is a discipline to apply analytical methods for better decisions. It has many synonyms such as management science, decision science and system science.
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38 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 ...
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55 views
Graduate research project in stochastic programming . [closed]
I don't know is this a good question or is this place is right to post this like question or not , but I need keen help, so I'm posting it.
I'm a graduate student & in this semester I've ...
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0answers
19 views
Job assignment problem
I want to solve job assignment problem using Hungarian algorithm of Kuhn and Munkres in case when matrix is not square. Namely we have more jobs than workers. In this case adding additional row is ...
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0answers
14 views
Is there belman continuous function?
Is there belman continuous function? If there is then how define it. please explain with example.
Thanks in advance.
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0answers
96 views
Help in finding a mathematical proof for the following problem…
I need to write a critique for an article but I am struggling
with understanding the equations. I am sure that it's not that complicated but for sum reason
I can't figure it out.
$$
...
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0answers
39 views
Inventory control. Calculating annual cost
I wish I could help solve this problem if you think it is too much trouble. This is a task townhalls and Operations Research. I will be grateful if you give me any suggestions or detail. The problem ...
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0answers
32 views
DP formulation for the shape of Water-drop?
There are different suggestions for the shape of water-drop such as Joukowskis and Piriform parametrization. I am trying to understand how the water-drop-shape is deduced.
Suppose a trivial case ...
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0answers
21 views
Finding “good” values with regards to split disjunctions
We've been given an assignment in a course on Mixed-Integer Optimization, and one of the questions is about split disjunctions, or more precisely, finding good values for a split disjunction in order ...
1
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0answers
23 views
Infinite loop in column generation algortihm
I have to program the following:
Input:
I have k commodities that have to go from place i to j with a certain demand
There are n nodes and the cost for traveling one piece between the nodes i and j ...
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0answers
22 views
Time complexity 2-opt method
I'm doing a practice test for a course on routing problems. There's a question asking to infere the time complexity of the 2-opt method.
I can see that the complexity per iteration is in O(n^2) ...
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0answers
29 views
Min cost flow problem with “time window” constraints
Are there any variants of the min cost network flow problem where the flow into/out of the demand nodes must happen within specific time intervals? I'm thinking of a model which would ideally ...
2
votes
1answer
154 views
How to solve this LP problem as a Dynamic Programming problem?
The standard form LP problem is
$$\min -3x_1-7x_2-10x_3 \text{ s.t. }$$
$$x_3\leq 2$$
$$40x_3+40x_2+20x_1\leq 180$$
$$x_1,x_2,x_3\geq 0$$
My last lecture covered the Bellman equation ...
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1answer
30 views
Cost-to-go form of Dynamic Programming algorithm?
My lecture of Mat-2.3148 (Finnish) defines dynamic-programming-algorithm so that$J_N(x_N)=g_N(x_N)$ and $J_k(x_k)=\min_{u_k}\left\{g_k(x_k,u_k)+J_{k+1}(f_k(x_k,u_k))\right\}$ where
the state ...
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votes
1answer
270 views
Example about the Reduced cost in the Big-M method?
I want to gather examples about the reduced cost in different cases, now for the Big-M method. I hope this makes the methods more accesible. So
How does the Big-M method work with the below?
...
1
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1answer
57 views
Meaning of the bar over $\bf{c}'$ in $\bf{\bar{c}}'=\bf c' -\bf c'_B \bf B^{-1} \bf A\geq \bf 0$?
I am trying to understand the page 87 Bertimas about Linear Programming. The author uses bolding and bars -- now I am starting to think that the bar means something else to vector, bolding apparently ...
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1answer
68 views
Reduced cost in the Phase II of the two-phase Simplex?
My lecture slides outline how the two-phase simplex works: this table shows the end result of the phase I for the standard-form problem and the auxliary table of the phase I here. I understood until ...
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1answer
49 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
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1answer
62 views
How do you call the operation of counting the number of euclidian division until the denominator is lower than the remainder?
I was looking for the minimum size of a base35 secret_key to be able to generate at least 1,000,000 secret key.
The result is 35*35*35*35 = 1500625
How do you ...
1
vote
1answer
64 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 $j \in N$
$F_j \geq 0$ ...
1
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0answers
95 views
Introduction into Operations Research
I am a first year graduate student who advisor wants me to learn about operations research and to use stochastic integer programming in my research. He keeps giving me papers to read but they ...
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1answer
20 views
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1answer
76 views
Transportation theory algorithms detail description
I'm currently study operations research and want to implement some of its algorithms programmatically. I'm now interested in these algorithms:
1.North west corner rule method in transportation theory.
...
2
votes
1answer
80 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
43 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, ...
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votes
1answer
69 views
Functions of random variables.
Two emergency response units patrol uniformly and independently a 10-mile stretch of road. An emergency incident occurs on the roadway and its position is uniformly distributed, independent of the ...
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0answers
39 views
Inquiry - Operations Research Book
anybody know whether there is a solution manual to the book "Urban Operations Research" by Richard C. Larson and Amedeo R. Odoni.
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0answers
10 views
Differential rents problem solving for transport problem
Sorry if question was asked, but I was unable to find the exact duplicate. Let's assume that we have transport problem.
Will optimal plan for transport problem be the same regardless the method I ...
2
votes
0answers
148 views
Reconstructing an optimal Simplex tableau from an optimal solution
I have here a bounded LP with infinite optimal solutions:
...
1
vote
1answer
444 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 ...
3
votes
1answer
166 views
The Hungarian Algorithm
In reading the proof of the Hungarian algorithm for the assignment problem in a weighted bigraph, I could not understand why the algorithm terminates. In the algorithm we choose a cover (namely labels ...
3
votes
2answers
58 views
Determine the equations needed to solve a problem
I am trying to come up with the set of equations that will help solve the following problem, but am stuck without a starting point - I can't classify the question to look up more info.
The problem:
...
0
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0answers
220 views
Time to reach 0
Given the following rules, what is the expected time before a person who starts at 1 goes to 0? The alpha and beta stand for the probabilities of moving to the different states.
About the problem: ...
6
votes
5answers
1k 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 ...
