I know if there are any videos/ tutorials/ study material available for the same?

Thank you

Power Network Expansion Planning is the problem of deciding the new transmission lines that should be added to an existing transmission network in order to satisfy system objectives efficiently. It is one of the main strategic decisions in power systems and has a deep, long-lasting impact on the operation of the system. Several challenges such as deregulation, renewable penetration, large-scale generation projects, market integration, and regional planning are discussed in the literature to some extent.

**In the context of the smart grid, what can be the potential future challenges in terms of different scenarios, applications, modeling, solution, and novel devices in the network?**For an Integer Linear Programming problem (ILP), an irreducible infeasible set (IIS) is an infeasible subset of constraints, variable bounds, and integer restrictions that becomes feasible if any single constraint, variable bound, or integer restriction is removed. It is possible to have more than one IIS in an infeasible ILP.

Is it possible to identify all possible Irreducible Infeasible Sets (IIS) for an infeasible Integer Linear Programming problem (ILP)?

Ideally, I aim to find the MIN IIS COVER, which is the smallest cardinality subset of constraints to remove such that at least one constraint is removed from every IIS.

Thanks for your time and consideration.

Regards

Ramy

Dear Experts,

I am looking for a solution for a convex optimization problem (linear programming) and I am thinking about evolutionary algorithms. Do you think it would be helpful?

When seeking a solution to a linear programming problem with fuzzy coefficients in the objective function, some technique must be applied to transform to crisp values, or to translate these fuzzy elements to real values. What techniques do you suggest?

I want the following help in linear fashion:

- I have a vector: P(n)=[1,2,3,4,5,...,n]
- I have binary variables with length of P: y(1),y(2).....y(n). These variables, y(i) can only take 0 or 1.

A new vector Q(n) is needed, such that, if y(i) is 1, then the ith element in Q(n) should be 0. And in rest of the places, the P(n) should get repeated.

- Example : if n=6, and y(1) and y(4) are 1 ,then Q(1) and Q(4), should be 0. The vector, Q will be as follows :

Q=[

**0**1 2**0**1 2].- Another example : if y(3) is 1, then Q should be as follows:

Q=[1 2

**0**1 2 3].Basically, beside the zeros on ith position, the vector P should repeat itself in non-zero positions of Q

Can you please help me formulating this problem?

Does someone have an excel file for formulating feeds using linear programming or a free online tool where this can be found?

My basic objective is to solve epsilon insensitive SVR using linear programming . Therefore I need the base code for LPSVR.

Dear all,

As we know, interval matrices are matrices with 0 and 1 entries with the property that the ones in each column (row) are contiguous. Interval matrices are totally unimodular (TU). Hence, the integer programming (IP) problems with such matrices of technical coefficients and can be solved as linear programming problems.

However, in the consecutive-ones with wrap around, the ones are wrapped.

For instance, in the following matrix, the ones are wrapped in columns 4 and 5:

1 0 0 1 1

1 1 0 0 1

1 1 1 0 0

0 1 1 1 0

0 0 1 1 1

This example is not TU with a sub-matrix with determinant 2 (deleting rows and columns 2 and 4).

Two questions:

1- When wrapping does not violate TU property?

2- Is there a general approach to solve IP problems with consecutive ones and wrapping around matrix of technical coefficients, efficiently?

Thank you for your kind help/

Any recommendation from a scientific journal to submit a paper on operations research applying linear programming and vehicle routing (VRP) using the B&B algorithm?

The routing problem can be easily solved using ILP or mixed ILP, why metaheuristic algorithms are required to solve this problem?

where matrices

**A**and**B**are known while**X**and**Y**are to be solved.For example,

**A**=[a 0;

0 b];

**B**=[a a 0;

0 0 b;

0 0 b;];

a and b are known elements.

It is easy to see that the solution is

**X**=t*[1 1 0;

0 0 1;];

**Y**=1/t*[1 0;

0 1;

0 1;];

where t is any non-zero real number.

But how to derive this solution step by step in a systimatical way?

It would be better if there is a programmable approach.

I noticed that many studies which treat Electric Vehicle charging (in a V2X scenario) as an MILP (Mixed-Integer Linear Problem) problem, consider a constraint to prevent that an EV (Electric Vehicle) could simultaneous charge and discharge during the same time slot (the duration of this inteval varies from a study to another; the most used are: 15 minutes, 30 minutes; 1 hour).

I'm agree in considering that charging and discharging an EV at the same continuous time instant is not a realistic scenario, but which could be the reason of preventing this situation during a time inteval which lasts 15 minutes or 1 hour?

PS: I guess that it's done to simplify the complexity of the problem, but I'm wondering if there are other reasons.

Dear Colleagues,

I am running a time series regression (OLS) based on stationary dependent variables and log form of explanatory variables. Very few of logged exp. variables are stationary. When I took 1st difference, I could not get any significant results, plus, also the 1st difference did not make much sense to me when I analyzed it graphically. My question is, will my regression results be untrusted if I report such an analysis. I asked a similar question and got some replies that even if you log your variables, still you have to test it for a unit root; however, I am observing several papers with log variables where stationarity was not taken into account. Thank you beforehand.

Best

Ibrahim

Multi-Market-Models were much famous a decade ago to carryout policy simulations. Are they still famous in economics now? Scope for publication in the present time?

Thanks in advance

I need to model a construction and demolition waste management network in order to maximize waste recycling. I read some works that use MILP. Among the software used are GAMS, JULIA, MATLAB and R. Are there other software that can be used?

Hi All,

Are there any opinions and experiences of the LocalSolver solver?

Comparing for example accuracy, speed, etc. to other solvers, etc.

Interesting to hear about them ...

/Lars

Please suggest a collection of examples of Zimmerman approach to solve fuzzy linear programming problems?

Any bibliographic recommendations on the problem of routing vehicles with multiple deposits, homogeneous capacities? less than 10 nodes

Hi, I have an optimization problem (primal problem) which is solved by the duality theorem. So I have constraints of the dual and its variable's value. it is worth mentioning the problem is linear. how can I calculate primal variables indirectly and by the dual answer?

I am formulating a multi-objective linear programming model. It is a pure linear program and I plan to only use scalars to convert multiple objectives into one single objective. Before then, I need to make sure the Pareto front is in a convex form. I know for MIP problems, it could be non-convex. Is the linear programming model a sufficient condition for the convex Pareto front? Thanks.

If I'm not wrong, there can be non linear programming problems solved by iteratively calling the simplex algorithm on a modified sub-problem.

Are there optimization problems which require both the primal and dual simplex?

Hi,

I am working on a MIP problem, my program runs too long or does not find the result as I change my parameters. I have been dealing for a long time, although I have made many changes to the code, I don't think of a solution anymore.

If you are interested, I can send my model and code.

Hello,

Recently, I was reading about several techniques that solves Unconstrained Mixed Integer Linear Programs (UM-ILP) using a meta-heuristic algorithm called simulated annealing. I was thinking about the Constrained zero-one ILP. I have a linear objective function with a linear set of equality/inequality constraints and I'm thinking about reformulating the problem using the kkt/Lagrangian function. However, I'm not sure if it is even the right approach given that my optimization problem have binary variables and it is linear and hence, solutions such as the penalty method and barrier log would work best for me. My goal is to transform a constrained problem to non-constrained then apply an optimization method like simulated annealing to solve my new formulation of the problem but i'm not really sure which method is even the right approach? Also from what I read the problem will not be a simple minimization problem anymore but instead a saddle point problem.

Thank you all for your time and replies.

I want to run a MILP problem that is time dependent for a given duration (i.e. something like a for loop situation). I have parameters that change with time and the results from the previous simulation affect the next simulation. I am using CPLEX solver in MATLAB how can I achieve this.

Some years ago I wrote some command line using linear programming to optimize production for table water company using table water and sachet water as two product and using production hours of the two and number workers with profit made as constraints, I need some help in changing my command lines to software algorithms in order to develop an useful and helpful App.

A machine manufactures spare parts at the rate of 20, 000 per month. A second machine uses those spare parts at the rate 50 00 per month and remainder put into stock. It cost ₦100, 000 to set up the machine the company establish their stock hold costs 20% per annum of the average stock value each parts costs ₦250 to make. Required What batch size should be produced on the first machine and what frequency.

I have a question regarding making the dual of the MILP model. More precisely, I am working on the job-shop scheduling problem, and I want to have a dual problem of that.

How can I create the dual constraints for integer variables?

I understand the idea of Best Worst Method for multi criteria decision making

and i know that there is a solver to get the weights but i need to understand the mathematical equation and know how to solve it with my own self.

Can any one help me?

{|𝑤𝐵 − 𝑎𝐵𝑗𝑤𝑗|} ≤ 𝜉

*L*for all j{|𝑤𝑗 − 𝑎𝑗𝑊𝑤𝑊|} ≤ 𝜉𝐿 for all j

Σ𝑤𝑗 = 1, 𝑤𝑗 ≥ 0 for all j

I have formulated an Integer programming problem with around variables and 30 constraints. I observe that the relaxed LP takes same time to execute (around 5 minutes) as the original IP. How is it possible when Linear programming problem is polynomial time solvable and IP is not?

Simplex method in linear programming.

Based on your expertise, what is the better optimizer tool between GAMS ( https://www.gams.com/ ) and Gurobi ( https://www.gurobi.com/ )?

Please also let me know your field of research.

It will be helpful if you can give me some references if there are MINLP optimization problems solved by PSO.

What is the best commercially available non-linear optimization problem evolutionary solver/ algorithm?

Must be freely or easily obtainable.

Not necessarily free.

relatively Easy to install and use.

Anything better than excel solver's evolutionary algorithm?

What impact does the initial solution have in the case of non-linear optimization problems and (solved by) evolutionary algorithms?

For instance, initial solutions have an impact with linear programming.

Would it have any effect to rerun a non-linear optimization problem after a certain or good initial solution was found (and the evolutionary algorithm stopped)? Particularly/ for example in cases with many possible local solutions, or local solutions rather close to each other.

Would the latest known initial/ best solution affect something like solution space sampling or local solution sampling?

With non-linear optimization, when you are interested in the different possible local solutions, because it can help you towards the optimal (global) solution, and to identify the optimal solution, particularly when you have a hint or idea what it would or would not look like, what would be an effective way to surface possible local solutions?

Do you simply note and cross out the local solutions found, as they are found?

Is it simply a matter of your initial solution sample or set?

what is the best way to search or interrogate an initial solution of a non-linear optimization problem you (strongly) believe is close to the optimal solution?

is there a better approach or strategy than to incrementally or iteratively increase a band of floors and ceilings around the initial solution, until this no longer has any effect? this approach should be better than starting with a wide band around the initial solution from the onset?

What is the best way to choose initial solutions for a non-linear optimization problem sensitive to the initial solution?

If you have a significant number of optimization problem coefficients (50 in this case), and your optimization problem is such (non-linear with multiple possible local solutions) that it is sensitive to the initial solution, what are the best ways to choose (a set of) initial solutions?

Will the excel solver evolutionary algorithm do this?

With a non-linear optimization problem, can insensitivity to the initial solution be interpreted as a global solution, or (high) probability of a global solution?

PLEASE Refer to Document containing Data Set

Suppose that the minimum number of security staff required at different hours are at the ith hour (

*i*=1,2,…,24) are outlined as follows (refer to doc)I'm not able to figure out how to develop a model for this issue and I need assistance in developing a linear programming model to minimize total cost.

This may be a repeat of a previous question i asked, but i want to make such a statement in a paper, and want to evaluate if it can be refuted beforehand:

Are there (non-linear) optimization problems where it is not/ no longer possible to walk from one local solution, to a better local solution?

And can one define the global solution in this way - the inability to walk from a local solution to a better local solution?

Then, Can one base this on higher order partial derivatives?

I am currently using higher order partial derivatives to indicate if steps are still possible, post excel solver NLP (and evolutionary), and to identify such steps.

If i obtain steps still possible this way, i am walking to better solutions.

If i no longer am able to identify steps through higher order partial derivatives, can i say i have reached the global solution?

A higher order partial derivative would be the delta in objective function in response to a delta change in 3 or more coefficients. It differs from 2nd order partial derivatives, and this is evident when you consider the actual calculation.

Why would an (the excel) evolutionary algorithm be better at, or simply be able to, solve what seems to be a linear problem, when the LP (and also NLP) algorithm struggle to, or simply fail to.

The problem is of the form:

Max X; X = x1 + x2 + x3...

x1 = (k1 × z1) + (k2 x z2) + (k3 x z3)...

x2 = (k1 x y1) + (k2 x y2) + (k3 x y3)...

x3 = (k1 x q1) + (k2 x q2) + (k3 x q3)...

k are the coefficients of the problem to optimize; z, y, q are factors and are given/ constants.

The evolutionary algorithm can find a (better) solution (to the initial solution). The LP algorithm occasionally finds a solution, and not better (mostly worse) than the evolutionary algorithm. The NLP algorithm does not really find a solution at all.

Can higher order partial derivatives be used to move non-linear programming problems from local solutions towards the global solution?

That is, Partial derivatives of order greater than 2nd order.

Suppose we have a linear programming model in the below:

Model:

Max = 3*x1+5*x2

x1 <= 4

3*x1 + 2* x2 <= 18

x1, x2 >=0

Calc:

! I would like to do some calculation here using to the optimization result obtain from the above model

For example: Y = x1+ x2

EndCalc

End

Any answer will be appreciated, thanks

Few days earlier on a project presentation on Stochastic Programming Real life applications, i constructed 3 real life scenario based Stochastic Models:

**A Farmer's Problem, Container Allotment Problem and another on Stochastic Arc Routing**. Also solved them for particular scenario.As stochastic linear programs are lengthy programs with a lot of constraints, it is long-time process to solve a stochastic linear program. And therefore i used LINDO solver to solve the problem. I have a L-shaped algorithm based example too.

But the examiner said me that, why you didn't used the general solving procedure to solve these LP problems? I explained about the long programs and complexity. In reply, I found complement that

**all credit goes to the LINDO solver, not you**.I am wondering that advances in Science could make our works easier and faster. Shouldn't we take these type of advances in our daily life?

Is linear programming one part of convex optimization?

Deterministic Global optimization relies on convex relaxation of the non-convex problems. Certain nonlinearities are duly converted into linear forms underestimators to be solved by efficient MILP solvers (e.g. signomial functions/ bilinear terms).

Most nonlinearityies are approximated to linear functions by piece-wise linearizations. However, I am wondering if this linearizations guarantees that the approximations are understimators of the original nonconvex problem (i.e. for all x in Domf, f(x) >= u(x) where u is the understimator)

because otherwise the understimator may miss the global optimum during the branch and bound process.

**Can the solver still converge even if the relaxation is not an understimator**?

Is there essentially a difference? Which one is optimal or low complexity ? is here a relation with the rank?

I have been reading about performing sensitivity analysis of the solution of Linear Programming problem (calculating shadow prices, reduced costs and intervals within which the basic solution remains valid). It is clearly described on academical problems with 2 or 3 variables, but in fact, when tried to apply the same logic for real-life, scalable problem, I didn't get promising results. This is because only a few of variables values matters for me, while other are rather placed for another purposes (like changing hard constraints to soft ones etc). But all of them are taken into account when checking if basic solution has changed, hence the interval that is returned by a solver is a way more narrow than I want it to be.

Where can I find an example of real applied sensitivity analysis, if there is any?

Hi,

In minimizing the difference between two variables inside an absolute term e.g., Min |a-b| . How to make the term linear so that can be solved by LP or MILP . Where a and b are free integer variable (they take positive and negative values).

Please give their appropriate cases.

The constraints include both linear constraints and nonlinear constraints. The essential issue lies in to how to deal with the nonlinear constraints.

It would be better if this algorithm can transform these nonlinear constraints into the equivalent linear ones.

Being Scandinavian I have read and seen countless of times some representation of the children's story about the emperor's new clothes - by Hans Christian Andersen.

As you might know the emperor's new costume is soooo fine that it is weightless, and no-one - but a child - dares to speak up to the emperor and exclaim that he in fact is naked! Thanks to the child, the curtain opens, and we truly see that he indeed is naked.

I find metaheuristics - to some degree - to be that, too, within the mathematical optimization domain: quite shallow, devoid of solid theory, and often (but not always) a game of draw, guess, and jump (I do not know the exact English translation of the name of the children's game). I have no problem with it when we are dealing with very complicated combinatorial/integer/bilevel problems in

**industry**, especially when we do not have an explicit formulation, such as when we need to deal with the use of simulations within the optimization, or uncertain coefficients. But then we are talking about industrial mathematics, which is something else than mathematics - which is an exact science.The theme of metaheuristics was, I hope, originally an attempt to find "reasonable" (however that is defined) feasible solutions to the most difficult and large problems, especially for nonlinear integer models in industry, with the explicit sign that with these techniques we might hope get a

**fairly good**solution if we are lucky, or we may**not**- as that is actually how it works: metaheuristics are NOT globally convergent in general, and they were - make a mental note of this - NOT EVEN CONSTRUCTED TO BE.Yet there are plenty of scholars - especially in this forum, for a reason I do not fully understand - that insist on applying their favourite metaheuristic(s) on just anything. Yesterday I think it was when I at RG found a paper on a metaheuristic used to "solve" a very, very simple linear program with one (1) linear constraint. I blew my top, as they say. WTF is going on? I blew my top because I know how to solve to guaranteed optimality such a problem in under a 1/1000 of a second on a slow computer. It's a problem of complexity O(n) - hence the easiest problem on this planet.

Can any sane person closer to that field address this, please? It is irrational, to begin with; or it is simply the fact that the world of scientific endeavours no longer are defined by codes of conduct? I am really troubled by more and more often seeing this unscientific methodology being used, and I sure hope it never will be seriously compared with mathematical optimization. Well, in fact, it is compared every day in industry, and math always wins.

Dear colleagues,

I would like to know of applications of fuzzy (and fully fuzzy) linear programming in optimal control.

Thank you.

I want to blend phosphate ore. Please consult the attached form.

For example:

max -1/3x

_{1}+x_{2}subject to 1) -x

_{1}+x_{2}<=-0.5 2) -0.5x

_{1}+x_{2}=0.5 3) 0.5x

_{1}+x_{2}<=1.5In Matrix form

A=[-1 1; -0.5 1; 0.5 1]; b=[-0.5; 0.5; 1.5]; so A*x<=b

In this case constraint number 2) is not needed. The solution will be the same when inequality number 2) is omitted.

In my problem the size of the A matrix is 264x100. Is there a way to find out which constraints or inequalities are not needed?

Basically a way to find unnecessary inequalities for defining a problem?

I have a project about operatios research. In my case I have several-vary vehicles but one source and one target. Vehicles have const and they must assign some areas. Like vehicle 1 must carry a type product , vehicle 2 must carry b type product etc.. But all products stored same place. I can not find problem type for this case.

Hi,

I am interested in techniques that can prove that an integer linear program has no solutions. I am just looking at feasibility and have no objective function to maximize etc.

This is part of the best known algorithm for calculation optimal addition chains. The system I want to check for infeasibility is quite simple. It's just the Frobenius diophantine equation with an upper bound on the variables.

$\sum_{i=1}^{z}a_{i}x_{i}=n$

With $1\leq x_{i}\leq u$. $a_i$ and $n$ are constants determined by a partial search for an addition chains.

The code that uses this will try to solve billions of small problems like this.

I currently use branch and bound to try and prove there are no solutions or reject the few there are with additional problem constraints.

Mixed-Integer Linear Programming,

Exact algorithm

An optimization problem must be expressed mathematically with the least number of variables or the mathematical formulation that allows to demonstrate its optimal solution, however it requires to increase the number of variables. How should it be expressed?