# Questions tagged [assignment-problem]

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

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### Identifying problem: Assignment + Job Shop Scheduling

I am new to OR. Hence, I want your advice on the problem I am trying to solve: Given: $O_1 \rightarrow O_2 \rightarrow O_3 \rightarrow ... \rightarrow O_n$: the sequence of operations to produce $1$ ...
1 vote
98 views

### How to solve assignment problem with additional constraints?

The assignment problem is defined as: Let there be n agents and m tasks. Any agent can be assigned to perform any task, incurring some costs that may vary depending on the agent-task assignment. We ...
1 vote
136 views

### How to solve assignment problem with type constraints?

There are $n$ jobs and $m$ machines. Assigning job $i$ to machine $j$ yields a profit of $c_{ij}$. Each job has a type $t_i$. Machine $j$ can take on up to $a_j$ jobs, but the number of job types must ...
55 views

### Load to ship assignment problem

Problem We’d like to optimize the delivery of loads across a network using a fleet of ships. Assume there is a set of $\mathcal{S}$ ships that need to deliver the set of $\mathcal{L}$ loads in a ...
1 vote
32 views

### Blended or hierarchical objectives if solving speed is more important

When optimizing a two objective task assignment problem, is it generally better to use blended objectives or hierarchical objectives if the speed to obtaining a near-optimal solution is more ...
189 views

### Use GA for Assignment Problem?

I have a two-objective assignment problem that appears to converge really slowly to a solution. Even if we just have 1 objective that minimizes costs, it appears to be very slow for a worker-task ...
60 views

### LP Objective function for distributing workload

In this example, we have a group of students that each needs to be paired with a teacher. Each student has a different number of questions to ask the teacher, and each student-teacher pairing has a ...
312 views

### Difference between solving Assignment Problem using the Hungarian Method vs. LP

When trying to solve for assignments given a cost matrix, what is the difference between using Scipy's linear_sum_assignment function (which I think uses the ...
31 views

### Solving minimum bipartite matching with missing edges using Hungarian algorithm

I am interested in a minimum bipartite matching problem, where some edges are missing (i.e., not valid). An intuitive way to solve the problem is to add very large costs for these missing edges and ...
1 vote
57 views

### Assignment Problems With More than One Class of Resource

I am working on a dispatch optimization problem in the trucking industry. I have a first algorithm - a vehicle routing algorithm - that produces a series of tours. I will need a second algorithm that ...
3k views

### A Stack Overflow user's curious problem of maximising unsortedness

User ddofborg posted on Stack Overflow a programming question which hides a combinatorial optimisation problem. The idea is the following: given a list of URLs with their respective domain names, he ...
156 views

### How to solve a minimum cost flow problem with time constraints

In the following picture, the decision-maker has to make deliveries to node $V=\{1,2,3,4,5,6\}$. He has two options: use cars or bikes. In both cases, he has to make a stop at a relay point where the ...
129 views

### 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: $$min \sum\limits_{i=1}^{N}\sum_{j=1}^{N}c_{ij}x_{ij}$$ ...
69 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 ...
1 vote
174 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 ...
68 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 ...
1 vote
63 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 ...
238 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 ...
1 vote
66 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 ...
373 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 ...
93 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 (...
1 vote
123 views

### 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: ...
211 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 ...
141 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, ...
123 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 \\ &\...
207 views

### 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 ...
81 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 ...
489 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, ...
266 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 ...
1 vote
538 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 ...
1 vote
81 views

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1k views

### 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 ...
519 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, ...
261 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 ...
204 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 ...
325 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 ...
235 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 ...
124 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 ...