0
votes
1answer
52 views

Relation between arg min of two functions

When is $u_F(x) = \underset{u}{\text{argmin}}(F_1(x),\cdots,F_u(x),\cdots,F_U(x))$ $\le$ $\underset{u}{\text{argmin}}(G_1(x),\cdots,G_u(x),\cdots,G_U(x)) = u_G(x)$ where $u \in \{1,2,\cdots,U\}, x \in ...
1
vote
0answers
22 views

Highest (lowest) index of positive time-indexed variable

I have a simple problem involving a variable $x_{it}$ representing the amount of a resource allotted to a task $i$ in time $t$. The quantity of the (renewable) resource is constrained at a value $R$ ...
3
votes
0answers
54 views

Operational Research. (Ressource Management)

I am looking for a solution that i know exists already in the field of "Operational Research"... I Just can't put my finger on the name of the thing. An heuristic to solve a very common and simple ...
0
votes
0answers
57 views

Simply formulated but hard problem on system of linear equations

When does the below system has a solution? $$AX=B\\ X > 0$$, where $A$ is $n\times n$ symmetric positive definite matrix and $X$ is a $n\times 1 $ column vector. Note: (I'm trying to use Farka's ...
1
vote
1answer
976 views

Linear Programming Inventory Problem

I'm still trying to get used to the nature of these problems and I'd appreciate some further explanation. ...
2
votes
1answer
735 views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
1
vote
0answers
602 views

Graphically solving a Linear Programming Problem?

I was given the following linear programming problem and have been asked to find all optimal solutions graphically. I am quite new to the subject, so please forgive my naivety. ...
4
votes
1answer
100 views

Mathematical formulation in operations research

Does anyone know how I would enforce the following constraints using a mathematical formulation? Any help or feedback is appreciated. a) If person A is given project 1, then person D must be given ...
1
vote
0answers
22 views

Complexity of Earlist Avaible Due Date for Scheduling Problem 1|ri, pi=1|Lmax

Let us consider the scheduling problem 1|ri,pi=1|Lmax (basically, this means there is one machine on which we have to schedule n jobs (all with identical procssing time 1) in such a way that the ...
0
votes
1answer
46 views

Checking whether a solution to MIP is optimal

Consider a binary integer program \begin{align} \min \quad &\sum _{j \in J}f_j x_j +\sum _{i \in I} c_i y_i \notag \\ \mbox{s.t.} \quad &\sum _{j \in N_i} x_j \ge 1-y_i, \quad \forall i\in I ...
0
votes
1answer
63 views

How would I answer this question? (Reworded)

George wants your help to work out how many of each type he should stock in order to maximise his profit. There are three types of Snackboxes: A, B and C. A and C both cost 5 to produce, and B cost 7 ...
0
votes
3answers
70 views

Summation notation [duplicate]

Does anyone have any suggestions as to how I would be able to formulate this problem using summation notation for those of you who are familiar with it? Hermione has been busy packing her bag with ...
0
votes
2answers
86 views

Operations research - summation notation [duplicate]

Outline: Hermione has been thinking about the imminent return of the Dark Lord, so she has been busy packing her bag with all the items required for her survival. Because she has so many different ...
2
votes
1answer
68 views

Software for Binary Integer Linear Programs

I am aware that there is good software out there to solve integer linear programs (ILPs). However, is there (preferably free or low cost) software I could use to solve large binary integer linear ...
0
votes
1answer
107 views

Partial linear relaxation yields an integer solution

Consider a binary integer program \begin{align} \min \quad &\sum _{j \in J}f_j x_j +\sum _{i \in I} c_i y_i \notag \\ \mbox{s.t.} \quad &\sum _{j \in N_i} x_j \ge 1-y_i, \quad \forall i\in I ...
0
votes
1answer
110 views

integer programming formulation problem

Consider a problem with three variables: $u$, $\sigma_l$, and $\sigma_w$ where $\sigma_w > \sigma_l$. I want to represent the following relationship using integer programming. \begin{equation} u = ...
1
vote
1answer
661 views

Warehouse Location Problem as an integer progam instead of a mixed-integer program

Given a set of costumers $M = \{1, \dots , m \}$ and a set of of factories $N = \{1, \dots , n\}$ we have $c_{ij} \geq 0$ costs to deliver to costumer $i \in M$ from factory $j \in N$ $F_j \geq 0$ ...
2
votes
1answer
286 views

Unimodular matrix definition?

I'm a bit confused. Based on Wikipedia: In mathematics, a unimodular matrix M is a square integer matrix having determinant +1, 0 or −1. Equivalently, it is an integer matrix that is invertible ...
1
vote
1answer
82 views

exchanging operators in max-max function

I am trying to determine if the following holds. $\max_{i\in I}\max_{a_j \in P_j}\{\sum_j a_{ij}x_j - b_i\}=\max_{a_j \in P_j}\max_{i\in I}\{\sum_j a_{ij}x_j - b_i\}$ $P_j$ is a closed convex set, ...
1
vote
1answer
737 views

A question about the operation research and simplex method

For the simplex method, we need to add slack variables. My question is how to determine how many slack variables should be considered in the LP problem? I don't quite get why in the cases to find out ...
6
votes
7answers
2k views

Operations research book to start with

for somebody having a quite strong background in Mathematics, which are some good books for the domain of Operations research? I guess there are textbooks covering topics like linear and nonlinear ...