# All Questions

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### Partial derivative of LP solution $(x_1 , \ldots, x_n)$ w.r.t. $x_i$ or $a_i$

Suppose I have an optimal solution and I want to know how the solution would (likely) change if one of the coefficients in the objective function changes, or if I add a constraint that forces $x_i$ ...
44 views

### CPLEX CP Optimizer Java API function missing

I can not seem to find the needed functions to model the following problem through the Java API (CP Optimizer): a machine that has downtime and sequence-dependent setup times, with the extra ...
39 views

### How to make constraints satisfy disciplined convex programming guidelines?

How do I turn my convex constraints (described below) into constraints that are DCP so that I can solve them in CVXPy? Is there some cheat sheet'' of standard tricks? I'm trying to implement the ...
437 views

### Modeling the Choose function

In statistics, one often encounters the choose function ${x \choose y}$ which encodes the number of ways of choosing $y$ items from a set of $x$ items. How would one go about modeling a choose ...
71 views

73 views

### Solving large-scale stochastic mixed integer program

What are some methods or algorithms for solving a large-scale stochastic mixed-integer optimization problem that runs on an hourly dataset for a year? Do we employ some kind of decomposition? (the ...
66 views

### Having trouble with objective function in Python: “GurobiError: Variable not in model”. What else could I try?

I am trying to figure out how I can write this objective function into python using Gurobi. I have to minimize the sum of the product of three dictionary's values. The reason I am confused is that ...
2k views

### Where to search for PhD level jobs in OR?

I started hunting for jobs and I'm not sure what are good websites I should be keeping an eye on. I'm interested mainly in Europe.
112 views

### Conditions for minima in calculus of variations

In the calculus of variations (unconstrained), one applies a first-order variation on a general functional of the form $$\int_{a}^{b}F(x,y,y')\,dx$$ to obtain the first-order necessary condition for ...
675 views

### How can I add this conditional constraint to my model in Python?

I am creating an optimization model with 2 sets of binary decision variables. The first, site, is regarding which of 380 cities to place manufacturing sites in, and ...
45 views

### Buyback policy in a supply chain

Consider a three level supply chain consisting of a manufacturer, a wholesaler and a retailer. Suppose I wish to include a buyback contract to this network. Then am I right when I say that wholesaler ...
659 views

### Holding cost vs carrying cost vs storage cost

I was reading an article on supply chain management and encountered a number of inventory costs like ordering, carrying, shortage, holding, storage costs. I cannot understand the difference between ...
843 views

### Is This Constraint Convex?

I have a constraint that I believe to be convex and not affine which I think means that I can implement a relaxation. I will first define the full constraint, and then build up my (informal) reasoning ...
288 views

### Linearization of a scheduling objective function

I am trying to maximize the workload per employee. An example: $e$ the index of an employee $j$ the index of a project decision variable: $x_{e,j} \in \mathbb{Z}$ and $0 \leq x_{e,j} \leq 100$ ...
24 views

### In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples

Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion. ...
309 views

### Duality in mixed integer linear programs

I know that the standard duality theory for the linear programming problem does not hold for mixed integer linear programming problems. I was wondering why an integer program does not have a dual ...
66 views

### In portfolio optimization, how do we estimate the variance of a new asset?

Say I want to do Portfolio Optimization using the mean-variance approach (i.e Markowitz model), but that some of my assets are new with no returns history. I can use a judgmental (expert knowledge, ...
67 views

### How to use the principle of duality to solve this linear program?

$$\begin{array}{ll} \text{minimize} & 2x + 3y + 3z\\ \text{subject to} & 2x + 3y + 4z \geq 20\\ & 4x + 2y + 2z \geq 10\\ & x,y,z \ge 0\end{array}$$
369 views

It seems like most solvers that can tackle nonlinear nonconvex optimization problems (e.g. IPOPT) operate on ultimately solving for the first-order optimality conditions. Can it therefore be assumed ...
47 views

### Question about a queueing problem

Arrivals at a telephone booth are considered to be Poisson with an average time of 10 minutes between one arrival and the next. The length of phone calls is assumed to be distributed exponentially, ...
74 views

### Count this to the family of Job Shop Problem?

I will explain the problem in a simplified version. Three Tasks: $T_1, T_2, T_3$ Four Machines: $M_1, M_2, M_3, M_4$ The machines $M_2$ and $M_3$ make the same processing, so they are parallel. ...
54 views

### Optimal resource allocation - 3 step process

I have a 3 step process. Step A takes 20 min, Step B : 60 min, Step C : 20 min Steps in production of output "news nuggets" is as below: Step A : Do Secondary Research Step B : Analyse the data, ...
235 views

### Convexity of a QP

In quadratic programming (QP), you encounter an objective of the following form: $$x^TQx + c^Tx$$ and often it's desirable to know if the QP is convex. One method to check for convexity is by ...
113 views

### Parallel nonlinear solvers

I've noticed that parallel (CPU or GPU) nonlinear programming solvers are few and far between. It seems that if any parallelization is involved at all, it generally applies to solving the underlying ...
653 views

### Modeling the Round (Nearest Integer) function

Modeling various non-differentiable functions is quite common knowledge including $\operatorname{abs}$, $\min$ and $\max$ functions. How would one go about modeling the nearest integer function, say ...
162 views

### Do the KKT conditions hold for mixed integer nonlinear problems?

I was wondering if the KKT conditions are applicable for for MINLPs, and if not, why not? What about the case when the integer variables are modeled using constraints involving just continuous ...
49 views

### What Improvements to make in resume , looking for Operations Research Analyst and Similar Positions? [closed]

I am an Industrial Engineering Master's Student, specializing in operations research, searching for full-time positions. Need suggestions/feedbacks over the resume so that, I can atleast land ...
133 views

### Shipments consolidation - how to model mutually exclusive items with OR-Tools CP Solver in Python (multi-knapsack, updated)

I am implementing a solution for packages consolidation (basing on Nurse Problem solution) with OR-Tools CP Solver. There is a factory that manufactures some small Packages that need to be ...
54 views

71 views

### Help in solving resource allocation optimization problem

I've been pondering on this question for some work optimization, and I need some help in being directed to the right direction. I have multiple customers that require an amount of $X$, $Y$ and $Z$ ...
149 views

### Does this $0-1$ integer program have any speciality?

Given matrix $A \in \{0,1\}^{m \times n}$ and vector $b \in (\mathbb{Z^+})^m$, where $\mathbb{Z^+}$ is the set of positive integers, \begin{array}{ll} \text{maximize} & c^\top x\\ \text{subject ...
119 views

### Network flow model - How can I turn this diagram into a matrix that when converted to RREF solves for max flow?

I have the following network flow model diagram and I have already calculated maximum flow using the R package igraph to be 28. However, what I would like to know ...
63 views

### Stabilization techniques in column generation when subproblems are not solved optimally

Which stabilization techniques in column generation, like penalty function approaches and dual price smoothing, can be used when subproblems are not solved optimally? (I am particularly interested in ...
99 views

### How To Linearize $X = \max\{x_1,x_2\}$

I am new to thinking about math programming and I have a particular constraint I am hoping to reformulate, I just don't know the proper mathematical translation for what I am hoping to do. Enforcing ...
84 views

### Constraint to state the relation between 2 binary variables

I'm trying to deal with a process planning and machine layout allocation simultaneously. I have the following variables: $X_p{_w}_{cj}=1$ if an operation $p$ is done by a machine $w$ with a ...
173 views

### Standard cumulative distribution function with optimization model variable

We all know that expressions in mathematical optimization models can't contain "black boxes" around a decision variable since everything has to be written using mathematical expressions. For example, "...
140 views

### Optimal set order to maximize stochastic reward

You have a ticket allowing you to visit up to $n$ of $M$ carnival booths offering games of chance. At each booth you have probability $p_{i}$ of winning a reward with average value $r_{i}$. Each booth ...
Suppose I have a set $S=\{1,2,\dots,500\}$ and some function $f(\sigma)$ from the permutations $\operatorname{Perm}(S) \rightarrow \mathbb{R}$ to be minimized. The function is complex (simulation ...