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I have written two constraints for Mixed integer linear problem. I am working on the scheduling problem i.e., Scheduling of hybrid appliances.

For example, the washing machine is appliance indicated by i, which has set of the task like washing, rinsing and spinning etc., indicated by j. Here we divided the 24 hours into 96-time slots each time slot has 15 min indicated by k.

The constraint 1. Says that the tasks of the task of the appliance have to exclusive. It means they should not overlap with each other.

$X_{k,u,i,j} + Y_{k,u,i,j} + Z_{k,u,i,j}$ $\leq$ $X_{k,u,i,j-1} + Y_{k,u,i,j-1} + Z_{k,u,i,j-1}$ --------------- 1

$j \in \{2,. . .n_i\}$

The constraint 2 says that the task of the appliances has to sequential and operate continuously without any interruption.

$\sum_{k=t}^{t+H_i -1} \sum_{j=1}^{n_i} X_{k,u,i,j} + Y_{k,u,i,j} + Z_{k,u,i,j} \geq 1$ --------------- 2

$\forall i \in N$,

$j \in \{1,. . .n_i\}$,

$k = \{1,2,. . .96\}$,

$u \in \{1,2,3. .. 50\}$,

$X_{k,u,i,j}, Y_{k,u,i,j}, Z_{k,u,i,j} \in \{0,1\}$

$X_{k,u,i,j}$ indicates whether task j of appliance i at time slot k processed by electricity or not; 1 = task processed; 0 = not processed

$Y_{k,u,i,j}$ indicates whether task j of appliance i at time slot k processed by natural gas or not; 1 = task processed; 0 = not processed

$Z_{k,u,i,j}$ indicates whether task j of appliance i at time slot k processed by hot water or not; 1 = task processed; 0 = not processed

i index of the appliance.

j index of the task of the appliance.

k index of the time slot(1time slot = 15 min).

u index of each home.

$H_{i}$ is the operation time of the appliance i.

Do both constraints satisfies my condition?.

It would be great if somebody validates.

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    $\begingroup$ This kind of "here's my answer -- is it correct?" question isn't well-suited to Stack Exchange. We're really looking for questions that will be useful to people other than just the person who asked them. Being blunt, grading students' work is the least interesting part of teaching and the part people are least likely to want to do for free in their spare time. I realise you're not literally asking us to grade your work but it's the same principle. $\endgroup$ – David Richerby Aug 29 '18 at 10:24