problem formulation for a production facility

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hamza addi

2023年06月02日 07:27

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I have a production unit for product A divided into four periods of the year: Q1, Q2, Q3, and Q4.

The constraints are as follows:

1. Production of product A in each period should not exceed the sum of the existing capacity (Capac_existante) and the additional capacity (Cap_unit * Unit_to_add[A]).

   • The production of product A in each period (p) should be less than or equal to the existing capacity plus the additional capacity: production[A, p] <= Capac_existante + Cap_unit * Unit_to_add[A], for each period p in periods.

2. The sum of the production of product A and the remaining demand (reliquant_demand[A, p]) should be equal to the total demand (total_demand[A, p]) in each period.

   • The sum of production and remaining demand should equal total demand: production[A, p] + reliquant_demand[A, p] = total_demand[A, p], for each period p in periods.

The decision variables are:

1. production[A, p]: The production quantity of product A in each period p.
2. Unit_to_add[A]: The additional units of capacity to be added for producing product A.
3. reliquant_demand[A, p]: The remaining demand for product A in each period p.

The objective function is to minimize the total cost, which includes the cost of adding units of capacity (cost * Unit_to_add) and the cost of the remaining demand (cost * reliquant_demand).

• The objective function to minimize the cost is: min(cost * Unit_to_add + cost * reliquant_demand).

i want to add the storage capacity and use it in the model. As if there is another storing location where i can store the amount of product A in the previous periods so it can be used for the next periods.

Thanks in advance

関連

• Modeling

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  Jaromił Najman

  • Gurobi Staff

  2023年06月05日 07:53

  Hi Hamza,

  Could you clarify what exactly your question is?

  The modeling idea looks good. There is lots of papers on production facility problems. Maybe you can find what you are looking for in the literature.

  Best regards, 
  Jaromił

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  hamza addi

  2023年06月05日 08:41

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  thanks for your answer,
  
  My question is giving the model i provided. I want to incorporate the possibility of storage in the previous periods, so it can be used in the next period when there is not enough capacity to fulfill the demand in that period.
  
  I'm having a bit of hard time modelling that. I will try to look into production facility problems.
  
  Thanks in advance

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  Jaromił Najman

  • Gurobi Staff

  2023年06月05日 09:39

  Usually, one introduces additional variables for warehouses and handles them similar to a producting facility with the difference that it does not produce but only holds products if they have been delivered to the warehouse before or if there are products available from the start. Maybe our facility location showcase gives you some inspiration (note that it does not account for production in given time periods).

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  hamza addi

  2023年06月05日 09:41

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  Okay thank you very much,
  
  That will help for sure! 

   

  Best regards.

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