My question is about of constraint in problems of design or utilization.
An example is the design of a fleet of vehicles in problems of routing, the objective is the minimization of costs, the solution is the obtain of the quantity of vehicles and the trips of these vehicles to satisfy the demand of the clients.
Another example is the problem of uncapacitated facility location, the problem consists of a set of potential locations of plants, the solution is obtain the best locations for the plants.
In these problems the constraint of design are dependent of the objective function, an example is if a vehicle is used the constraint utilize a binary variable with value of 1 that indicate "this vehicle is utilized", but if the vehicle is not used this variable have the value of 0 (this vehicle is not used) or 1 , but the objective is the minimization of costs, this decision variable is equal zero for the objective
example
Xik .- binary variable of trips (i) of a vehicle (k)
Yk.- binary variable of utilization de vehicle (k)
m.- quantity of trips maxim
Sum (i,Xik)
Okey, excellent observation, these constraints could be me very important in my works
thanks by the information
I am familiar with Minimum weight design problems for structures. That could be another example.
In Minimum weight design problems, constraints are commonly imposed on design variables (ti or di)) to be larger than minimum gage thicknesses (ti0) or minimum diameters (di0).
for example,
Minimize structural weight which is an implicit function of (ti, di, materials, geometry, etc.)
where ti >=ti0 and di>=di0
You may view such classes of problems at:
https://www.researchgate.net/publication/259298637_Organization_of_PARS__A_structural_Resizing_System?ev=prf_pub
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