# Questions tagged [scheduling]

For questions about methods that assign resources to work requests (e.g. processor time to tasks) usually minimizing some cost measure (e.g. makespan).

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### Is this classed as a version of jobshop? How should it be approached?

I'm looking at a problem that seems quite like flexible jobshop, but as I understand it jobshop is basically all about finding the order/sequence of tasks (across multiple machines potentially), ...
62 views

### How to define the sequence depending setup time based on a time index formulation

I am working on a scheduling problem in which I have used two different MIP formulations and also based on the time index variable. My problem is in the class $P_{j} | \ r_{j}, SDST \ | C_{Max}$. ...
1 vote
73 views

### Optimize cherry picking runs

I am trying to optimize a cherry picking procedure on 96-well microplates. The plates are 12X8 (12 columns, 8 rows). We pass a command file that has many lines like this to a robot: ...
92 views

### Formulation for choosing how many items to manufacture

I am working on a scheduler for a manufacturing plant. I have currently set it up so the decision variables are set up as binary variables: $x_{m,p,s}$ = 1 if machine m is running part p on shift s ...
1 vote
67 views

### Scheduling repeated tasks with minimum duty cycles

Several tasks need to run repeatedly in a channel, one at a time, over a repeating time frame of length $T$. Associated to each task $i$ is the duration $L_i$ the task will take to run, and a maximum ...
1 vote
67 views

### In a routing and scheduling problem with break consideration, How can I determine whether a node is met before a break or after it?

I'm working on a routing and scheduling problem in the home care services context. I consider a break as a dummy patient, so routing and scheduling are also implemented for the break node (with some ...
1 vote
63 views

### Linearization of Conditional Constraints for MIP using Cplex

I'm currently working on a mixed-integer programming (MIP) problem and I'm trying to implement a set of conditional constraints in CPlex. These constraints involve decision variables that are indexed ...
200 views

### Compute overlapping time

I am trying to solve an optimization problem in which there is a set of tasks, $S$, where $s_i$ and $e_i$ are the starting and ending time of task $i \in S$. Each task $i$ must be done within its ...
113 views

### How to fill the days in sequence?

I have a scheduling problem. 20 hours of work load should be assigned to different days (max 4 days are available and the capacity of ech day is 8 hours max) $\sum_i h_i = 20$ $0 \leq h_i \leq 8$ The ...
323 views

### Scheduling to minimize total "wait to start" time

I have a scheduling problem I am trying to work through. As I was outlining the problem, I realized it is probably of a known problem type, but I am unsure of what keywords to search for or what ...
105 views

### Meaning of the domain propagation in the context of mixed-integer programming

In the literature, domain propagation defines the process of inferring sequences of local domain reductions at the current node of the branch-and-bound tree. The goal is to shrink the size of the ...
1 vote
154 views

### Best algorithm for scheduling interviews

I posted the same question on stackoverflow and immediately referred to post it here. I want to think about the best algorithm which let the interviewer meet maximum number of candidates. Suppose that ...
98 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 ...
1 vote
90 views

### Modeling of a special form of the precedence constraint

There exists a scheduling problem in which some tasks should be processed on some resources. Additionally, each task needs to be assigned to a specific position on each resource. Let the decision ...
52 views

### Help finding linear constraint - LP

I have the following question. I have two variables $w_{nds}$ and $m_{nd}$. The first variable indicates whether a nurse $n$ works shift $s$ on day $d$. The second one indicates the motivation of ...
79 views

### Nurse Rostering constraints - LP

I am fairly new to linear programming since I came across this topic at university this semester. We mainly focus on nurse rostering. In the lecture, we created a very basic rostering model with an ...
113 views

### Linear Programming - Model understaffing

I am reading up a bit on Linear Programming and have taken a lot from "Scheduling Emergency Room Physicians" (by Michael W. Carter & Sophie D. LaPierre, Health Care Management Science 4, ...
62 views

### How to linearize the waiting time

My question is this: I want to express the time it takes for multiple servers to complete tasks for multiple users. I divide the time into $t$ time slots, and each task may occupy multiple time slots. ...
53 views

### Machine Scheduling with simultaneous processing of jobs

I am searching for a keyword that describes a machine scheduling problem in which machines are allowed to process multiple jobs at a time. Each job requires a given capacity on the machine. At any ...
1 vote
79 views

### Workforce scheduling MIP formulation

I am working on a large scale workforce scheduling problem with a large number of hard and soft constraints. The soft constraints are modeled as objectives with penalties for violating them. So my ...
1 vote
341 views

### About circuit constraints in OR - tools

I am trying to implement a scheduling problem to solve with CP-SAT from OR-tools. There, in particular, for every machine I want to add a time transition constraint from every task that is performed ...
214 views

### Quantifying a measure of standard deviation in MILP

I am trying to set up a MILP for production scheduling. The specific details I'm not sure are important but in general a plant has M machines running N parts, each part requiring W workers. The model ...
1 vote
68 views

### How to tackle online scheduling problems?

In scheduling problems, one usually has different options as objective functions (makespan, tardiness, etc). However, for any such type of scheduling problem one can consider an online version of it ...
1 vote
110 views

### Solver for Flexible Job Shop Scheduling Problem

I have a FJSSP that I would like to solve. However, the jobs in this problem have deadlines and in addition there are setup times between two jobs. Because of this, my objective function is not just ...
1k views

### Identifying the minimum number of required machines to schedule jobs

I am relatively new to the topic of optimization. I am currently trying to address the following problem: We are given a set of jobs, say $J$ with release times, deadlines and duration. Jobs can be ...
1 vote
70 views

### Scheduling tasks to minimize the total number of utilized cores

I currently have a scheduling algorithm which computes an approximate solution, say S, for the nominal scenario of a given problem instance, say N. Given that N changes in a way and becomes infeasible,...
43 views

### Creating a simple class in python for doing simulation of MDP

I am currently learning Python and doing object-oriented programming. I am trying to create a simulation for MDP. My problem statement is: "I have four stages of process. Each stage has two ...
141 views

### Definition of a modified scheduling problem where jobs are halted based on the shifts of employees

I am looking for the name of a scheduling problem in literature with some references. Here is the variant that I have in mind. Given a set of jobs, employees have certain shifts that they can work on ...
111 views

### constraint set for a scheduling problem with machine availability

I have a set of tasks $I$ with processing times $p_i, \forall i \in I$. There exists a set of machines $M$ and each machine has availability time ranges in a given time horizon. For instance, given a ...
558 views

### Alternative way to restrict an employee to work on multiple jobs

Suppose I have a set of employee $E$ and set of jobs $J$ in a given time horizon $T$. I would like to make sure that no employee works on multiple jobs where each job $e\in E$ takes a certain amount ...
526 views

### Doubles Round Robin Sorting Algorithm

Background: I have a group of 6 guys that get together and play pickleball every week. We play 2v2 and 2 players sit each game. We play 2 sets of 6 games each week (12 total games) - in each set, ...
124 views

### Rolling Horizon approach for solving a job scheduling problem

I am trying solve a scheduling problem adopting a rolling horizon approach. I have developed an Integer programming model and seek to speed up execution. I am seeking advice on beginner level ...
1 vote
121 views

### Gurobipy trip scheduling empty stop problem

I am trying to create an optimizing model for a roadtrip: 10 cities in 14 weeks. For each city I have: a distance matrix to every city The rain for every week of the year My goal is to minimize the ...
148 views

### How to code this constraint in CPLEX?

$$\sum_{j\in M}\sum_{k=i}^{\rm until}x_{aijk}\cdot b_{kj}=d_{ai},\quad\forall i\in N,\forall a\in B\cap A_1;{\rm until}=\min(i+v_a,n)$$ How to code this linear program in CPLEX?
312 views

### Determining the problem type - Vehicle Routing - Task assignment

I want to figure out what problem I'm dealing with so I can move in the right direction of research. I'm still at the very beginning of formulating the problem. What I've done so far is figure out ...
1 vote
48 views

### Objective function for employee assignation problem solved with simulated annealing

Imagine you have a total number of employees assigned to a task. Each task requires N quantity of employees for it to be 100% efficient, something like this: Each employee is assigned to a task in ...
319 views

### CP-SAT solver doesn't use all space available for scheduling

This problem is a continuation of this problem. The issue here is the solver doesn't use the whole space available for the scheduling and thus some jobs are not being scheduled. For example: we need ...
64 views

### Assignment/scheduling how to formulate considering job time and job cost

I have the following problem that I do not know how to formulate. There are a fixed number of workers $w_i \in W$ for $i \in [1…N]$. Also, there are a fixed number of jobs that must be assigned to ...
1 vote
134 views

### How to formulate fleet Assignment Problem?

I do want to formulate a fleet assignment problem. The following table is available It shows the departure/arrival location and time I am trying to find the min number of required planes to assign to ...
1 vote
84 views

### Minimize cost given working days/hours/required hours per job/start & end dates

I am trying to solve an optimization problem on Excel or Python. My constraints are the available number of employees (=20), the number of working days/month (=20), the number of working hours/day (=8)...
215 views

### Accelerating an integer programming model

I am working on a scheduling problem, where I am solving it through column generation. The pricing problem of this algorithm is an integer programming model as follows: \begin{equation} F_1 \Big\{V^...
555 views

### What is the difference bewteen CP and MILP approaches in Job Shop Scheduling?

My understanding is Constraint programming (CP) is a sub-set of MILP but in MILP we not only try to find a feasible solution (like CP) but also we should optimize an objective function. I do have a ...
163 views

### Scheduling optimization, Adding 4 day same shift and 3 day off weekly constraint

Am writing a small scheduling program in C# for a group of 7 staff who will be working in three shifts daily for 4 weeks. Am using the google OR-Tools Template, but i have modified it abit This is the ...
128 views

### Np-hard sequencing or packing problems with total ordering between elements

I would like to know if anyone is aware of any Np-hard problems in scheduling or packing where there is total ordering between tasks or items to be packed together. The objective can be anything. For ...
349 views

### Visualizing results to the RCPSP

Bot for getting better insight and reporting purposes, I am looking for a way to visualize results to the Resource-Constrained Project Scheduling Problem (RCPSP). I am aware that such results are most ...
214 views

### How to model this user packing problem?

I have a system with $N$ resources. There are $K$ users in the system demanding these resources. The demand of resources for a given user $k$, $d_k$ follows $d_k\in\{1,3,6\}$ The constraints for this ...
279 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 $1$ ...
143 views

### Project task scheduling based on available budget per period

I have a challenge that is a bit backwards from the usual labour resource leveling problem. In my case I have a fixed budget pool over a period to deliver some of the work packages (not enough per ...
I am working on a crew scheduling problem formulated as a MIP binary optimization where each employee is represented by a binary variable $X_{ids}$ s.t. $i \in I$ is $i$th employee, $d \in D$ is the ...