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March 19th, 2016, 10:58 AM  #1 
Newbie Joined: Oct 2013 Posts: 29 Thanks: 1  Integer linear programming  auxillary binary range constraint variable
Hello, I'm currently facing this problem in ILP: I have two matrices of dimension 1*n of variables : $$s_i,x_i$$ I would like to create a matrix of new variables (dimension n*k, where k is an arbitrary natural number). Using constraints, I would like the variables to have the following function: $$z_{ij} = \begin{cases} 1 & \text{if } j \geq s_i \text{ and } j \leq x_i\\ 0 & \text{otherwise} \\ \end{cases} $$ For example: $$ s_i = 4 \\ x_i = 8 \\ z_{i5} = 1 $$ My question is, how would I formulate the constraints of $$z_{ij}$$? 

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auxillary, binary, constraint, integer, linear, programming, range, variable 
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