# 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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### Linear Programming - Model understaffing

I am reading up a bit on Linear Programming and have taken a lot from "Scheduling Emergency Room Physicians" (by Michael W. Carter & Sophie D. LaPierre, Health Care Management Science 4, ...
21 views

### LP Sensitivity Analysis with multiple simultaneous changes

TLDR: When doing sensitivity analysis (specifically the objective coefficients), there maximum allowable increase and decrease before the solution changes is only valid when a single coefficient ...
90 views

### Find the minimum number of equipment required for a service period

I'm starting to learn operations research and trying to get my head around this problem that I have. Problem statement: Find the minimum number of equipment needed to run a service schedule. There are ...
1 vote
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### Conditional Statements in an LP model

I am currently working on a large workforce/manpower planning model for an aviation company. This model should decide whether to hire a new pilot or to let pilots fly overtime. It has two skillsets. ...
74 views

### Mixed Integer Programming - How to model a term in objective function with a constant multiplied by (1-Decision Variable)

I am solving an optimization problem, where I want to minimize the objective function $$Z = \sum_q \left(D_q \text{fare}_q - \sum_{p \ne q} \Delta D^p_q \text{fare}_q \right) (1-Z_q)$$ Each $q$ is an ...
90 views

### What are some good references of OR techniques applied to revenue management?

For teaching purposes, I am looking for some nice examples of revenue management problems which are tackled with optimization techniques, ideally linear programming (including MIPs). For example, this ...
225 views

### Upper bound on length of solution of linear program

Consider the linear program: $$\text{maximize} ~~ c\cdot x \\ \text{subject to} ~~ A\cdot x\leq b, ~~x\geq 0.$$ Suppose $A$ is an $m\times n$ matrix, $b$ an $m\times 1$ vector and $c$ an $n\times 1$ ...
103 views

### Determine the daily production program that maximizes the company's output

The problem: The mechanical workshop can produce $600$ units of part #1 or $1200$ units of part #2 per shift. The production capacity of the thermal workshop, where these parts are sent for heat ...
1 vote
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1 vote
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### How to perform clustering of a large number of nodes?

I have a clustering problem with around 400-500 nodes. The edge between any two nodes has a weight (between 0 and 1, 0: can be considered as there is no edge/connection between these two nodes) as ...
26 views

### When Supply < Demand - distributing resources v/s meeting as much demand

In network modelling LP , when Supply < Demand and we use normal balance of flow rule for all the constraints, i.e. (inflow - outflow) <= supply or demand, we say we are trying to redistribute ...
1 vote
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Let $K$ and $Q$ be two variables, and $Q_\min$ and $Q_\max$ be two parameters. I need a series of linear constraints to define $Q$ vis-a-vis the value of $K$ based on the following rules: If $K \le ... 0 votes 0 answers 52 views ### Multi-Scenario Gurobi Python Output I have an lp and am trying to solve multiple scenarios at once. One of my scenarios is infeasible though this is not the issue. For some reason, when I print m.status, both solutions have a status of ... 1 vote 1 answer 123 views ### Solver for quadratically constrained mixed-integer linear programs I have an optimization problem with vectors$x$,$y$, and$z$, where$x$is an integer vector. My objective function is linear (i.e.$\|y\|_1$), but one of my constraints is quadratic ($x^Ty \leq z$). ... 1 vote 1 answer 69 views ### Single item unconstrained lot-sizing with multiple suppliers and minimum order quantities Variation of the traditional lot-sizing problem - with some additional complexities: multiple suppliers (S1, S2, S3), with different procurement lead-time Suppliers have to be allocated based on a ... 3 votes 2 answers 148 views ### How to find the maximizing number of expected delivered units of a probabilistic minimum cost flow problem? I am a Bitcoin / Lightning Network open source developer and researcher and new here but very active on the sister site. In the context of my research I discovered the field of operations research ... 2 votes 1 answer 131 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 ... 1 vote 0 answers 34 views ### Budgeted uncertainty on the RHS Suppose we consider budgeted uncertainty (Bertsimas and Sim, 2002) for the following scenario. We have a binary decision variable$x_{i,j}$, where$i \in I$and$j \in J$(two sets). We then have the ... -2 votes 1 answer 62 views ### Mixed Integer programming - Problem modelling coincidence restriction in scheduling match problem I am trying to model and solve a problem for maximize audience of matches that must be scheduled in different slots (I am using python PulP library). Below I explain the problem and the model process ... 2 votes 3 answers 244 views ### Identifying the minimum number of required machines to schedule jobs I am relatively new to the topic of optimization. I am currently trying to address the following problem: We are given a set of jobs, say$J$with release times, deadlines and duration. Jobs can be ... 2 votes 0 answers 28 views ### Recoverable Robustness for an optimization problem I am relatively new to the concept of recoverable robustness. I am researching the robust version of an optimization problem. I currently have methods to address the problem with perfect knowledge. ... 1 vote 1 answer 107 views ### Mixed Integer Programming - How to model objective function with variables that depends on the solution? [duplicate] I am modelling an optimization problem that is described as follows: I would like to maximize audience for scheduling matches. There are n eligible teams and n/2 different slots. Teams will only play ... 1 vote 1 answer 59 views ### Scheduling tasks to minimize the total number of utilized cores I currently have a scheduling algorithm which computes an approximate solution, say S, for the nominal scenario of a given problem instance, say N. Given that N changes in a way and becomes infeasible,... 0 votes 0 answers 55 views ### Gamma uncertainty in the RHS of a constraint I am new to the concept of robust optimization.I am trying to formulate the robust variation of a Binary Integer Program. Suppose we have a constraint of the form$\sum{x_{i,j}} \geq b_j$for$ i \in ...
Suppose I want to minimize a linear function $f$ over a convex set $K$ and I have only access to a separation oracle, that is, given a point, the oracle returns yes if the point is in $K$ and ...