Operations Research Stack Exchange
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If a problem is inapproximable for $(2-\epsilon)$, can we conclude there exists no PTAS for it?

If we prove that: The existance of a $(2-\epsilon)$-approximation algorithm for Problem P1 implies $P = NP$, can we conclude: There exists no PTAS for Problem P1, and so P1 is APX-hard?
Mostafa
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Safety stock for log-normal distribution demand

I came across this example on how to model your lead time demand as a log-normal distribution and calculate the safety stock. https://www.linkedin.com/pulse/why-you-keep-missing-your-service-level-targets-stefan-de-kok/ I don't understand the part…
Nishant Kumar Gupta
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Approximate average waiting time when a m\m\1 queue shows transient behavior

I have an m/m/1 queue and a set of arrival rate $\{\lambda_{t_1}, \lambda_{t_2} ...., \lambda_{t_n}\}$ and a fixed service rate $\mu$. I want to calculate the average waiting time during each time interval. On the book "Operations research…
Santo
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Relative Weakness of Rolling Horizon Optimization

I am running a fairly complex and dynamic(multi-period) model, and as a result of the complexity, solvers are not able to solve the problem in a reasonable time frame. I have since discovered the rolling-horizon method which could help to alleviate…
GrayLiterature
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Guidelines for adding user cuts to models

Given that you have identified a new class of valid inequalities. What are some guidelines on when and how many and which of the violated user cuts you add to the model? I know that this involves a lot of benchmarking, but are there some common…
user3680510
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Which EOQ-based $(r,Q)$ approximation has a fixed worst-case error bound?

There are two common approximations for the $(r,Q)$ inventory optimization problem that use the EOQ model. It is well known that one of them has a fixed worst-case error bound, but there is confusion in the literature about which one it…
LarrySnyder610
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Requiring exactly $n_j$ slots for job $j$ (if scheduled)

Let $x_{j}(t)=1$ iff job $j$ is scheduled at time $t$. I want to say that if the job is scheduled at all, then it is scheduled at $n_j$ slots. I wrote this as: $$x_{j}(t)\sum_{s=1}^{T}x_{j}(s)=n_jx_{j}(t).$$ Is it possible to write this as linear…
zdm
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Local minimization of a function over a line

Let $f:\mathbb{R}^n \mapsto \mathbb{R}$ be a differentiable function. Suppose $x^*$ is a local minimizer of $f$ along every line that passes through $x^*$. This means that the function $$g(\alpha) = f(x^* + \alpha d)$$ is being minimized for $\alpha…
independentvariable
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How can I represent null or dashes in a cost matrix or incidence matrix in CPLEX?

In the image below, the cost matrix of customers and supplier has several dashes which indicates the impossibility of certain suppliers with certain customers. How can I represent these dashes in CPLEX?
21vs
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Help with a MILP formulation for service scheduling

I'm trying to formulate a MILP for scheduling service jobs for multiple devices. Let's assume that each device $i$ has a life $\ell_i$ and that I have $n$ total service visits to allocate at times $\{M_1,\ldots,M_n\}$. Each device must be serviced.…
Chris Healey
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Minimizing $x_1/x_2$ over a simplex in the positive orthant

I need to solve the following problem \begin{align}\min&\quad x_1/x_2\\\text{s.t.}&\quad Ax \leq b\\&\quad x > 0\end{align} where $A$ is a positive matrix. The best thing I can think of is to put $x_1 = e^{z_1}, x_2 = e^{z_2}$. Then the objective…
P.T.
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Where can I find resources to learn mathematical modelling for real life operation research problems like combinatorial optimization?

I find it hard to form math models for real life operations research problems, how can I learn this? Any books, tutorials available?
21vs
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Best method to optimize the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimize the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for this reason I looked at a chance constrained model.…
danielcharters
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Dual variables associated with same equation for different time instants

I have three equations that are essentially the same equation defined for three time instants. The equations are basically calculating the state of energy of an energy storage facility. \begin{align} e(t) &= e(0)-d(t)+\eta \cdot c(t);&&t=1\\ e(t) &=…
S_Scouse
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Linearizing objective function with variables inside an indicator function

I am working on a problem in which I am trying to maximize the average of a variable only for the data that meet a certain condition with a constraint on the number of data that meet this condition. I am actually interested in constructing this…
Pierre
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