# Questions tagged [assignment-problem]

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

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### 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 ...
132 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 ...
1 vote
382 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 ...
61 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 ...
67 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 ...
817 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 ...
157 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 ...
102 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 ...
111 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
77 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 ...
236 views

### 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 ...
1 vote
106 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 ...
133 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 ...
521 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 ...
128 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 $V$, ...
261 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
104 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
164 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 ...
182 views

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### 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 ...
284 views

### 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
529 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
186 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 ...
93 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
39 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 ...
238 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 ...
143 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 ...
1k 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 ...
49 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
74 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 ...
702 views

### How to keep solutions stable/persistent in a problem with many equally good solutions?

Suppose we have a worker-assignment problem where we seek to assign Alice, Bob, Chris, ... to jobs A, B, C, ... subject to various constraints and some objective function based on these assignments, ...
345 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 ...
167 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: $$min \sum\limits_{i=1}^{N}\sum_{j=1}^{N}c_{ij}x_{ij}$$ ...
107 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
362 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 ...
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 ...