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Transportation and assignment problems with r.

In the previous post “ Linear Programming with R ” we examined the approach to solve general linear programming problems with “Rglpk” and “lpSolve” packages. Today, let’s explore “lpSolve” package in depth with two specific problems of linear programming: transportation and assignment.

1. Transportation problem

unbalanced transportation problem in r

Code & Output:

The solution is shown as lptrans$solution and the total cost is 20500 as lptrans$objval.

2. Assignment problem

unbalanced transportation problem in r

Similarly, the solution and the total cost are shown as lpassign$solution and lpassign$objval respectively.

guest

This article was really helpful, but I am facing issue while solving unbalanced transportation problem when there is excess demand. Could you please guide me on what has to be done in this case.

Bakula Venroo

Hello sir, this article was really helpful. But, I am facing issue while solving unbalanced transportation problem when there is excess demand, it gives solution as no feasible solution. works perfectly fine for balanced and excess supply problems. Could you please guide me on why this issue is occurring and a possible solution for the same. Thank you.

SCDA

  • Linear programming

Solving linear transport problem with lp.transport in R, using lpSolve

  • Linnart Felkl

unbalanced transportation problem in r

The transportation problem is one of the classical problems teached in linear programming classes. The problem, put simply, states that a given set of customers with a specified demand must be satisfied by another set of supplier with certain capacities (“supply”). For a detailed explanation of the transportation problem you can, e.g. read this:  https://econweb.ucsd.edu/~jsobel/172aw02/notes8.pdf .

The lpSolve package available in R can be used for modelling and solving the transportation problem.

I will show how to do this. I define a problem in which 3 suppliers seek to satisfy 4 customers. The suppliers have capacities 100, 300, and 400, respectively. The customers have demand 100, 100, 200, and 400, respectively. Furthermore, the cost for supplying customer i by supplier j is defined for every possible combination and stated in a cost matrix.

Using this information we can model and solve the transportation problem (deciding which demand to fulfill by which supplier) with the lpSolve package in R.

First, I prepare the modeling-part:

Then, I solve the problem:

Let us review the “optimal” costs:

Let us review the optimal solution of the transportation problem (i.e., the optimal material flows to this problem):

The assignment problem is another classical problem, and you can see how I solved it in R here: Cost minimal production scheduling – solving the assignment problem with lpSolve, using lp.assign.

unbalanced transportation problem in r

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hi. I am trying to “go to the next level”. I want to look deeper than this and say, “OK, truck A costs me $100 and takes 3 weeks, but flight A costs me $200 and takes just 1 week to move the good” For me, i am still trying to move things from A to B, but now i am expanding it to try and look at the total cost of holding the inventory, reduction in cash flow and the cost of delivery. I want to “optimise” my transportation so that maybe 90% of my forecast is shipped via truck, then i can “top up” with the flight if demand requires. Any suggestions how to approach this issue or where to turn for some guidance? Thanks

thanks for your comment.

You can try to formulate your problem as a linear optimization problem, from scratch. For example, the cost of holding inventory can be derived from the travel time, and the travel time depends on transportation distance (one variable) and transportation mode (binary or integer variable).

The objective of covering 90% of your forecast by truck could be formulated as a constraint, or maybe a better approach would be to define two objective functions, and to apply multi-goal linear programming.

If you provide some more info I might very well try to model it and post it, maybe in a simplified version!

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Transportation Problem | Set 5 ( Unbalanced )

An introduction to the transportation problem has been discussed in

article. In this article, the method to solve the unbalanced transportation problem will be discussed. Below transportation problem is an unbalanced transportation problem.

unbalanced transportation problem in r

The problem is unbalanced because the sum of all the supplies i.e.

is not equal to the sum of all the demands i.e.

In this type of problem, the concept of a dummy row or a dummy column will be used. As in this case, since the supply is more than the demand so a dummy demand column will be added and a demand of (total supply – total demand) will be given to that column i.e.

117 – 95 = 22

as shown in the image below. If demand were more than the supply then a dummy supply row would have been added.

unbalanced transportation problem in r

Now that the problem has been updated to a balanced transportation problem, it can be solved using any one of the following methods to solve a balanced transportation problem as discussed in the earlier posts:

  • NorthWest Corner Method
  • Least Cost Cell Method
  • Vogel’s Approximation Method

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Class imbalance-handling imbalanced data in r.

Posted on May 6, 2021 by finnstats in R bloggers | 0 Comments

[social4i size="small" align="align-left"] --> [This article was first published on Methods – finnstats , and kindly contributed to R-bloggers ]. (You can report issue about the content on this page here ) Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

Class Imbalance classification refers to a classification predictive modeling problem where the number of observations in the training dataset for each class is not balanced.

In other words, the class distribution is not equal or close and it is skewed into one particular class. So, the prediction model will be accurate for skewed classes and we want to predict another class then the existing model won’t be appropriate.

The imbalance problems may be due to biased sampling methods or may be due to some measurement errors or unavailability of the classes.

Let’s look at one of the datasets and how to handle the same in R.

Stock prediction in R

Load Library

Getting data.

The dataset you can access from here . Total 400 observations and 4 variables contains in the dataset.

Let’s convert the admit variable into factor variable for further analysis.

Based on summary data 273 observations pertaining to not admitted and 127 observations pertained to students admitted in the program.

Paired t test tabled value vs p value

Class Imbalance

unbalanced transportation problem in r

Based on the plot it clearly evident that 70% of the data in one class and the remaining 30% in another class.

So big difference observed in the amount of data available. If we are making a model based on these a dataset accuracy predicting students not admitted will be higher compared to students who are admitted.

Data Partition

Lets partition the dataset into train dataset and test dataset based on set.seed.

Predictive Model Data

Let create a model based on the training dataset and look at the classification in the training dataset.

You can see that 188 observations in class 0 and 97 observations in class 1.

Discriminant analysis in R

Based on proportion table 65% in one class and 34% in another class.

Predictive Model

The Random Forest model is using for prediction purposes.

Predictive Model Evaluation with test data

Let’s cross-validate based on test data. In this case, we are mentioning positive=1.

Confusion Matrix and Statistics

Now you can see that model is around 66% and based on 95% confidence interval accuracy is lies between 57 & to 75%.

How to do data reshape in R?

Sensitivity also is around only 30%, we can clearly mention that one of the classes is dominated over another class. Suppose if you’re interested in zero class then this model is quite a good one and if you want to predict class 1 then need to improvise the model.

Over Sampling

This is based on resampling and now both the classes are equal.

Random Forest Model

Rank order analysis in R

Now the accuracy is 60% and sensitivity is increased to 50%. Suppose our interest is predicting class 1 this model is much better than the previous one.

Under Sampling

Instead of using all observations will take relevant observations from class zero respected to class1.

Suppose class 1 contain97 observations we need to take only 97 observations from class 0.

Now you can see that accuracy reduced by 58% and sensitivity increased to 63%.

Under-sampling is not suggested because the number of data points less in our model and reduces the overall accuracy.

How to integrate SharePoint & R

Both (Over & Under)

This table is not exactly equal but similar to original situation class1 is higher than class 0.

Model accuracy is 53% and sensitivity is 70%.

Now sensitivity is increased into 70% compared to previous model.

Naïve Bayes Classification in R

ROSE Function

When we do rose function closely watch the minimum and maximum values of each variable.

Recollect when we created summary based on original data gre maximum value is 800 based on the rose function it’s increased into 887.

This won’t make any changes in the model but we need-aware about these changes and we can make use of this function for further analysis.

LSTM Networks in R

Based on this model accuracy is come down and sensitivity also reduced in this model.

But some other data set models can perform better. For getting repetitive results every time you can make use of seed function everywhere.

Conclusions.

Sensitivity is always closer to 100 is better, this is the way we can handle class imbalance problems efficiently & smartly.

Decision Trees in R

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ANOTHER APPROACH OF SOLVING UNBALANCED TRANSPORTATION PROBLEM

Profile image of Yashesh Zaveri

Solution of any Transportation Problem (TP) necessitates Initial Basic Feasible Solution (IBFS) to get optimal schedule of shipment of goods. The better the initial solution is, less computational efforts and less time is required to generate optimal solution. One of the most powerful methods to determine IBFS is Vogel’s Approximation Method (VAM) among many other methods available in the vast literature of TP. Very few literature are available on handling unbalanced TP using VAM. Initial solution of unbalanced TP is very much based on how VAM process ‘ZERO’ in the dummy cells. For this purpose we have presented another approach of getting IBFS of unbalanced TP using VAM and to test efficiency of proposed heuristic with the existing methods for the same VAM and VAM-Total Opportunity Cost (TOC).

Related Papers

Seyed Mohamed Buhari

unbalanced transportation problem in r

Journal of Supply Chain Management System

Publishing India Group

For any manufacturing firm, transportation cost could be a considerable part of the logistics cost. This along with the mounting fuel cost is ultimately passed on to the customers. With rising competition, firms are forced to find out methods of optimising the transportation cost thereby reducing the total cost. There are many methods available in solving a transportation method. However, the traditional Vogel's approximation method has many drawbacks when dealing with situations where the supply and demand are unbalanced. This study examines the effectiveness of using the modified Vogel's method when compared to the traditional approach with the help of a case study. The study found that the use of the proposed method will bring in considerable cost reduction in transportation thereby increasing the profitability of the firm. Moreover the proposed method is easy to implement and will be highly beneficial for the decision makers.

International Journal of Advanced Research in Computer Science

Surjit Paul

ashwin suryavanshee

This paper presents a comparative study of various methods of obtaining Initial Basic Feasible Solution (IBFS) to Unbalanced Transportation Problem viz., NWCR, Matrix-minima method (least cost method), VAM, VAMT-TOC, and method given by Kirca-Satir(1990)) with our Cost-Sum method using statistical experimental design. The measure of the quality and the effectiveness for comparison of these methods are average relative deviation and the number of iterations to reach the optimality. It is also presented that how many instances gives the IBFS≡ OBFS cost which proves the superiority of Cost-Sum method as compared to other methods.

International Journal of Industrial and Systems Engineering

Jihene Kaabi

International Journal of Engineering Research and Technology (IJERT)

IJERT Journal

https://www.ijert.org/advanced-vogels-approximation-method-avam-a-new-approach-to-determine-penalty-cost-for-better-feasible-solution-of-transportation-problem https://www.ijert.org/research/advanced-vogels-approximation-method-avam-a-new-approach-to-determine-penalty-cost-for-better-feasible-solution-of-transportation-problem-IJERTV3IS10120.pdf In Operation Research, obtaining significant result for Transportation Problems is very important now-a-days. Vogel's Approximation Method (VAM) is the very efficient algorithm to solve the transportation problem for feasible solution which is nearer to optimal solution. In this paper we identified a computational error in VAM and approach a logical development of VAM algorithm. The main concept of VAM is to determine penalty cost which obtains from the difference of smallest and next to smallest cost in each row or column and make maximum allocation in lowest cost cell of that row or column which have largest penalty. The difficulty arises when smallest cost and next to smallest cost have same magnitude. In that case we find a very logical concept to resolve this and developed a new algorithm "Advanced Vogel's Approximation Method (AVAM)" to find a feasible solution of transportation problem which is very close to optimal solution more than VAM.

American Scientific Research Journal for Engineering, Technology, and Sciences

Thomas Ugbe

A modified Vogel Approximation Method is proposed and compared with those of the existing methods available for solving balanced transportation problems (in linear programming) for Basic Feasible Solutions (IBFS). The method is shown to be better than existing ones (excluding Vogel Approximation Method) since it does not only considers each unit cost in its solution algorithm, but also minimises total cost (comparatively) just like Vogel Approximation Method.

Md. Ashraful Babu

In Operation Research, obtaining significant result for Transportation Problems is very important now-a-days. Vogel’s Approximation Method (VAM) is the very efficient algorithm to solve the transportation problem for feasible solution which is nearer to optimal solution. In this paper we identified a computational error in VAM and approach a logical development of VAM algorithm. The main concept of VAM is to determine penalty cost which obtains from the difference of smallest and next to smallest cost in each row or column and make maximum allocation in lowest cost cell of that row or column which have largest penalty. The difficulty arises when smallest cost and next to smallest cost have same magnitude. In that case we find a very logical concept to resolve this and developed a new algorithm “Advanced Vogel’s Approximation Method (AVAM)” to find a feasible solution of transportation problem which is very close to optimal solution more than VAM.

Chowdhury Kibria

Transportation modeling is a technique that is used to way out the shipping of supplies from a number of sources to a number of destinations as well as to minimize the total shipment cost. This kind of problem is known as transportation problem (TP). Solution procedure of TP plays a vital role in operation research for its wide application in real world. In the solution procedure of a TP, finding an initial basic feasible solution (IBFS) is necessary to obtain the optimal solution. Least Cost Method (LCM) is one such procedure which is based on cost cells. This solution procedure starts with allocating as much shipments as possible to the cell with the smallest unit cost cell. In this paper we propose an effective improvement of LCM in the solution procedure to obtain a better IBFS for the TPs. To verify the performance of the proposed method, a comparative study is also carried out. Simulation results show that Improved Least Cost Method (iLCM) yields better IBFS in 80% cases than LCM.

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transport Computation of Optimal Transport Plans and Wasserstein Distances

  • Package overview
  • aha: Solve Transportation Problem by Aurenhammer-Hoffmann-Aronov...
  • all.equal: Methods for Judging Near Equality of Objects of Class pgrid,...
  • compatible: Test whether Two Objects are Compatible
  • matimage: Plotting Matrices as Images
  • methods: Print and Summary Methods for Objects of Class pgrid, pp and...
  • pgrid: Constructor for the pgrid Class
  • pgrid-object: Class of Pixel Grids
  • plot: Methods for Plotting Objects of Class pgrid, pp and wpp
  • plot_apollonius: Plot Apollonius Diagram
  • plot.ubtrans: Plot Unbalanced Transport Information
  • power_diagram: Compute the Power Diagram of Weighted Sites in 2-Dimensional...
  • pp: Constructor for the pp Class
  • pp-object: Class of (Unweighted) Point Patterns
  • random: Images to Illustrate the Use of transport.pgrid
  • ret_message: Return Text Strings for lbfgs Return Codes
  • semidiscrete: Find Optimal Transport Partition Between pgrid and wpp.
  • semidiscrete1: Compute Semidiscrete Optimal Transport for Euclidean Distance...
  • shielding: Compute Optimal Transport (Cost/Plan) Using the Multiscale...
  • starting_solutions: Compute starting solution for the transportation problem
  • subwasserstein: Approximate Computation of Wasserstein Distances via...
  • transport: Find Optimal Transport Plan Between Two Objects
  • transport-internal: Internal Functions in Package 'transport'
  • transport-package: Optimal Transport in Various Forms
  • transport_track: Create a Dynamic Visualization of a Transference Plan Between...
  • trcontrol: Set the Control Parameters Used by 'transport'.
  • unbalanced: Unbalanced Optimal Transport between pgrid Objects
  • wasserstein: Compute the Wasserstein Distance Between Two Objects
  • wasserstein1d: Compute the Wasserstein Distance Between Two Univariate...
  • wpp: Constructor for the wpp Class
  • wpp-object: Class of Weighted Point Patterns
  • Browse all...

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UNBALANCED TRANSPORTATION PROBLEM

Unbalanced transportation problem is a transportation problem where the total availability at the origins is not equal to the total requirements at the destinations. For example, in case the total production of 4 factories is 1000 units and total requirements of 4 warehouses is 900 units or 1,100 units, the transportation problem is said to be an unbalanced one. To make an unbalanced transportation problem, a balanced one, a dummy origin(s) or a dummy destination (s) (as the case may be) is introduced with zero transportation cost per unit.

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unbalanced transportation problem in r

Balanced and Unbalanced Transportation Problems

The two categories of transportation problems are balanced and unbalanced transportation problems . As we all know, a transportation problem is a type of Linear Programming Problem (LPP) in which items are carried from a set of sources to a set of destinations based on the supply and demand of the sources and destinations, with the goal of minimizing the total transportation cost. It is also known as the Hitchcock problem.

Introduction to Balanced and Unbalanced Transportation Problems

Balanced transportation problem.

The problem is considered to be a balanced transportation problem when both supplies and demands are equal.

Unbalanced Transportation Problem

Unbalanced transportation problem is defined as a situation in which supply and demand are not equal. A dummy row or a dummy column is added to this type of problem, depending on the necessity, to make it a balanced problem. The problem can then be addressed in the same way as the balanced problem.

Methods of Solving Transportation Problems

There are three ways for determining the initial basic feasible solution. They are

1. NorthWest Corner Cell Method.

2. Vogel’s Approximation Method (VAM).

3. Least Call Cell Method.

The following is the basic framework of the balanced transportation problem:

Basic Structure of Balanced Transportation Problem

The destinations D1, D2, D3, and D4 in the above table are where the products/goods will be transported from various sources O1, O2, O3, and O4. The supply from the source Oi is represented by S i . The demand for the destination Dj is d j . If a product is delivered from source Si to destination Dj, then the cost is called C ij .

Let us now explore the process of solving the balanced transportation problem using one of the ways known as the NorthWest Corner Method in this article.

Solving Balanced Transportation problem by Northwest Corner Method

Consider this scenario:

Balanced Transportation Problem -1

With three sources (O1, O2, and O3) and four destinations (D1, D2, D3, and D4), what is the best way to solve this problem? The supply for the sources O1, O2, and O3 are 300, 400, and 500, respectively. Demands for the destination D1, D2, D3, and D4 are 250, 350, 400, and 200, respectively.

The starting point for the North West Corner technique is (O1, D1), which is the table’s northwest corner. The cost of transportation is calculated for each value in the cell. As indicated in the diagram, compare the demand for column D1 with the supply from source O1 and assign a minimum of two to the cell (O1, D1).

Column D1’s demand has been met, hence the entire column will be canceled. The supply from the source O1 is still 300 – 250 = 50.

Balanced Transportation Problem - 2

Analyze the northwest corner, i.e. (O1, D2), of the remaining table, excluding column D1, and assign the lowest among the supply for the appropriate column and rows. Because the supply from O1 is 50 and the demand for D2 is 350, allocate 50 to the cell (O1, D2).

Now, row O1 is canceled because the supply from row O1 has been completed. Hence, the demand for Column D2 has become 350 – 50 = 50.

Balanced Transportation Problem - 3

The northwest corner cell in the remaining table is (O2, D2). The shortest supply from source O2 (400) and the demand for column D2 (300) is 300, thus putting 300 in the cell (O2, D2). Because the demand for column D2 has been met, the column can be deleted, and the remaining supply from source O2 is 400 – 300 = 100.

Balanced Transportation Problem - 4

Again, find the northwest corner of the table, i.e. (O2, D3), and compare the O2 supply (i.e. 100) to the D2 demand (i.e. 400) and assign the smaller (i.e. 100) to the cell (O2, D2). Row O2 has been canceled because the supply from O2 has been completed. Column D3 has a leftover demand of 400 – 100 = 300.

Balanced Transportation Problem -5

Continuing in the same manner, the final cell values will be:

Balanced Transportation Problem - 6

It should be observed that the demand for the relevant columns and rows is equal in the last remaining cell, which was cell (O3, D4). In this situation, the supply from O3 was 200, and the demand for D4 was 200, therefore this cell was assigned to it. Nothing was left for any row or column at the end.

To achieve the basic solution, multiply the allotted value by the respective cell value (i.e. the cost) and add them all together.

I.e., (250 × 3) + (50 × 1) + (300 × 6) + (100 × 5) + (300 × 3) + (200 × 2) = 4400.

Solving Unbalanced Transportation Problem

An unbalanced transportation problem is provided below. Because the sum of all the supplies, O1, O2, O3, and O4, does not equal the sum of all the demands, D1, D2, D3, D4, and D5, the situation is unbalanced.

Unbalanced Transportation Problem - 1

The idea of a dummy row or dummy column will be applied in this type of scenario. Because the supply is more than the demand in this situation, a fake demand column will be inserted, with a demand of (total supply – total demand), i.e. 117 – 95 = 22, as seen in the image below. A fake supply row would have been introduced if demand was greater than supply.

Unbalanced Transportation Problem - 2

Now this problem has been changed to a balanced transportation problem, and it can be addressed using any of the ways listed below to solve a balanced transportation problem, such as the northwest corner method mentioned earlier.

Frequently Asked Questions on Balanced and Unbalanced Transportation Problems

What is meant by balanced and unbalanced transportation problems.

The problem is referred to as a balanced transportation problem when both supplies and demands are equal. Unbalanced transportation is defined as a situation where supply and demand are not equal.

What is called a transportation problem?

The transportation problem is a type of Linear Programming Problem in which commodities are carried from a set of sources to a set of destinations while taking into account the supply and demand of the sources and destinations, respectively, in order to reduce the total cost of transportation.

What are the different methods to solve transportation problems?

The following are three approaches to solve the transportation issue:

  • NorthWest Corner Cell Method.
  • Least Call Cell Method.
  • Vogel’s Approximation Method (VAM).

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Unbalanced Transportation Problem

So far we have assumed that the total supply at the origins is equal to the total requirement at the destinations.

Specifically,

But in certain situations, the total supply is not equal to the total demand. Thus, the transportation problem with unequal supply and demand is said to be unbalanced transportation problem .

How to solve?

If the total supply is more than the total demand, we introduce an additional column, which will indicate the surplus supply with transportation cost zero. Similarly, if the total demand is more than the total supply, an additional row is introduced in the table, which represents unsatisfied demand with transportation cost zero. The balancing of an unbalanced transportation problem is illustrated in the following example.

Example of Unbalanced Transportation Problem

The total demand is 1000, whereas the total supply is 800.

Total supply < total demand.

To solve the problem, we introduce an additional row with transportation cost zero indicating the unsatisfied demand.

Using matrix minimum method , we get the following allocations.

Use Horizontal Scrollbar to View Full Table Calculation.

Initial basic feasible solution

50 X 28 + 450 X 26 + 250 X 12 + 50 X 16 + 200 X 0 = 16900.

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Understanding Unbalanced Transportation Problem: Definition, Methods, and Applications

Table of Contents

If you are an Operations Research student, you may already know what a transportation problem is. But have you ever heard of the unbalanced transportation problem? In this blog, we will explore this special case of transportation problem, its definition, methods to solve it, and real-world applications.

What is the Unbalanced Transportation Problem?

In a regular transportation problem, the total supply is equal to the total demand. However, in the unbalanced transportation problem, the supply and demand are not equal. This can happen when the production capacity of a factory is greater or lesser than the demand for its products. It can also happen when the cost of transportation varies for different sources and destinations.

The unbalanced transportation problem is typically solved by adding a dummy source or dummy destination to balance the supply and demand. The dummy source represents an artificial supply, and the dummy destination represents an artificial demand.

Types of Unbalanced Transportation Problems

There are two types of unbalanced transportation problems:

  • Under-supply problem: This is when the total supply is less than the total demand. In other words, there is not enough supply to meet the demand.
  • Over-supply problem: This is when the total supply is more than the total demand. In this case, there is too much supply and not enough demand.

Solutions to Unbalanced Transportation Problems

To solve unbalanced transportation problems, we can use several methods, including:

Dummy Source or Dummy Destination Method

In this method, we add a dummy source or dummy destination to balance the supply and demand. For example, in an under-supply problem, we can add a dummy source with a supply equal to the difference between the total demand and total supply.

Proportional Distribution Method

In this method, we distribute the transportation costs proportionally based on the actual supply and demand. For example, in an under-supply problem, we can calculate the percentage of each demand point and allocate the transportation cost accordingly.

Transportation Algorithm Method

In this method, we use the transportation algorithm to solve the problem. First, we add a dummy source or destination to balance the problem. Then, we apply the transportation algorithm to find the optimal solution.

Applications of the Unbalanced Transportation Problem

The unbalanced transportation problem can arise in many real-world situations. For example, a company may have excess inventory in one location and a shortage in another. By using the unbalanced transportation problem, the company can determine the most efficient way to transfer the excess inventory to the location with a shortage.

Another application is in the field of agriculture. Farmers may have more produce than they can sell locally, but there may be a shortage of that same produce in other regions. By using the unbalanced transportation problem, farmers can determine the most efficient way to transport their produce to regions with a shortage.

The unbalanced transportation problem is a special case of the transportation problem that arises when the supply and demand are not equal. By adding dummy sources or dummy destinations, this problem can be solved using similar methods to those used to solve the balanced transportation problem. The unbalanced transportation problem has many real-world applications, including inventory management and agriculture. By understanding this problem, Operations Research students can gain a deeper understanding of the transportation problem and its practical applications.

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Operations Research

1 Operations Research-An Overview

  • History of O.R.
  • Approach, Techniques and Tools
  • Phases and Processes of O.R. Study
  • Typical Applications of O.R
  • Limitations of Operations Research
  • Models in Operations Research
  • O.R. in real world

2 Linear Programming: Formulation and Graphical Method

  • General formulation of Linear Programming Problem
  • Optimisation Models
  • Basics of Graphic Method
  • Important steps to draw graph
  • Multiple, Unbounded Solution and Infeasible Problems
  • Solving Linear Programming Graphically Using Computer
  • Application of Linear Programming in Business and Industry

3 Linear Programming-Simplex Method

  • Principle of Simplex Method
  • Computational aspect of Simplex Method
  • Simplex Method with several Decision Variables
  • Two Phase and M-method
  • Multiple Solution, Unbounded Solution and Infeasible Problem
  • Sensitivity Analysis
  • Dual Linear Programming Problem

4 Transportation Problem

  • Basic Feasible Solution of a Transportation Problem
  • Modified Distribution Method
  • Stepping Stone Method
  • Unbalanced Transportation Problem
  • Degenerate Transportation Problem
  • Transhipment Problem
  • Maximisation in a Transportation Problem

5 Assignment Problem

  • Solution of the Assignment Problem
  • Unbalanced Assignment Problem
  • Problem with some Infeasible Assignments
  • Maximisation in an Assignment Problem
  • Crew Assignment Problem

6 Application of Excel Solver to Solve LPP

  • Building Excel model for solving LP: An Illustrative Example

7 Goal Programming

  • Concepts of goal programming
  • Goal programming model formulation
  • Graphical method of goal programming
  • The simplex method of goal programming
  • Using Excel Solver to Solve Goal Programming Models
  • Application areas of goal programming

8 Integer Programming

  • Some Integer Programming Formulation Techniques
  • Binary Representation of General Integer Variables
  • Unimodularity
  • Cutting Plane Method
  • Branch and Bound Method
  • Solver Solution

9 Dynamic Programming

  • Dynamic Programming Methodology: An Example
  • Definitions and Notations
  • Dynamic Programming Applications

10 Non-Linear Programming

  • Solution of a Non-linear Programming Problem
  • Convex and Concave Functions
  • Kuhn-Tucker Conditions for Constrained Optimisation
  • Quadratic Programming
  • Separable Programming
  • NLP Models with Solver

11 Introduction to game theory and its Applications

  • Important terms in Game Theory
  • Saddle points
  • Mixed strategies: Games without saddle points
  • 2 x n games
  • Exploiting an opponent’s mistakes

12 Monte Carlo Simulation

  • Reasons for using simulation
  • Monte Carlo simulation
  • Limitations of simulation
  • Steps in the simulation process
  • Some practical applications of simulation
  • Two typical examples of hand-computed simulation
  • Computer simulation

13 Queueing Models

  • Characteristics of a queueing model
  • Notations and Symbols
  • Statistical methods in queueing
  • The M/M/I System
  • The M/M/C System
  • The M/Ek/I System
  • Decision problems in queueing

Balanced and Unbalanced Transportation Problem | Operations Research

unbalanced transportation problem in r

After reading this article you will learn about balanced and unbalanced transportation problem.

Balanced Transportation Problem:

For a transportation problem:

unbalanced transportation problem in r

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COMMENTS

  1. Operations Research with R

    Unbalanced Transportation Problems: cases where the total supply is not equal to the total demand. When the supply is higher than the demand, a dummy destination is introduced in the equation to make it equal to the supply (with shipping costs of $0); the excess supply is assumed to go to inventory.

  2. Transportation and Assignment problems with R

    1 2 lp.transport(cost.mat, direction="min", row.signs, row.rhs, col.signs, col.rhs, presolve=0, compute.sens=0, integers = 1: (nc*nr)) Code & Output: The solution is shown as lptrans$solution and the total cost is 20500 as lptrans$objval. 2. Assignment problem Assignment problem, Frederick & Mark (2014, p.99) Usage: 1

  3. Efficient Transportation Planning using R: Solving ...

    The transportation problem has several variations, such as the unbalanced transportation problem, where the total supply is not equal to the total demand, and the capacitated...

  4. Solving linear transport problem with lp.transport in R, using ...

    The problem, put simply, states that a given set of customers with a specified demand must be satisfied by another set of supplier with certain capacities ("supply"). For a detailed explanation of the transportation problem you can, e.g. read this: https://econweb.ucsd.edu/~jsobel/172aw02/notes8.pdf.

  5. Transportation Problem

    The problem is unbalanced because the sum of all the supplies i.e. O1 , O2 , O3 and O4 is not equal to the sum of all the demands i.e. D1 , D2 , D3 , D4 and D5 . Solution: In this type of problem, the concept of a dummy row or a dummy column will be used.

  6. Class Imbalance-Handling Imbalanced Data in R

    ShareTweet. Class Imbalance classification refers to a classification predictive modeling problem where the number of observations in the training dataset for each class is not balanced. In other words, the class distribution is not equal or close and it is skewed into one particular class. So, the prediction model will be accurate for skewed ...

  7. Solving the Transportation Problem

    The transportation problem is a type of linear programming problem designed to minimize the cost of distributing a product from M M sources to N N destinations. The transportation problem can be described using examples from many fields. One application is the problem of efficiently moving troops from bases to battleground locations.

  8. Another Approach of Solving Unbalanced Transportation Problem

    Summary Results Table - 12 clearly shows that, for unbalanced Transportation Problem, applying VAM-R is more efficient than original VAM and VAM-TOC heuristics in terms of percentage of best solutions and average number of iterations required to reach optimal solution. 5 REFERENCES 1. S. D.

  9. transport source: R/unbalanced.R

    aha: Solve Transportation Problem by Aurenhammer-Hoffmann-Aronov... all.equal: Methods for Judging Near Equality of Objects of Class pgrid,... compatible: Test whether Two Objects are Compatible matimage: Plotting Matrices as Images methods: Print and Summary Methods for Objects of Class pgrid, pp and... pgrid: Constructor for the pgrid Class pgrid-object: Class of Pixel Grids

  10. Unbalanced Transportation Problem

    UNBALANCED TRANSPORTATION PROBLEM. Unbalanced transportation problem is a transportation problem where the total availability at the origins is not equal to the total requirements at the destinations. For example, in case the total production of 4 factories is 1000 units and total requirements of 4 warehouses is 900 units or 1,100 units, the ...

  11. Transportation problems and their solutions: literature review

    The transportation problem is a classic problem in operations research that involves finding the optimal way to move goods from one place to another. With the increase of globalization and the development of complex distribution networks, the transportation problem has become increasingly important in the field of operations research. This ...

  12. matrix

    I'm trying to set up a linear program on how a commodity will move between states. I'm working with R studio, using the lpSolve package. I'm very new to R so excuse the basic language! But I've looked through the help files and can't seem to work out what the problem is. States are both "suppliers" (m) and "demanders" (n). I want a matrix of ...

  13. PDF A new approach to solve unbalanced transportation problems in imprecise

    In this paper, a method is proposed for solving unbalanced fully fuzzy transportation problems. The fuzzy optimal solution, obtained by the proposed method, is in terms of the original sources only and total demand is also satisfied. From the fuzzy optimal solution obtained it can be found that the availability of which source should be increased.

  14. PDF A New Approach for Solving Unbalanced Fuzzy Transportation Problem

    A fuzzy number . A. is said to be non-negative fuzzy number if and only ( ) 0, 0. A xx 2.4 Definition. A fuzzy number . in R is said to be a triangular fuzzy number if its membership

  15. Imbalanced Classification Problems in R

    Therefore, an imbalanced classification problem is one in which the dependent variable has imbalanced proportion of classes. In other words, a data set that exhibits an unequal distribution between its classes is considered to be imbalanced. For example: Consider a data set with 100,000 observations.

  16. PDF Method for Solving Unbalanced Transportation Problems Using Standard

    The unbalanced transportation problem is a particular class of transportation problem, which is associated with day-to-day activities in our real life and mainly deals with logistics. It helps in solving problems on distribution and transportation of resources from one place to another.

  17. Balanced and Unbalanced Transportation Problems

    Unbalanced transportation problem is defined as a situation in which supply and demand are not equal. A dummy row or a dummy column is added to this type of problem, depending on the necessity, to make it a balanced problem. The problem can then be addressed in the same way as the balanced problem. Methods of Solving Transportation Problems

  18. Unbalanced Transportation Problem, Examples

    The total demand is 1000, whereas the total supply is 800. Total supply < total demand. To solve the problem, we introduce an additional row with transportation cost zero indicating the unsatisfied demand. Using matrix minimum method, we get the following allocations. 50 X 28 + 450 X 26 + 250 X 12 + 50 X 16 + 200 X 0 = 16900.

  19. (PDF) A new approach to solve unbalanced transportation problems in

    Rani and Gulati [8, 9] proposed a new method to find the optimal solution for the unbalanced transportation problem whose parameters are imprecise. Saad and Abbas [10] gave a parametric study on ...

  20. Understanding Unbalanced Transportation Problem: Definition, Methods

    The unbalanced transportation problem is typically solved by adding a dummy source or dummy destination to balance the supply and demand. The dummy source represents an artificial supply, and the dummy destination represents an artificial demand. Types of Unbalanced Transportation Problems There are two types of unbalanced transportation problems:

  21. Transportation Problem Using R Programming

    #TransportationProblem #LinearProgramming #RProgramming* World's Premium Training Academy*Our comprehensive Learning management system is powering internatio...

  22. Balanced and Unbalanced Transportation Problems Explained

    An unbalanced transportation problem is a situation where the supply and demand are unequal. In such cases, a dummy row or column is added as needed to balance the problem. The problem can then be solved in the same way as a balanced problem. Crack UGC NET/SET Batch 2.0 with India's Best Teachers & Coachings.

  23. Balanced and Unbalanced Transportation Problem

    Unbalanced Transportation Problem: ADVERTISEMENTS: If in a transportation problem, the sum of supply available from all sources is not equal to the sum of demands of all destinations, i.e. the problem is said to be unbalanced transportation problem.