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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16
votes
4answers
794 views

Best model for precedence constraints within scheduling problem

Suppose I'm modeling a problem where I want to compute the start time bucket for some jobs. All time buckets have equal duration. There are some additional constraints involved but I also have to ...
12
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3answers
1k views

Number of aircraft to operate in an airline company

Suppose that an airline company has X planes, in general the companies keep a number of these aircraft (say 80% of X) in reserve in case of hazards. My question is how the airline companies compute ...
12
votes
3answers
799 views

How to model a mixed-integer linear programming formulation in Python using Gurobi?

I can remember that I spent some time in understanding how to formulate my first model. So I aimed at presenting a complete model here, wishing to save some time for students or researchers needing it....
12
votes
1answer
330 views

Job Shop Scheduling: what objectives are harder?

It is well known that job shop scheduling problems are notoriously hard from a computational point of view. Many papers exist for the makespan objective, and some report on min sum objectives (like ...
12
votes
1answer
97 views

Improving cuts from sub-problem with problem-specific hierarchical information

I'm solving an assignment-alike problem with a Logic-based Benders decomposition-alike (LBBD) method. The master problem provides an assignment, which is checked in the sub-problem. Define the set of ...
11
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5answers
806 views

How to implement a “generic” solver for scheduling problems?

I have been accepted for an internship for 6 months. The aim of this internship is to implement a "generic" solver for scheduling/production planning problems. This solver will bill a small prototype ...
10
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5answers
357 views

Dealing with non-overlapping constraints

Let us consider the following problem: Let $T$ be a set of tasks. Each task $t \in T$ has a duration $d_t$ and a target start time $s_t$. No two tasks can be executed in parallel. The objective is to ...
10
votes
1answer
179 views

Algorithm for workforce scheduling for call volumes

I am trying to solve a workforce scheduling and optimization problem. Available data: daily level forecasted call volumes, shift schedules, resource utilization at the aggregate level, AHT at ...
9
votes
2answers
415 views

What is the difference between job shop scheduling and resource constrained project scheduling?

I read here https://slideplayer.com/slide/3353960/ that RCPS is a generalized version of job shop scheduling. I'm new to this area and I'm trying to classify a specific variation of these types of ...
9
votes
2answers
320 views

What is this type of scheduling problem called?

I am currently working on software that deals with a specific type of scheduling problem, and I want to improve the scheduling algorithms that it uses. However, when I tried to research algorithms ...
9
votes
1answer
98 views

How to model 24 hours demand into a daily shift schedule?

I am working on a weekly staff scheduling optimization problem with 24/7 demand. The binary decision variable is: $X_{\text{staff},\,\text{day},\,\text{shift}}$ whether to assign the staff $s$ to day ...
9
votes
1answer
152 views

How to tackle large nurse scheduling problem?

I have a nurse-scheduling type of problem with a time span of a year and many employees. Formulation My main variables are: \begin{align}x_{e,t} &= \begin{cases}1 \text{ if employee } e \text{ ...
9
votes
1answer
172 views

How to classify and model this problem?

I was given the task to model the following problem and find a solution for it, but as I do not have any experience in this field, I already have trouble classifying it. There are a number of ...
8
votes
3answers
621 views

Maximize assigned tasks to each worker

In a scheduling problem I want to assign the maximum number of tasks to one worker before assigning it to another. For example, if I have $10$ tasks and $2$ workers, the best assignment would be $(10, ...
8
votes
1answer
392 views

Finding minimum time for vehicle to reach to its destination

Given a set of Vehicles with source and destination I need to find the minimum time of travel for all the vehicles, there are also some charging stations and its necessary for vehicles to charge 1 ...
8
votes
1answer
118 views

Workforce Scheduling problem - Modelling to minimize resources

I am working on a scheduling program for a service desk. I want to decide the number of people required to come in at each shift. The data I have is: There are 4 overlapping shifts Arrival pattern at ...
8
votes
1answer
104 views

Scheduling events in order to maximize preparation time

Problem statement I'm given a set of events $E$, and $\forall e \in E$ also: a set of plausible dates on which the event can happen $D_e$ importance (weight) $w_e$ ideal preparation time duration $...
8
votes
1answer
128 views

Extract info from Gurobi binary variables during run-time

Actually the question below is not specific to Gurobi, but that's the tool I am using. Consider a scheduling problem where a 2D array of binary variables $Z(i,v)$ is defined, where $i$ is index of ...
8
votes
1answer
102 views

What class of scheduling problem models jobs which require multiple machines simultaneously?

In the Flow/Job Shop problems, and other related scheduling problems, a common assumption is that at any given time, a particular job will be being processed on at most one machine (usually... none). ...
8
votes
0answers
81 views

Examples for a kind of “set family hitting” problem

Given a ground set, say $[n]=\{1,2,\dots,n\}$, and a collection of subset families $\mathcal F_i\subseteq 2^{[n]}$, $i=1,2,\dots,m$, I want to select $m$ sets $B_i\in\mathcal F_i$ such that the ...
7
votes
1answer
1k views

How to use the least number of colours to colour different routes of a bus route such that no two intersecting routes will have the same colour

I would like to know of a method in which if provided say 10 routes with details regarding which route intersects with which another route, we can use the least number of colours to colour the routes, ...
7
votes
2answers
177 views

CPLEX CP Optimizer Java API function missing

I can not seem to find the needed functions to model the following problem through the Java API (CP Optimizer): a machine that has downtime and sequence-dependent setup times, with the extra ...
7
votes
2answers
570 views

Finding an Objective Function for Assigning Employees to Sequence Dates

I am using a mixed-integer-program to schedule employees to projects. These projects can have a time window to get completed from a few weeks to a few months. At the moment I am working in a ...
7
votes
1answer
95 views

Variant of job shop scheduling problem

I'm looking to identify a problem in the literature that I'm currently solving. I have a set of jobs each having a set of operations. Each operation has a duration. An operation may be done by a ...
6
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3answers
373 views

Scheduling problem data generation

I compare the strengths and weaknesses of paradigms and approaches within those paradigms for solving machine scheduling problems. The amount of real-world data I have is limited and (random) ...
6
votes
3answers
113 views

Trouble with scheduling problem assumptions

Reading the famous book by Pinedo, I came across : Usually, the subscript $j$ refers to a job while the subscript $i$ refers to a machine. If a job requires a number of processing steps or ...
6
votes
2answers
114 views

Is this another variant of Job Shop Scheduling Problem?

The problem is as follows: there are $n$ jobs $\mathcal{J}=\{J_1,\ldots, J_n\}$, each of which could be done. There are $k$ machines $M_1,\ldots,M_k$ that work in parallel, independently of each other,...
6
votes
1answer
231 views

Multi-period linear dynamic programming with differing in-period dependencies and changes

I’m not sure if I’m wording this right but in a nutshell, my problem is: I’m modelling potential actions a boat owner can do to their boat. Let’s say he wants to know over the 50 year lifespan of the ...
6
votes
1answer
88 views

CVRP with vehicles blocking each other

I have a standard CVRPTW (capacitated vehicle routing problem with time windows). The instance is given by a (not complete) graph $G$ with weighted $w$ directed edges $e \in E$, and I have a limited ...
6
votes
1answer
112 views

Optimal Energy Charging/discharging Scheduling Problem

I'm new to IBM CP optimizer. I want to make charging / discharging scheduling based on cost (value will change on time) and my objective function is $$\sum_{t=1}^{24}\sum_{j=1}^5x(1)^{(t,j)}x(2)^{(t,j)...
6
votes
1answer
124 views

How to solve this variant of RCPSP

We have $m$ projects in parallel that require shared resources the resources has time varying capacities (i.e $B_{rt}$ is the units of resource $r$ available in period $t$). For each project there is $...
6
votes
0answers
76 views

Building the Scheurman's Model II constraints for a multi period linear program

Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also ...
6
votes
0answers
114 views

Modelling issue with precedence constraint in OR-Tools

I'm trying to solve an RCPSPDc model It is infeasible, although Ilog Cplex solves it, so I think I have a modelling issue. I have more constraints but the precedence is the one that makes it ...
5
votes
3answers
561 views

How to determine if this problem is NP-HARD or NP-COMPLETE?

Suppose that I have a pool with N nodes and I have to move the nodes one by one to another pool. For each move, consider a value on the edge linking the two pools. The goal is to find a order of nodes ...
5
votes
1answer
133 views

Scheduling with transition costs - DOCPLEX

I am dealing with a kind of scheduling problem. I have a set of tasks to be executed by a set of machines. It is known that different machines are able to execute the same task, but each machine can ...
5
votes
0answers
76 views

Quantifying Feasibility

I have a scheduling model formulation ( experimental setup) that takes in product states as input (sample points) and checks the model status (response) and returns feasible or infeasible. My plan is ...
4
votes
3answers
633 views

Job shop scheduling advice

I changed jobs recently to a manufacturing firm. Job shop scheduling is made 100% manually and intuitively in Excel. Very time consuming and they have no idea if the schedule made is something close ...
4
votes
1answer
218 views

Scheduling Optimization Problem

I want to solve below optimization problem. This is scheduling problem where I seek to complete as many of the jobs $\xi_l$ (objective function and constraint 1), with $T_C$ being the last time until ...
4
votes
1answer
100 views

Is it possible to solve VRP using OR-Tools CpModel, instead of RoutingModel?

Is it possible to solve VRP using OR-Tools CpModel, instead of RoutingModel? I want to do synchronized VRP, which is combining vehicle routing and scheduling constraints
4
votes
1answer
134 views

How exactly does OptionalIntervalVar work in OR-Tools?

I created OptionalIntervals for a number of tasks: ...
4
votes
1answer
60 views

Business/industrial applications of the single machine scheduling problem

There is a lot of resources talking about the applications of scheduling in business in general. I would like to know about the applications of the particular case of single machine scheduling. Any ...
4
votes
1answer
213 views

XOR constraint representation

In an scheduling optimization problem, for job $l$, $\xi_l$ is binary variable that $\xi_l=1$ shows job $l$ is selected. $t_{r,l}$ and $t_{e,l}$ are registration time and time that job is completed. ...
4
votes
0answers
61 views

Best known results on the flexible jobshop benchmarks

Is there a website that compiles the best known results on the flexible jobshop problem ? I know there was a blog post/article by Quintiq, a (deleted) blog post on CP Optimizer, some more recent ...
3
votes
2answers
340 views

How to add logical OR constraint in OR-Tools?

Let's say nurses normally do 1 shift for d in all_days: for s in all_shifts: model.Add(sum(shifts[(n, d, s)] for n in all_nurses) == 1) But I want to ...
3
votes
2answers
98 views

Relaxation and complexity of two formulations

I have two different MILP formulations for the same scheduling problem with the same complexity but with different running times. Why it is recommended to compare the relaxed versions of each ...
3
votes
1answer
75 views

What are the flow based formulations?

What are the flow-based formulations? For what optimization problems are they applied, and in which form? Which are the specificities of such a formulation? Also, the same question for the time staged ...
3
votes
2answers
96 views

How is this problem called in literature?

I have a scheduling problem but rather than having a fixed duration of each task, we have another "concept" that verifies the following property. Let's say task A requires a default 200 ...
3
votes
2answers
123 views

Limit number of switches in employee scheduling problem

Here is a scheduling problem I need to solve. Given the demand for 2 positions in 1 week with 3 shifts per position, I need to allocate the employees accordingly with some extra operational ...
3
votes
1answer
127 views

Resource constraint with MIP model

My question is how to model a resource constraint with MIP model (how should I modify it?) A factory is making blocks. If there is space left at that time, the block can be assembled. (If the factory ...
3
votes
1answer
112 views

Space constraint in scheduling problem

I'm studying an MIP model with a scheduling problem and I'm wondering if the space constraint is correct. If there is space in the factory at that time, the block can be processed, where $i$ is the ...