# 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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### Identifying problem: Assignment + Job Shop Scheduling

I am new to OR. Hence, I want your advice on the problem I am trying to solve: Given: $O_1 \rightarrow O_2 \rightarrow O_3 \rightarrow ... \rightarrow O_n$: the sequence of operations to produce $1$ ...
118 views

### Project task scheduling based on available budget per period

I have a challenge that is a bit backwards from the usual labour resource leveling problem. In my case I have a fixed budget pool over a period to deliver some of the work packages (not enough per ...
1 vote
73 views

### Help with dual of a problem

Could anyone confirm me if I write the correct dual for my problem? The different sets confuse me a lot. $s$ is the source node and $t$ the sink node. I'm uncertain if the last dual constraint in ...
419 views

### What would be a representative/appropriate name for operations research?

Assuming you have a masters degree in operations research and this masters degree is offered in an economics department of your university. What would be a representative/appropriate name to describe ...
120 views

### How to input this LP model of a buffer allocation problem in Gurobi?

I am doing research on optimizing a simple buffer allocation and need to run my model. I am new to this but someone told me about using Gurobi and I do not for the life of me know how to create the ...
138 views

### How to put this restriction using Gurobi in python

I am doing an optimization problem for the filling and extraction of a warehouse. One of the constraints is that the filling volume cannot exceed a given limit for one day: For example, on the 3rd of ...
60 views

### Methods to solve integer linear inequalities with products of two variables

I'm interested in solving the following system of equations over the integers: \begin{align*} x_l^3 &\le x_l^1x_l^2 & \text{ for } l = 1,\ldots,s \\ A x &\le b \\ 0 &\le x \end{align*} ...
87 views

### On the non-sufficiency of total unimodularity of the constraint matrix in the definition of an integer polytope

Is there an example of an $m\times n$ integer matrix $A$ and an integer vector $b\in \mathbb {Z}^{m}$ such that the polyhedron $P := \{ x\in \mathbb {R}^{n} \mid A x \leq b\}$ is integer, while $A$ is ...
149 views

### How to use condition in cplex?

I want to use conditions to my variable. dvar boolean x[I][J][K][L] dvar in h[i] my code is ...
105 views

### How to formulate cumulative sum of LpVariable in Pulp Python

I have a Multiple product LP optimization problem in which the product(B1,B2,D) will be received in variable quantity with respect to date column. The Optimizer should LP variable Output as Assy Out ...
1 vote
77 views

### Solving Graph Partitioning Problems with Gurobi and Pyomo

I am trying to solve a graph partitioning problem for a large number of structurally similar random graphs with an 0-1 LP. Most of these problems are solved within 0.x seconds. Some graphs take the ...
48 views

### bilinear problem proof for NP-completeness of degeneracy check

In the paper "Some NP-complete problems in linear programming" (https://doi.org/10.1016/0167-6377(82)90006-2), there are several proofs given to show that testing for degeneracy in LPs is NP-...
55 views

### Robust Linear Optimization for avoiding diminishing returns

My engineering problem can be formulated as an LP as shown below \begin{align} \max_{\mathbf{x}}~~&\mathbf{a}^T\mathbf{x} \\ \mbox{s.t.}~~~&\mathbf{b}^T\mathbf{x} \leq B~~,~~\mathbf{1}^T\...
1 vote
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### How to solve this problem with Gurobi add-in Opensolver excel

My main problem is that, when I try to solve an optimization using Gurobi with the OpenSolver add-in, I get the error that there is no feasible solution. To summarize, my variable $X_i$ has a maximum ...
779 views

### how to "calm down" optimizer

I want to optimize a charging schedule for Battery Electric Vehicles (BEV) along a grid line, taking into account customer wishes (when to be done with charging with what State of Charge (SOC)) and ...
118 views

### Warm starting ideas for iteratively solving a model with a few additional constraints

I'm trying to solve a MILP model iteratively, and at each iteration a few constraints are added to the problem that cut off the previous optimal solution. I'm trying to figure out ways to implement a ...
230 views

### Common problems/puzzles that can creatively be solved with linear programming?

I am interested in common problems/puzzles that have a clear set of rules/constraints and objective that lends itself to modeled and solved with a linear program. Especially for people new to LPs, I ...
55 views

### Load to ship assignment problem

Problem We’d like to optimize the delivery of loads across a network using a fleet of ships. Assume there is a set of $\mathcal{S}$ ships that need to deliver the set of $\mathcal{L}$ loads in a ...
62 views

### Decision whether to serve the current table now or skip it

Can the following problem be formulated as a LP/IP problem, where an agent (waiter) that has just arrived at a certain table has to decide whether to visit that table now, or skip the current table ...
95 views

### Linearizing this absolute difference objective function $\min\sum_{i=1}^{I}\sum_{j=1}^{i}|x_i-x_j|$

For $x_i>0, i=1,\ldots,I$, I tried to linearize this objective function $$\min\sum_{i=1}^{I}\sum_{j=1}^{i}|x_i-x_j|$$ as $$\min\sum_{i=1}^{I}\sum_{j=1}^{i}y_{ij}$$ subject to \begin{align} & y_{...
62 views

### How to optimize multiple linear regressions based on cost?

I have an optimization problem where I'd like to maximize revenue and I have separate variables for cost and revenue. Building a single unit of a product takes 100 hours of labor I have a list of ...
155 views

### How to use max flow to schedule machines? (building a network)

Suppose you manage a machine shop with $k$ machines and have $n$ jobs to process today. Each job $i=1,2,3,4,5,\ldots,n$ requires $p_i>0$ minutes of processing time on any machine and has a ...
232 views

241 views

### Python Pulp - LpMinimize Not Returning Expected Output - Scheduling Problem

I'm working on my first pulp model and something isn't going quite right. It looks like it's close, but for some reason it is not respecting one of my constraints... It's a scheduling problem and I am ...