-1
votes
0answers
21 views

Model If-Then-condition [closed]

Is there a possibility to model the condition: "If x > 0 , then y = 1" with linear (in-) equalities, if $x \geq 0$ and $ 0\leq y \leq 1 $ and integrality is not allowed in the model? If I could ...
0
votes
0answers
10 views

Difficult transition between homogenous and heterogeneous paramaters

I'll start with an example in queueing theory. Lets assume a M/D/k queue, i.e. a queue with $k$ servers where arrival rate is determined by a Poisson process. We try to find the mean waiting time. ...
1
vote
0answers
21 views

Multivariate Dynamic Optimization Model with Costs

I'm looking for kinds of models able to describe a situation such as the one described below (what I'm actually dealing with is load balancing but this is a more concrete example): We've a got a ...
1
vote
0answers
21 views

Highest (lowest) index of positive time-indexed variable

I have a simple problem involving a variable $x_{it}$ representing the amount of a resource allotted to a task $i$ in time $t$. The quantity of the (renewable) resource is constrained at a value $R$ ...
0
votes
1answer
74 views

Are my linear program equations correct?

Here's the problem: "An electronics company has a contract to deliver 21,475 radios within the next four weeks. The client is willing to pay 20 dollars for each radio delivered by the end of the first ...
0
votes
0answers
38 views

How to linearize a Maxmin constraint

Currently I have this linear programming model: Max_a(X) s.t. Max_c(Min_b(F(a,b,c))) <= some constant *Max_c meaning to maximize the following equation by just changing c, and the same applies ...
1
vote
0answers
39 views

Linear Programming- are my equations correct?

A dairy produces cheese, milk, sour cream, and yogurt. Suppose: Every 100 lbs of cheese requires 2 units of plant capacity, 3 workers, and 7 gallons of culturing additive, and gives $1,500 in ...
0
votes
0answers
90 views

Mathematical modeling- oil spill?

An oil spill has fouled 200 miles of shoreline. The oil company responsible has been given 14 days to clean up the shoreline, after which a fine of $$10/day$ will be imposed. The local clean up crew ...
1
vote
1answer
764 views

Linear Programming Inventory Problem

I'm still trying to get used to the nature of these problems and I'd appreciate some further explanation. ...
2
votes
1answer
570 views

Linear Programming: Three variable graphical solution

A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to ...
1
vote
2answers
108 views

Summation notation problem

Any help is greatly appreciated! Outline: Hermione has been thinking about the imminent return of the Dark Lord, so she has been busy packing her bag with all the items required for her survival. ...
3
votes
0answers
40 views

How to visualize a function to aid in optimization?

I am working on minimization of a function with more than two parameters. I want to see variations, local extremes, saddle points, etc. of this function to get some idea of how is this function in ...
0
votes
0answers
78 views

Create theoretical model for scheduling and allocation problem

I want to create a theoretical model for my scheduling and allocation problem instance, but I'm having some difficulties with a clear definition, since I have slightly different circumstances than the ...
2
votes
0answers
69 views

How to define an objective function that conveys the concept of selecting the best elements in a set

Consider a set of tasks $\mathcal{T} = \{t_1, \ldots, t_I\}$. Consider also a set of workers $\mathcal{W} = \{w^1, \ldots, w^J\}$, where each worker $w^j \in \mathcal{W}$ is associated with a value ...
1
vote
1answer
99 views

Creating a model

Here's a seemingly simple pondering. If one item is more valuable the higher it is (i.e., $a=5$ is worth more than $a=2$) and another item is more valuable the lower it is (i.e., $b=2$ is worth more ...
175
votes
17answers
7k views

Optimizing response times of an ambulance corp: short-term versus average

Background: I work for an Ambulance service. We are one of the largest ambulance services in the world. We have a dispatch system that will always send the closest ambulance to any emergency call. ...
1
vote
0answers
143 views

Modeling propositional formulas in integer programming

Say I have an binary integer programming problem: \begin{equation*} \begin{aligned} & \underset{\mathbf{x,y}}{\text{minimize}} & & f_0(\mathbf{x,y}) \\ & \text{subject to} & ...
1
vote
0answers
27 views

How can I learn to create and solve Rational Choice models?

I have some scenarios I would like to model using rational choice theory (i.e. utility maximizing agents). For example, a two population type (I suspect this means two representative agents), two ...
2
votes
2answers
739 views

How to 'minimize' correlation between series

Hi fellow mathemagicians, let's say that I have 3 series of numerical results (they represent 'drawdowns') : ...
5
votes
3answers
781 views

How to formulate constrained optimization problems

For a constrained optimization problem, there can be different formulations. For example, consider the problem with the following formulation: $$\min_{x \in X \subseteq \mathbb{R}^n} \, f(x), $$ ...