How to set constrains for this problem

[DanielZhang]

Hi guys,

I am having trouble to add the new constraints for this kind of problem. The work I am doing is managing the pump and valve running over the 24 hours from 8 am to 7 am the next day.

set<num> = {8,9,10,11,...7};

set PUMP = /Pump1 Pump2 Pump3/;

var PumpStation{TIME,PUMP} Binary;

The objective function is minimized power usage. 

The constraints I am working on is once the pump is on, it has to run for at least 2 hours.

The valve is the following :

var Valve{TIME} Binary;

var ValveFlow{TIME} integer;

con Flow_pb: ValveFlow[t] >= 200*Valve[t];

con Flow_lb: ValveFlow[t] <= 1000*Valve[t];

The new constraints adding in the valve is once the valve is open, the flow needs to be same for at least 4 hours.

Thank you.

[RobPratt]

Do you want the schedule to repeat every day?  I'm wondering about whether activities just before 7am need to "wrap around" to the beginning of the day.

[DanielZhang]

Hi there,

I only need it for one day. So starting at 8 am and ending at 7 am the next day. doesn't need to wrap it up. Thanks.

[RobPratt · Accepted solution]

I recommend declaring your time periods as follows, with the interpretation that 0 corresponds to 8am:

set TIME = 0..23;

Then declare the following additional binary variable and linear constraints:

var StartPumpStation{TIME,PUMP} binary;

/* if PumpStation[t,p] = 1 and PumpStation[t-1,p] = 0 then StartPumpStation[t,p] = 1 */
con StartPumpStationCon1 {t in TIME, p in PUMP: t-1 in TIME}:
   PumpStation[t,p] - PumpStation[t-1,p] <= StartPumpStation[t,p];

/* if StartPumpStation[t,p] = 1 then PumpStation[t-1,p] = 0 */
con StartPumpStationCon2 {t in TIME, p in PUMP: t-1 in TIME}:
   StartPumpStation[t,p] <= 1 - PumpStation[t-1,p];

/* if StartPumpStation[t,p] = 1 then PumpStation[t,p] = PumpStation[t+1,p] = 1 */
con StartPumpStationCon3 {t in TIME, p in PUMP, t2 in t..t+1: t+1 in TIME}:
   StartPumpStation[t,p] <= PumpStation[t2,p];

For the valve flows, define lower and upper bounds in the declaration:

var ValveFlow{TIME} integer >= 0 <= 1000;

Then declare another binary variable and linear constraints:

var StartValve {TIME} binary;

/* if Valve[t] = 1 and Valve[t-1] = 0 then StartValve[t] = 1 */
con StartValveCon1 {t in TIME: t-1 in TIME}:
   Valve[t] - Valve[t-1] <= StartValve[t];

/* if StartValve[t] = 1 then Valve[t-1] = 0 */
con StartValveCon2 {t in TIME: t-1 in TIME}:
   StartValve[t] <= 1 - Valve[t-1];

/* if StartValve[t] = 1 then Valve[t] = 1 */
con StartValveCon3 {t in TIME}:
   StartValve[t] <= Valve[t];

/* if StartValve[t] = 1 then ValveFlow[t] = ValveFlow[t+1] = ValveFlow[t+2] = ValveFlow[t+3] */
con StartValveCon4 {t in TIME, t2 in t..t+2: t+3 in TIME}:
   ValveFlow[t2] - ValveFlow[t2+1] <= (ValveFlow[t2].ub - ValveFlow[t2+1].lb) * (1 - StartValve[t]);
con StartValveCon5 {t in TIME, t2 in t..t+2: t+3 in TIME}:
   ValveFlow[t2+1] - ValveFlow[t2] <= (ValveFlow[t2+1].ub - ValveFlow[t2].lb) * (1 - StartValve[t]);

[DanielZhang]

Thank you very much Rob