# Questions tagged [assignment-problem]

Questions on problems whose solution space are one-to-one mappings between two sets.

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### A variant of weighted perfect bipartite matching

I am currently working on weighted perfect bipartite matching, i.e., assignment problem. Formally speaking, it could be formulated as follows: $$min \sum\limits_{i=1}^{N}\sum_{j=1}^{N}c_{ij}x_{ij}$$ ...
63 views

### Optimization Problem: Recommending Service Providers to Clients

I am new to optimization, not sure if the problem described below is trivial. Any guidance on solution or nudge in the right direction would be very helpful. Problem: There are two groups – clients ...
62 views

### Adding sequence constraints to the assignment problem- Python

This is an online assignment problem and yet can be considered as an assignment problem with a sequence. Assume that workers are coming into the system sequentially and I want to assign a task to them ...
53 views

### Print Intermediate Solutions of Scheduling Problem and tackling FLAGS in jupyter notebook

I tried this code and it goes on and I'm clueless when it'll end so I manually interrupt it. Is there any way we can see intermediate solutions that are feasible solutions and can we limit time or ...
56 views

### Resource scheduling problem with synchronization constraints: Weak LP relaxation

I have a resource assignment/scheduling problem which involves assigning jobs to $m$ workers. There are 2 sets of different jobs, $J^1$ and $J^2$, and a set of periods $T$. Let $d_{jt}$ be the number ...
141 views

### How to solve large scale generalized assignment problem

I am looking for a way to solve a large scale Generalized assignment problem(To be precise, it is a relaxation of the Generalized assignment problem, because the second constraint has $\le$ instead of ...
53 views

### Employee allocation based on ranking: Mathematical Model

Suppose I have three employees and I have to assign three employees based on their ranks. If an employee has rank 1 that means he is best. Say, I have the following table ...
330 views

### Assignment and scheduling problem with resource constraints

I have 10 tasks with 6 workers. Each worker can only serve one task at a time and must complete the task before moving on to the next task. Each worker has a maximum work output value and each task ...
84 views

### Relationship aware task scheduling heuristics

I have a task scheduling/assignment on machines problem (like a classic bin packing problem) with a twist in which the placement/assignment of one task affects the placement/assignment of other tasks (...
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### LP instead of IP formulation of assignment problem

In the example files of GLPK, the assignment problem is written as a linear program. I don't understand why this isn't an integer programming problem. The problem formulation: ...
188 views

### Assignment problem with batching costs

I am studying an assignment problem with batching costs, and I would like to know if there is a standard name or algorithm for this problem. I know this problem can be formulated as mixed-integer ...
95 views

### Assignment Problem With Weighted Bipartite Graph

I have the following problem: Given $n$ workers and $n$ tasks I have to assign a worker to each task where each worker has a time to get to the task, and each task has a preparation time. for example, ...
95 views

### NP-hardness of a special case of multiple choice knapsack problem

Let us consider the following problem: \begin{align} \max &\quad\sum_{i=1}^n\sum_{j=1}^m v_{i,j}\cdot x_{i,j} \\ \text{s.t.}&\quad \sum_{i=1}^n x_{i,j} =1 &\forall j =1,\dots,m \\ &\...
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### How to determine least time required to complete all tasks?

I am trying to figure out how can I assign tasks to workers in a way that maximum time required to complete all tasks is minimum. Suppose I have following matrix ...
65 views

### Greedy algorithms for assignment problems --- prediction doesn't match simulation

I'm considering the following basic assignment problem: a group of $n$ people is to be assigned, in one-to-one fashion, a set of $n$ jobs. Write $C_{ij}$ for the cost incurred when person $i$ gets ...
334 views

### Simplex (GLPK) doesn't find a feasible solution on this simple assignment problem, but there is an obvious one

Problem Assign 11 projects to 11 students, based on their preference. For this example, each students chooses only one project, for simplicity shake (as shown below). Student 1 one chooses project 1, ...
205 views

### Counting the number of matchings in a complete bipartite graph

I am trying to count the number of matchings in a complete bipartite graph (perfect as well as imperfect). It's relatively easy for me to convince myself that there is $n!$ perfect matchings in the ...
277 views

### Modeling an assignment/scheduling problem to minimize total wait

I have an assignment type problem in which there is a set of students, $S$, and a set of training classes $T$. Each training has a fixed start and end day and can accommodate at most 1 student. In ...
382 views

### How to allow multiple assignments for jobs in Hungarian Algorithm?

In the Hungarian Algorithm, the assignment for a bipartite graph considers the restriction of assigning a single job to a single person for example. Can this restriction be relaxed? I would like to ...
79 views

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### Open Source MILP software for Python with user-friendly API to define the optimization problem

Following the accepted answer to Assignment problem where assignments must be done sequentially I would like to write a Python script which can solve the problem defined there. It's a Mixed Integer ...
402 views

### Assignment problem where assignments must be done sequentially

I have a weird planning problem. I think it falls under the assignment category, but I'm not sure because I'm not familiar with assignment problems, and also because there is a "temporal" angle to it, ...
237 views

### Generalized Assignment Problem as the sub-problem

I was wondering what is the state-of-the-art for solving the Generalized Assignment Problem (GAP) and if there are special cases that are polynomially solvable? Moreover, is there any usage of this ...
193 views

### Difficulties with finding equivalent problem on literature

I'm working with a sort of pickup delivery problem right now. We need to assign vehicles to routes and requests to those vehicles. Each request has its due date, client and may be delivered in one of ...
1k views

### Excel Solver linear programming - Is it possible to use average of values as a constraint without #DIV/0! errors or sacrificing linearity?

I'm trying to create an assignment optimization model where the areas are assigned to either the south or north school districts so that the total distance is minimized. Each school must have at least ...
222 views

### Assignment Problem with Decreasing Costs

Problem: I have $i$ jobs that I can assign to $j$ workers. Each job has a cost. Each worker can perform up to an arbitrary max number of jobs. However, there is a cost efficiency for each job that is ...
102 views

### Modelling resource dependency in the assignment problem

The assignment problem is well-studied and has a nice polynomial time algorithm. I'm interested in an extension of this problem where all edges are in a certain group and taking multiple edges from ...
There are five jobs to be assigned to five machines and associated cost matrix is as follows  \begin{matrix} \text{Machine} & 1 & 2 & 3 & 4 & 5 \\ \text{Job A} & [11, &...
Suppose I'm solving a minimum-weight matching problem in a bipartite graph with sets $\mathcal{I}$ and $\mathcal{J}$, where $w_{ij}$ denotes the weight of matching item $i$ to $j$. I can model the ...