# Questions tagged [linear-programming]

For questions related to problems that optimize (i.e., minimize or maximize) a linear objective subject to linear constraints.

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### Condition for an integer program and its linear relaxation to have the same value

Let $A$ be a $(0,1)$-matrix where no row or column is a zero vector, and consider the following optimization programs \begin{align}(1):\min&\quad y\cdot1\\\text{s.t.}&\quad yA\ge w\\&\quad ...
198 views

### Why is the Lagrange Multiplier not equal the Shadow Price (Excel solver, Matlab linprog, Gurobi)?

I have a LP with equality and inequality constraints. When solving the LP with the excel-solver (GRG Nonlinear) the sensitivity report returns the lagrange multiplier for all constraints. When solving ...
99 views

### Modelling a data-sensitivity scenario as an ILP problem

I am new to linear programming, and I recently came across the following exercise, which I do not know how to solve: When publishing data, it is sometimes important to "suppress" sensitive ...
79 views

### Building the Scheurman's Model II constraints for a multi period linear program

Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also ...
80 views

### Can CPLEX output LP solution with primal variables only?

CPLEX writeSolution method outputs both primal and dual variable values of a LP. I know how to parse through the solution file to extract specific primal variable ...
154 views

### Linearize sum of continuous and boolean variable

For maximizing the objective function $\sum_i{d_i y_i}+ A x - B \cdot \mathbb{I}_{x>0}$, how can I linearize $A x - B \cdot \mathbb{I}_{x>0}$ term where $d_i, A$ and $B$ are positive constants ...
86 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 ...
94 views

### How this problem can be defined as MultiObjective optimisation

I need to optimize the end-to-end latency of a multi-component application. Assuming that the application has 10 components, component 1-5 is hosted by device 1, and device 2 is hosting the other 5 ...
87 views

### Specific usecase of two-phase simplex algorithm

The problem below aims to find to most optimal way to transport the fuel : A company Er must transport a type of fuel from its two refineries Ra and Rb to its two points of sale PV1 and PV2. The ...
111 views

### How to write distance specific constraint?

Suppose there are a few plants (p) and few customers (c). The supply (Sp), distance (Dpc), cost (COSTpc) and demand (DEMANDc) between them is given. I have a constraint that 90% of total demand of all ...
122 views

### Is my formulation correct and how to formulate this IF-THEN constraint?

I have system with $N_U$ users and $N_T$ transmitters. Multiple transmitters can transmit to a single users and one transmitter can transmit to many users, i.e., two sets of transmitters serving two ...
82 views

### How would you linearize this scheduling problem? Or how would you solve this? It is variation of a set coverage problem for OpenSolver

So, it's been about 15 years since I took my OR class in college. I'm not versed in any programming language besides a little bit of VBA. A client of mine is looking to solve the following problem. I ...
101 views

### Formulating these logical constraint in an ILP

I have these two constraints : $z \leq My$ $t \leq M'y$ where $z$ and $t$ are two integer variables $z, t\geq 0$, $y$ is a binary variable, and $M$, $M'$ are two big numbers. So basically these ...
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### High-mix manufacturing capacity

I'm not an expert in OR but I would like to determine what is the maximum manufacturing capacity of a plant (or how much a plant can produce of mix products). Each person in the plant has a known set ...
104 views

### Provide basic solution to CLP

I'm using Pyomo to formulate an LP with approx 500,000 constraints and 200,000 decision variables. The LP is solved using CLP. Some instances fail to return even a feasible solution after many ...
281 views

### Automating the column generation decomposition process

When trying a decomposition technique such as column generation, most of the times my approach is to look at the problem and then: Decide what a column should represent Write the Master Problem Write ...