# Questions tagged [reduced-costs]

The tag has no usage guidance.

21 questions
Filter by
Sorted by
Tagged with
1 vote
73 views

### The dual values and change in the variables values

For a constraint as Ax <= b, the dual shows the change in the objective function if the RHS increases by 1 unit. Now my question is that how we can determine how the optimal values will change by 1 ...
125 views

### Can one strengthen the Lagrangian dual bound in column generation when there are multiple subproblems?

Consider a Linear Programme (LP) \begin{align} \min && \sum_{i \in I} c_i x_i \\ \text{s.t.} && \sum_{i \in I} a_{ij} x_i &\geq b_j & \quad & \forall j \in J \\ && ...
1 vote
375 views

### Sign of the reduced cost in LP

I'm new to operation research. I'm confusing about the sign of reduced cost and I have a few questions that I'd like to ask. Suppose that I solve a maximization problem, considering a variable x with ...
134 views

### Must the Newly Generated Column be used in RMP in the Column Generation Method?

When I used Column Generation, I found a column with reduced cost < 0, and added it to the Restricted Master Problem. Must the newly added column be used in the solution of RMP at once? If not, ...
146 views

### Reduced cost fixing for binary programs

Consider the binary program $$\min_{ x \in \{0,1\}^N } \left\{ c^T x \mid Ax \leq b \right\}$$ where $A$ and $b$ are real matrices with appropriate dimensions. I am interested in solving large binary ...
214 views

### Understanding reduced costs and dual values

I have a headache regarding calculating the reduced costs of a linear program. I am using Pulp for modelling and CBC for solving. What I do is, I model a linear programming problem based on a rhs ...
163 views

### How to calculate EOQ in this problem?

I am trying to solve a problem that requires I find the EOQ. This problem is from the book (translation from greek) Operational Research: Theory, Algorithms and Applications by authors Coletsos John &...
505 views

### Good references for reduced cost fixing?

Reduced cost fixing is a technique used by mixed integer programming (MIP) solvers to safely fix variables to certain values. While this technique is well-known among the MIP community, I don't know ...
286 views

### Inconsistent teachings on how to choose a non basic variable to enter the basis (primal simplex)

During the primal simplex algorithm, a non-basic variable must be chosen to enter the basis. Many resources on the subject choose a variable based solely on its coefficient in the row of the tableau ...
265 views

### Column generation: decreasing value of restricted master problem

I am using column generation to solve a minimization problem. At a given iteration, my subproblem finds a column with reduced cost $-1$, and in the following restricted master problem, this new column ...
1 vote
648 views

### How to obtain reduced cost in the graphical sensitivity analysis?

According to some tables in the book Operations Research by Hamdy Taha(7th edition), it seems that for a variable whose optimal value is zero, reduced cost can be evaluated by the following formulas: ...
5k views

### Interpretation of Reduced Costs

I am looking for an answer to a question I can't quite get behind. (continuation of Linear Programming: Integer and non-integer decision variables) I am given the following mathematical optimization ...
2k views

### What is the relation between dual variables and reduced costs?

My background: Pure math current Undergrad, learned the theory of Operations Research, but pretty basic. All we covered have been dealing with problems that have only 1 constraint matrix. I have dealt ...
695 views

### Minimizing cost of transportation and storage of items

I am looking for an optimization algorithm to minimize the cost of transportation and storage cost in warehouse. Let's assume the following table gives us the weekly forecast of Demand. ...
397 views

### Dual of a model to obtain reduced costs

I have the following model which I am going to solve with column generation. \begin{align} \max & \sum_{b \in B} \sum_{s \in S} \sum_{r \in \Omega_s}\beta_{bs}p_r y_{br}\label{objective-set1}\\ ...
145 views

### Simplex method on graphs: How do I find a basic solution using the Ford-Fulkerson algorithm?

I'm tasked with solving a minimal cost flow problem. I'm asked to first use the Ford-Fulkerson algorithm on my graph to find a basic solution that will then be used to do the simplex method on that ...
1 vote
148 views

### Expansion heuristic using gurobi reduced cost / shadow price (LP)

Gurobi 9.0.0 // C++ // LP Let us assume the following problem with three nodes: (1)-----(2)-----(3) node (1) is producing ...
201 views

### When using column generation, can I delete a node with negative reduced cost from my subproblem?

I am solving a minimization problem with a column generation procedure. The master problem is of the form $$\min \sum_{i\in \Omega}c_i \lambda_i$$ subject to  \sum_{i\in \Omega \mid v \in i } \...
156 views

### Preemptive Goal programming by fixing nonbasic variables with non-zero reduced costs

I have been using the method of fixing nonbasic variables with non-zero reduced costs to do preemptive goal programming. It works for the most part. But I have recently noticed in a certain instance ...
I am observing something unusual : after solving a linear program, some basic variables have negative reduced costs (instead of $0$) : ...
I had a number of students claim on their homework that "All $z_j-c_j$ values are positive, therefore the solution is optimal." Of course, I noted that they should say "non-negative" instead of "...