TheSimpliFire
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2 answers
5 votes
152 views
Safety Stock with Fill Rate Criterion
Accepted answer
2 votes

We can work from scratch. Rearrange $\beta=1-n(S)/\mu$ to get $$-\frac{\mu\sqrt{2\pi}}\sigma(\beta-1)=e^{-z^2/2}-z\sqrt{2\pi}+z\int_{-\infty}^ze^{-t^2/2}\,dt$$ on using ${\cal L}(z)=\phi(z)-z(1-\Phi(z)...

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2 answers
7 votes
304 views
Is there a ranking of heuristics for the travelling salesman problem?
4 votes

What you are looking for is the term domination analysis. For instance, see: Punnen, A., Margot, F., Kabadi, S. (2003) TSP heuristics: domination analysis and complexity. Algorithmica 35(2):111-127. ...

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1 answers
5 votes
130 views
Do you know of any formula to calculate the difficulty score of Sudoku?
8 votes

In Pelánek (2011)1, Sudoku difficulty evaluation was investigated across four existing metrics. These are based on incidences of various logic techniques (see constant folding). Results based on ...

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1 answers
3 votes
105 views
How do I arrive at the form given in this paper, for the QUBO version of the number partitioning problem?
3 votes

\begin{align}\text{diff}^2&=c^2+4\left(\left(\sum s_jx_j\right)^2-c\sum s_jx_j\right)\\&=c^2+4\left(\sum s_j^2x_j^2+\sum_{\rm cyc}s_ks_\ell x_kx_\ell-c\sum s_jx_j\right)\\&=c^2+4\left(\sum ...

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1 answers
6 votes
135 views
Why is the Bellman-Ford's shortest path algorithm sometimes called Bellman-Kalaba?
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5 votes

Interesting historical question. In Section 8.7, Chapter 8 of Algorithms (2019)1, Erickson notes that The simplest implementation of Ford’s generic shortest-path algorithm was first sketched by ...

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5 answers
8 votes
682 views
Paper suggestions on local search algorithms
3 votes

Blot et al. (2018)1 did an extensive literature review on multi-objective LS algorithms. You may wish to take a look at Ishibuchi and Murata (2004)2 which focuses on issues in evolutionary algorithms. ...

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3 answers
0 votes
182 views
Scaling of standard deviation for forecast error
2 votes

Let $(x_i)_{i\le n}$ and $(\hat x_i)_{i\le n}$ be sequences of observed data and forecast values respectively. Suppose we wish to split each $x_i$ equally over $m$ elements so that $(x_i)_{i\le n}$ ...

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3 answers
2 votes
341 views
Find the farthest point in hypercube to an exterior point
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4 votes

As $x_i\in[0,1]$ we just need to compare the values of the endpoints since $(x_i-c_i)^2$ is minimised at $x_i=c_i$. It is easy to see that $x_i=0$ gives the maximum whenever $c_i\ge1/2$ and $x_i=1$ ...

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1 answers
3 votes
140 views
Radial unboundedness vs convexity
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4 votes

The notation $C^1$ means $f'$ is continuous (on $\Bbb R$ as the interval is not stated). In general $C^k(a,b]$ means that all of $f',f'',\cdots,f^{(k)}$ are continuous on $(a,b]$. You are correct ...

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2 answers
12 votes
189 views
Meta papers on operations research
6 votes

Is operations research really research?1 discusses how the Design Research paradigm can be used to evaluate OR problems. Reference [1] Manson, N. J. (2006). Is operations research really research?....

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2 answers
1 votes
122 views
Waiting time in M/M/n queue
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3 votes

Dyer and Proll (1977)1 showed that for an M/M/c queue, the mean waiting time is a strictly decreasing and convex function of c. Reference [1] Dyer, M. E., Proll, L. G. (1977). On the Validity of ...

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1 answers
4 votes
115 views
Mobile Sensor Placement for Optimal Coverage
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5 votes

Note that $\phi$ is a function of $q$ so $d\phi(q)$ is interpreted as w.r.t. $\phi(q)$, which is the same as $d\phi$. This is just shorthand for $\phi'(q)\,dq$.

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1 answers
4 votes
66 views
Optimize probability parameter in an optimal control problem
2 votes

Note that $V(O)$ is simply of the form $\sf Q_1/L_1$ where $\sf Q_1$ is a quadratic and $\sf L_1$ is a linear function of $p$. This can be written as ${\sf{L_2}}+c/\sf{L_1}$ where $\sf L_2$ is also ...

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7 answers
16 votes
2k views
Does there exist an aggregation of videos on optimization?
10 votes

In terms of conferences, the Egon Balas Symposium in 2019 contained numerous talks on mathematical optimization. For integer programming specifically, it includes the Geometric Firefighter Routing ...

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4 answers
6 votes
166 views
Sequential quadratic programming source
3 votes

In the book Nonlinear Optimization (2010) by Bomze, Demyanov, Fletcher and Telarky, there is the chapter The Sequential Quadratic Programming Method written by Fletcher.

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3 answers
13 votes
737 views
On using correct notation in research papers
4 votes

I think the first three are OK, more so the first two. I agree with what Larry said about defining all variables first before usage and in this case it means defining $t\in[T]$ first. However, the ...

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2 answers
11 votes
3k views
Is it necessary to study rigorous math courses in OR?
6 votes

I would not say that knowing such concepts is necessary unless you wish to not only apply certain results to solve OR problems, but also to understand why/how the results work mathematically. For the ...

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1 answers
4 votes
218 views
How to express this constraint?
7 votes

No. The constraint $a\ge\gamma b$ sets no upper bound on $a$ so it cannot be bounded above by $b$ as your second formulation suggests. There are a few posts here on the linearisation of the product ...

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2 answers
5 votes
1k views
VRP package for R
6 votes

The package netgen (v1.3) can be used to generate networks and benchmark instances of VRP and TSP. As this article shows it is also possible to solve a variant of VRP (CVRP) in R Shiny, which is ...

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4 answers
8 votes
381 views
Disciplined convex programming representation of $x\sqrt{1-x}$
6 votes

This is possible purely under DCP. As you are interested in the interval $[0,1]$, rewrite your function as $$x\sqrt{1-x}=\exp\left(\ln x+\frac12\ln(1-x)\right),\quad x\in[0,1].$$ Then the following ...

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1 answers
5 votes
823 views
Minimisation of shelving cost problem
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2 votes

I do not understand why the formula for $C_{0,4}$ is as such. A simple check reveals that the unit on the RHS are pounds / (pounds / inch2) = inch2 whereas the unit for the cost is pounds. We have ...

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1 answers
6 votes
208 views
When does the Junction Tree Algorithm work better than Variable Elimination?
2 votes

You may wish to take a look at the paper by Cozman (2000)1; the following is taken from the Introduction. One of the advantages of junction tree algorithms is that it is possible to efficiently ...

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1 answers
11 votes
344 views
Why is the sample variance of a Sample Average Approximation calculated in this way?
7 votes

Since $\hat q_{N'}(\hat x)\approx\Bbb E[Q(\hat x,\xi)]$ and $\Bbb V[\hat q_{N'}(\hat x)]=\Bbb V[Q(\hat x,\xi)]/N'$, we have \begin{align}\hat\sigma_{N'}^2(\hat x)=\Bbb V[\hat q_{N'}(\hat x)]&=\...

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2 answers
8 votes
170 views
Conditions for minima in calculus of variations
6 votes

It is possible to apply the notions of stationary points and the second derivative of a function to functionals. For $|\varepsilon|\ll1$ and and a differentiable function $h$, we can write, using ...

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4 answers
5 votes
557 views
Reference request for Evacuation Planning
3 votes

Goerigk et al. (2014) may be a good start to your literature search. It uses mixed-integer programming to propose a genetic algorithm that can be used for urban evacuation planning. Examples of ...

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3 answers
9 votes
491 views
Equipment replacement problem
5 votes

The constant car price means that $$c_{i,j}=12\,000-t_j+\sum_i^{j-1}m_i$$ where $t_j$ denotes the trade-in price on year $j$ and $m_i$ the maintenance cost on year $i$. Thus $$c_{i,i+1}=12\,000-t_{i+1}...

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6 answers
13 votes
213 views
How to formulate: each pair of elements in $A$ has one common unit in $B$
1 votes

If $B_i$ is the set whose elements are connected by $a_i$, then for the "at least" condition we want $$\sum_{b_k\in B_i\cap B_j\\\quad i\ne j}|b_k|>0\qquad\forall a_i,a_j\in A$$ where $k=1,\cdots,K$...

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2 answers
6 votes
173 views
Solving an exponential utility function
Accepted answer
5 votes

The utility function $u(x)=a-be^{-x/20\,000}$ with the conditions $u(0)=0$ and $u(100\,000)=1$ gives $$u(0)=a-be^{-0/20\,000}\implies 0=a-be^0=a-b\implies a=b\tag1$$ and $$u(100\,000)=a-be^{-100\,000/...

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4 answers
12 votes
2k views
Where to search for PhD level jobs in OR?
2 votes

If you are thinking about working in the UK, indeed.co.uk might be useful for preliminary searching. As you ask for PhD level jobs, this and this (both Operational Research Scientists) are good ...

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2 answers
6 votes
792 views
Solving a Certainty Equivalent (Decision Analysis) problem
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3 votes

If $u(d)=c$ then $d=u^{-1}(c)$ since $u\circ u^{-1}$ forms the identity. Thus in general, under suitable constraints for $a,b,c$,\begin{align}a(1-e^{-d/b})=c&\implies1-e^{-d/b}=\frac ca\\&\...

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