Question: Help with this please

 

 Data:

·        Sale [i,t]: Matrix (10x24).
·        Minimum Production [i]: Matrix [10x1].
·        Initial Stock [i]: Matrix [10x1].
·        Productiveness [i,j]: Matrix[10x10]. This is producing i coming from producing j. The productiveness is higher when I was coming from producing the same product (in this case, the higher values are in the diagonal).
 
Variables:
  • Production[i,j,t]: production of product i the day t, coming from producing j. Takes the value 1 if i its produced and 0 otherwise. This is a 3D Matrix[10x10x24].
  • Stock[i,t]: stock for every day in month. It must be positive for all days.Matrix[10x24].
  • StockDays[i,t]: this is Stock[i,t]/Sale[i,t]. It must be positive for all days.Matrix[10x24].
  • GanttProduction[i,t]: This is important. This variable shows me a Gantt chart for the entire monthly production. It’s a Matrix [10x24].
 
Objective Function
 
t(∑i(∑jProductioni,j,t)*Productivenessi,j)
 
Constraints.
 
  1. t(∑jProductioni,j,t*Productivenessi,j)>=MinimumProductioni
 
  1. i(∑jProductioni,j,t)= 1
 
  1. Stocki,1 = InitialStocki +((∑jProductioni,j,1)*Productivenessi,j) – Salei,1
 
  1. Stocki,t= Stocki,t-1 + ((∑jProductioni,j,t)*Productivenessi,j) – Salei,t
 
  1. jProductioni,j,t-1 = ∑jProductionj,i,t
 
  1. StockDaysi,t = Stocki,t / Salei,t > = 0
 
  1. GanttProductioni,t = ∑jProductioni,j,t
 
All variables must be positives.
 
Here come the questions:
 
How can I write the variable Production in Maple (3D Matrix)?
I see that it’s difficult to write the number 5 constraint in maple…how can I do that? (Note that in this case and in constraint number 3, we have to take the time for the second day and go on).
And…How can I solve this with NLP???
 
Thanks for any help.
 

 

 

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