# Questions tagged [modeling]

For questions related to the process of converting a real-world problem into a mathematical model. Can include questions related to linearization, logical constraints, tightness of formulations, and so on.

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### Validation and verification of mathematical models

Within the subject of simulation I have found some literature on validation and verification (e.g. Sargent's paper). My question is, what techniques do you use to validate and verify your mathematical ...
266 views

### Difference between Chance constraints and logical constraints

A logical constraint combines linear constraints using logical operators, such as logical-and, logical-or, negation (that is, not), conditional statements (that is, if ... then ...) to express complex ...
696 views

### Running a linear programming model to maximize binned predictions

I have a dataframe like: ...
86 views

### NPV calculation using monte carlo simulation [closed]

I need help in solving part b). I need to solve it using excel can someone help? a) Conduct a discounted cash flow calculation to determine the NPV of the following project, assuming a required rate ...
3k views

### Soft constraints and hard constraints

The terms "soft constraints" and "hard constraints" are used in the context of optimization modeling. Is there any standard way to figure out which is which in some of the complicated models?
147 views

### Structural Optimization

Currently, I am working on a problem in which I need to use MILP to model equilibrium equations in a lightweight structure. Although this is an application based question, I wondered if there is a ...
193 views

### Queuing models in R, $\lambda$ Little

It's noted that the number of folks in a stationary system will maintain an average equal to the rate of arrival multiplied by the mean of the service distribution. The formula $L = \lambda w$ is ...
254 views

### How to reformulate (linearize/convexify) a budgeted assignment problem?

I have a scheduling problem at hand. In my system, there is a service station with $M$ service outlets, therefore, the service station can serve $M$ users at a time. But, there are $N$ users $N>M$ ...
343 views

### How to formulate this scheduling problem efficiently?

Let there be $N$ users with individual demands (of some items). Some users can have higher demands while the others can have lower demands. There are exactly $N$ service points. There is a one-to-one ...
205 views

### Good sources on developing mathematical models [closed]

What are good sources (literature, internet, etc) on learning to model real-world problems using mathematical formulations? In particular, I would like to know sources which establish the relationship ...
1k views

### Examples of machine learning applied to operations research?

Can someone give me a few examples, if they exist, of problems in operations research that could be solved using machine learning. I am aware that machine learning examples are data-driven and do not ...
106 views

### Pricing of blends/mixtures across multiple timesteps

I have a simple blending problem, where each final product is a blend or mixture of several raw materials, and want to calculate the price per unit of weight for each of the products. So for a given ...
256 views

### Mathematically creating the 'perfect' permutation for reservations in a hostel

I am working at a hostel which uses a reservation system for each room and the beds in the room (e.g. $14$ beds in one room, bed numbers $1-14$.) When we get bookings for multiple people, we assign ...
940 views

### Bin Packing with Relational Penalization

There are $N$ bins with equal capacity $C$. In addition, there are $N$ objects $x_1, x_2, \dots, x_N$ that need to be accommodated using the least amount of bins. Each object $x_i$ has a volume ...
413 views

### As an Operations Research professional, how is your time divided when working on an optimization project?

When working on an optimization project, what is the typical time division (in percentage) between the various tasks that you have to work on: Problem understanding/definition (figuring out what is ...
2k views

### How to determine the correct level of detail when modelling?

"All models are wrong, but some are useful" - George E. P. Box I usually work on what one could call operational problems. There I usually do not have too much trouble figuring out the level of ...
172 views

### partitioning hub assignment models

When solving large-scale hub assignment models (1000+ candidate hubs and 1000+ demand nodes), it is possible that parts of a cost matrix are not connected to one another. A typical workflow would be: ...
124 views

### Does dispersion really matter?

Context: Given a counting process $\{N(t),\,t\ge 0\}$ which tracks the number of events (arrivals) by time $t$, the index of dispersion (for counts) is the variance-to-mean ratio of the cumulative ...
304 views

### How to linearize a constraint with a maximum of binary variables times some coefficient in the right-hand-side

I have the following constraint that I'd like to linearize: $P$ is a given set $b_p \in \{0,1\} , \forall p \in P$ a binary variable associated with each element of $P$ $c_p \in \mathbb{R}^+$, a ...
204 views

### Connectivity of two nodes in an arbitrary undirected graph

Is there an efficient way to model the connectivity of two nodes in an arbitrary undirected graph? I would like to have a binary variable representing this connectivity: 1 if there exists a path ...
276 views

### Tightness of an LP relaxation without using objective function

How can we measure the tightness of a linear programming relaxation for a mixed integer linear program without using the objective value? I would like to get a measure in terms of the feasible set and ...
832 views

### Modeling floor function exactly

Suppose we want to enforce a constraint $$y=\lfloor{x}\rfloor$$ where $x$ is some continuous variable. One option is to use $$x-1\leq{y}\leq{x},\quad y\in\mathbb{Z},$$ which fails on the edge case ...
181 views

### How to fit a Beta distribution to three estimates from “expert”?

I'm modeling a process time, $X$, for a simulation study and have an "expert" estimate of the minimum, $\hat a$, the most likely (mode), $\hat m$, and the maximum, $\hat b$. I'd prefer to avoid the ...
122 views

### Conditional Controls in MIP Models

Innocently cross-posted at Mathematics SE I am developing a model that operates in the realm of mixed integer programming, although I am fairly unfamiliar with this area of mathematics at the moment. ...
307 views

### How to handle real-world (soft) constraints in an optimization problem?

Cross-posted at Stats.SE (aka Cross Validated) I am working on a problem which involves optimizing for minimum power consumption in a large compressor network interconnected through pipelines (think ...
308 views

### Dealing with non-overlapping constraints

Let us consider the following problem: Let $T$ be a set of tasks. Each task $t \in T$ has a duration $d_t$ and a target start time $s_t$. No two tasks can be executed in parallel. The objective is to ...
119 views

### What are best practices for coding up MIP models? [closed]

When coding an application involving a MIP, what are the best practices I should follow? In particular, I mean: Domain-specific language (GAMS, AMPL) or General purpose (Python, C#)? Structure of the ...
205 views

### How to decide to write an objective function?

I'm working on this problem: In the Njaba river basin, the available water was allocated for the purposes of consumption, irrigation, and electric power supply among three communities. The water ...
191 views

### Symmetry-breaking ILP constraints for square binary matrix

Setup I have a binary $N \times N$ matrix. The objective is to minimize the number of ones in the matrix, subject to various constraints. This leads to symmetries by rotating 90 degrees and/or ...
365 views

### How to determine if a given problem seems to be a good fit to be solved using combinatorial Benders decomposition

Combinatorial Benders decomposition is a mathematical programming technique consisting into dividing a problem into a master problem and a sub problem. The master problem is solved to optimality (or ...
525 views

### In an integer program, how can I “activate” a constraint only if a decision variable has a certain value?

Suppose we have the constraint $$a_1x_1 + \cdots + a_nx_n \gtreqless b,$$ where $a_i$ and $b$ are constants and $x_i$ are decision variables. Suppose also that we want the constraint to hold if $y=1$ (...