How to model DummyJobs

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Martin Schönheit

January 31, 2022 09:26 Edited

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Hello :),

since I am new to Gurobi I have a question regarding how to model a Dummy Job in Gurobi for a distributed permutation flow shop scheduling problem. I tried to model the minimal sequence based model from Naderi & Ruiz (2010) (The distributed permutation flow shop scheduling problem). 

There is a need to define dummy jobs that preceed the first job in order to calculate the makespan correctly. A valid solution would be the following sequence for a scheduling problem of 5 jobs and 2 factories. 

[0, 3, 2, 0, 1, 5, 4]

Thereby the jobs 0 are the dummy jobs that separate the sequences in each factory. Jobs 3 and 2 are manufactured in factory 1 and jobs 1, 5 and 4 are manufactured in factory 2.

In theory thats crystal clear. I only face problems how the syntax has to be for generating a valid model with dummy jobs. One problem I face is conflicts regarding the indexing:

I defined a binary variable that starts at index to incorporate the dummy jobs.

J=range(0,NumberOfJobs)

x=mip.addVars(NumberOfJobs, NumberOfJobs, vtype=GRB.BINARY, name="x")

The problem is when modelling the dummy jobs this way, i get into trouble with the processing times, since indexing in Python starts with zero. At index zero there are the processing times of job 1. The problem is, when i define the processing times of the dummy job as additional job

NumberOfJobs = 5

NumberOfMachines = 2

p=[ [0,0],

    [4,4],

    [3,1],

    [2,2],

    [3,3],

    [5,5]]

 

I  distort the correct number of jobs. What is the proper way to model dummy jobs?

 

I thank you in advance.

Best regards Martin

0

• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  November 16, 2025 23:44

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
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  Jaromił Najman

  • Gurobi Staff

  February 01, 2022 09:24

  Hi Martin,

  From your post I assume that you don't need help with the modeling part but rather with the choice of correct indexing of your variables, is this correct?

  You don't have to use integer values for variable indices only. You could define your jobs + the dummy job as

  import gurobipy as gpm = gp.Model()
  
  NumberOfJobs=10
  indices = ["dummy"]
  for i in range(NumberOfJobs):
    indices.append(i)
  
  x = m.addVars(indices)
  
  # access variables
  print(x["dummy"])
  print(x[0])

  More often it is best to introduce a separate individual variable for special values, such as the dummy job in your case. So introducing an individual variable \(x_{d}\) might make modeling of your problem easier.

  Best regards, 
  Jaromił

   

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