18
votes
Is it necessary to study rigorous math courses in OR?
There are multiple levels to operations research. (Before continuing, I want to apologize to anyone about to be scandalized by my omission of their favorite journals.)
For some (many?) people working ...
- 40.1k
16
votes
Accepted
Reference for "expectation preserves convexity"
Reference "Convex Optimization" by Boyd and Vandenberghe https://web.stanford.edu/~boyd/cvxbook/, section 3.2.1, p. 79.
These properties extend to infinite sums and integrals. For example if
$f(x,...
- 13.8k
16
votes
Modeling the Choose function
I am going to assume that $x \in \mathbb{N}$ and $y \in \mathbb{N}$ are variables, and that $C \in \mathbb{N}$ is a constant. In this case, you can benefit from the fact that your equality constraint ...
- 6,362
13
votes
Accepted
Normal demand and normal lead time; is lead-time demand normal?
I had the same doubt, and I arrived at the conclusion that the formula given in the textbooks is, at best, a practical approximation. The lead-time demand, in fact, is not normally distributed.
Let $...
- 2,133
7
votes
Reference for "expectation preserves convexity"
$\newcommand{\E}{\mathbb{E}}\newcommand{\R}{\mathbb{R}}$Define $\phi(x) = \E[f(x-Y)]$ and assume that for all $x\in\R$, $f(x-Y)$ is measurable and integrable. Then, for $x,x'\in\R$ and $\alpha \in [0,...
6
votes
Is it necessary to study rigorous math courses in OR?
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 ...
- 5,452
6
votes
Accepted
The departure process of an $\rm M/M/\infty$ queue
The following proof approach for Bruke's Theorem was given in this Lecture by Richard Clegg:
Definition: A chain is called time-reversible if $p_{ij} = p^*_{ij}$ for all $i$ and $j$. This occurs if ...
- 8,677
4
votes
Normal demand and normal lead time; is lead-time demand normal?
I tried simulating lots of normally distributed lead times and the normally distributed demand in each. The lead time demand sure looks normal:
But a normality test gives $p = 0$ to at least 9 ...
- 13.2k
3
votes
Normal demand and normal lead time; is lead-time demand normal?
I've thought about this for a bit, and I now believe that leadtime demand in most common situations is not normally distributed, although it may be as usual a good approximation.
Of course, we know ...
- 1,542
3
votes
Question about a queueing problem
This is a $M/M/1$ queue with Poisson arrival distribution with $\lambda =1/10$ and Exponential service distribution with $\mu=1/3$. The proportion of the time that the system is busy can be calculated ...
- 8,677
2
votes
Accepted
Service probability for M/M/1 queue with reneging
The steady-state probability of being served for an M/M/1 queue with exponential reneging times and no balking is
$$
p_s=\frac{1+z}{1+r(1+z)}
$$
where $r=\lambda/\mu$ is the service intensity, and
$$
...
- 2,117
2
votes
Queuing Theoretic Model with Memory
Since you are assuming infinite capacity, this sounds like an $M/M/\infty$ queueing system.
- 40.1k
2
votes
Normal demand and normal lead time; is lead-time demand normal?
I have done extensive analysis of procurement lead time distribution across industries. In my experience, I found most of the distribution are heavily skewed towards the left.
Yes, you are right! ...
- 81
1
vote
Modeling the Choose function
AFAIK, some optimization software such as GAMS has some nice functions to deal with this. For example, function likes factorial (fact(x)).
Indeed, some estimations for the factorial function using the ...
- 9,248
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