Mathematical modeling and operational research. Also, I have a parameters L(k) and U(K), showing lower bound and upper bound for interval K (k=1,2,3)

Brenda Jordan

Brenda Jordan

Answered question

2022-11-05

Mathematical modeling and operational research
I have a variable TE which 0 T E 180
Also, I have a parameters L(k) and U(K), showing lower bound and upper bound for interval K ( k = 1 , 2 , 3 )
The value of these parameters are as follows: L ( 1 ) = 0 K ( 1 ) = 60 , L ( 2 ) = 60 K ( 2 ) = 120 , L ( 3 ) = 120 K ( 3 ) = 180
I need to find the related range of the variable TE. For example,
if ` T E = 12`, then ` K = 1`
if ` T E = 150`, then ` k = 3`
Which mathematical constraint(s) do this?

Answer & Explanation

Nigerkamg5

Nigerkamg5

Beginner2022-11-06Added 20 answers

Step 1
Depends on how you prefer writing down your answer. Boolean logic is a perfectly valid way of writing mathematical expressions. For example, the logical "box" function, taking only the values 0 or 1 can be defined as follows:
B O X ( T E , L , U ) = ( T E > L ) & ( T E < U )
Step 2
Then your entire choice can be written as
k ( T E ) = 1 B O X ( T E , L 1 , U 1 ) + 2 B O X ( T E , L 2 , U 2 ) + 3 B O X ( T E , L 3 , U 3 )
which will always work as long as the intervals do not overlap. One can also use the step-function to define the box-function. Defining a piecewise function, as you did in the description is also mathematically perfectly valid. Take your pick

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