# Questions tagged [assignment-problem]

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

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### How to represent the objective function of the Weapon Target Assignment problem in CVXPY?

I am trying to use CVXPY to analyse a problem and the objective function for this problem involves calculating a product and a sum as per the problem description below (taken from a draft paper I am ...
77 views

### Hungarian Algorithm returns Boolean value for Traveling salesman problem

I am trying to implement Hungarian algorithm right off the shelf on a cost dictionary as part of Traveling salesman problem. The goal is to get path with minimum cost which hopefully covers all cities ...
54 views

### Linear sum assignment, but with ranked assignments?

Let's say I have 5 tasks that I have to assign to 5 agents, with a cost matrix: ...
181 views

### Algorithms to use for an assignment problem

Here is my problem: There are five sewing lines. When sample orders arrive, we have to assign them to the available line which is more skilled on a particular garment. Each line is given a rank ...
46 views

### Reinforcement learning for a Assignment Problem

I was just wondering if it is technically possible to solve a general assignment problem using reinforcement learning? You could use the inverted objective function as a reward function, right? Have ...
1 vote
44 views

### Terminology for "One-time" vs. "Continuous Tasks"

I'm working on task scheduling for satellite constellations, and I'm trying to determine if there are any keywords related to a certain distinction in task allocation problem that I'm seeing. In many ...
97 views

### Assignment of colored boxes to groups

I am working on a problem that I think can be solved as an extension to the assignment problem, but am open to hear about other ways to solve. PROBLEM There are a lot of colored boxes. For each color ...
1 vote
556 views

### Google-OR Tools: Assignment minimizing overlapping members

I'm rusty on constraint optimization and am looking for help in this particular use case. There are individuals who are each member to several teams. This is a fixed many-to-many relationship and is ...
1 vote
66 views

### iterative geographic assignment problem

I would like to formulate the following problem: Each state has multiple counties and each county has multiple municipalities. I have treatment cities and possible control cities (more possible ...
153 views

### Reformulate this constraint optimization problem such that I do not have to divide 2 variables?

I have a constraint optimization problem as follows: I need to assign $m$ tasks to $n$ days, with $n \geq m$. Each day can host 0 to $m$ tasks. Each task either belongs to type $A$ or $B$. I want to ...
506 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 ...
277 views

### Adding linear penalties for multiple assignments

I have a multiple assignment problem, with an added cost for "repeat assignments". For example, consider the cost matrix: ...
1 vote
397 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 ...
149 views

### Effective methods for solving the assignment and packing problem

There are $m$ items to be allocated into $n$ bins. The profit generated by placing the $i$-th item into the $j$-th bin is $c_{ij}$, and the service level is $s_{ij}$. A allocation scheme is required ...
66 views

### Optimizing Storage Allocation and Supply for Manufacturing with Time Constraints

I am currently working on a storage location assignment problem (SLAP), which involves optimizing the allocation of various items with different dimensions to different storage areas. My model ...
90 views

### Formulating assignment problem with people attributes that need to be balanced per assignment attribute in or-tools, CP-sat

I'm trying to do an assignment problem with the following characteristics: I have two sets that need to be matched with each other, set A (Students) and set B (Class combinations). Set A and B have ...
833 views

### Modeling: How to force customers visit their NEAREST facility

Let set $I$ denote the facility location set, $N$ denote the customer set, and $d_{ni}, \forall n\in N, i \in I$ is the distance between customer $n$ and facility $i$. The problem is to locate ...
195 views

### Assignment Problem - Students and teachers

I ran across this problem at work and I'm sure that we can optimize it with OR. I have $n(T) = 4$ teachers and $n(S) = 7$ students that should have a weekly individual class. If a student $s$ has a ...
116 views

### Assignment problem with multiple precedence constraints

Objective and short problem description The objective is to load as many passenger vehicles as possible on an auto-train. The train consists of multiple wagons with two levels each. The wagons are ...
117 views

### Is there a name for this variation of the generalized assignment problem?

All the input variables are positive float (x > 0). We have $M$ agents with limited amount of time $t_1,\dots,t_M$, $N$ tasks $task_1,\dots,task_N$ associated with duration $d_1,\dots, d_N$. Cost ...
1 vote
94 views

### PuLP ensure first and last choice

I have an assignment problem where I have $N$ locations and $M$ dates for each location, and the goal is to choose $K$ location-date pairs that maximize revenue. There are a number of constraints, for ...
306 views

### How to do matrix multiplication in docplex in python?

Here's an applicative problem I'm trying to solve. Imagine there is a road that can be classified in 5 states. Can be something from good to bad etc. There are 4 maintenance actions possible. And the ...
1 vote
111 views

### Alternative Approaches to Assignment Problem

I have a real world use case where I aim to optimize the assignment of trucks to orders of different sizes over a time window by minimizing some cost function (e.g. total distance traveled). The below ...
592 views

### Minimize worker variance assignment problem

I have a problem, which is similar to Assignment Problem, described as follows: The problem instance has a number of workers and a number of tasks. Any task can only be assigned to a subset of the ...
131 views

### Expressing $\{0,1\}$ assignment across a matrix in MILP?

I have a MILP (Xpress) constraint, which is doing what I want it to, but I'm struggling to translate it into a LaTeX friendly mathematical expression. The below code enforces that in the matrix $V$, ...
1 vote
110 views

### How do I approach this optimization problem?

I'm a software dev that's pretty new to OR and want to solve a specific problem I came across at my job. From what I've researched it is a variation of resource-constrained assignment problem, but ...
1 vote
204 views

### Assignment problem with constrained number of unique tasks

I have an interesting assignment problem in which I have a cost matrix for workers and tasks, and need to assign each worker to exactly one task to minimize the cost. However, this is all subject to ...
188 views

104 views

### Assignment Problem with continuous decision variable

I have to solve a problem from industry where there are a number of machines which should be assigned to a number of tasks. The difference from the general assignment problem is tough, that the ...
1 vote
641 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 ...
2k 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 ...
1 vote
197 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 ...
98 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
47 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 ...
249 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 ...