I need to formulate a constraint for an uninterruptible operation in a linear mathematical form. this means, if this operation needs 4 time slots to be accomplished, they must assigned in a successive/sequential/consecutive way.
Thanks in advance..
Dear Zakaria, for "linear mathematical form" do you mean a linear equation or a simple mathematical model? If your time slots are (0, t1), (t1, t2), (t2, t3), (t3, t4), your constraint c(t) could have the mathematical expression c(t) = c1*chi(0,t1) + c2*chi(t1,t2) + c3*chi(t2,t3) + c4*chi(t3,t4), where ci are coefficients and chim(t) is the characteristics function of (tm-1, tm), that is chim(t) = 1 on (tm-1, tm), otherwise chim(t) = 0. Gianluca
Thanks Gianluca for your interest..
In my case, I assign time slots to customers by binary variable say u(i,t). It equals 1 if time slot t is assigned to customer i. Let's say for a customer, 4 time slots are required (N(i)=4). Generally, SUM u(i,t) should be >=N(i) for each customer. But I would like to guarantee that the four time slots are assigned in a successive way. For example time slots 7, 8, 9, and 10 are assigned to one customer.
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