My CPLEX Decision Variables shows "No Value"

Question

Good day, I’m currently using the CPLEX Studio IDE v.22.1.0 for my university project and it’s my first time. I am working on “Reducing Overcrowding in an Emergency Department” by optimizing five (5) hospital resources using a Stochastic Mixed Integer Program. I have successfully written the model but when I run, the decision variables shows “no value”. I would really appreciate some help with a correct version of the model please. Thank you

The model and dat.file is shown below

The Model:

{string} resources = {"Doctors", "Nurses", "Lab Scientists", "Imaging", "Beds"};

int capacity[resources] = [2, 3, 4, 2, 10];

// Defining the Indices for the Time Periods and Queues

//=====================================================

int t = ...;

int q = ...;

range timeperiods = 1..3;

range queues = 1..5;

// Defining the Scenarios

//=======================

range scenarios = 1..3;

// Defining the Arrival Rate of Patients and Service Capacity of Resources

//========================================================================

int arrivalrate[scenarios][timeperiods][queues] = ...;

int servicecapacity[scenarios][timeperiods][queues] = ...;

//Defining the Decision Variables

//===============================

dvar int R[timeperiods][resources];

dvar int W[scenarios][timeperiods][queues];

dvar int S[scenarios][timeperiods][queues];

//Objective

//=========

//Expressions

dexpr int WP = sum (s in scenarios, t in timeperiods, q in queues) W[s][t][q];

dexpr int SP = sum (s in scenarios, t in timeperiods, q in queues) S[s][t][q];

dexpr int NWP = WP - SP;

// Objective Function

//===================

minimize NWP;

//Constraints

//===========

subject to {

//Initialized Number of Patients Waiting in each Queue in each Scenario

//=====================================================================

forall (s in scenarios, t1 in timeperiods, q1, q2, q3, q4, q5, q in queues) {

W[s][t1][q1] == arrivalrate[s][1][q];

W[s][t1][q2] == 0;

W[s][t1][q3] == 0;

W[s][t1][q4] == 0;

W[s][t1][q5] == 0;

S[s][t1][q1] == 0;

S[s][t1][q2] == 0;

S[s][t1][q3] == 0;

S[s][t1][q4] == 0;

S[s][t1][q5] == 0;

}

//Update on the Number of Patients in each Queue at every Period

//==============================================================

forall (s in scenarios, t2, t3 in timeperiods, q1 in queues) {

W[s][t][q1] == W[s][t-1][q1] + arrivalrate[s][t][1] - S[s][t-1][q1];

}

forall (s in scenarios, t2, t3 in timeperiods, q1, q2 in queues) {

W[s][t][q2] == W[s][t-1][q2] + S[s][t-1][q1] - S[s][t-1][q2];

}

forall (s in scenarios, t2, t3 in timeperiods, q1, q3 in queues) {

W[s][t][q3] == W[s][t-1][q3] + S[s][t-1][q1] - S[s][t-1][q3];

}

forall (s in scenarios, t2, t3 in timeperiods, q2, q3, q4 in queues) {

W[s][t][q4] == W[s][t-1][q4] + S[s][t-1][q2] + S[s][t-1][q3] - S[s][t-1][q4];

}

forall (s in scenarios, t2, t3 in timeperiods, q2, q3, q5 in queues) {

W[s][t][q5] == W[s][t-1][q5] + S[s][t-1][q2] + S[s][t-1][q3] - S[s][t-1][q5];

}

// Bounds for Number of Patients Served in a Period

//=================================================

forall (s in scenarios, t in timeperiods, q in queues) {

S[s][t][q] <= W[s][t][q];  

}

// Limit for Number of Patients Served in each Queue at each Period

//=================================================================

forall (s in scenarios, t in timeperiods, q1 in queues) {

S[s][t][q1] <= sum (s in scenarios, t in timeperiods, q in queues) servicecapacity[s][t][1] * 1;    

}

forall (s in scenarios, t in timeperiods, q2 in queues) {

S[s][t][q2] <= sum (s in scenarios, t in timeperiods, q in queues) servicecapacity[s][t][2] * 1;

}

forall (s in scenarios, t in timeperiods, q3 in queues) {


S[s][t][q3] <= sum (s in scenarios, t in timeperiods, q in queues) servicecapacity[s][t][3] * 1;

}

forall (s in scenarios, t in timeperiods, q4 in queues) {


S[s][t][q4] <= sum (s in scenarios, t in timeperiods, q in queues) servicecapacity[s][t][4] * 1;

}

forall (s in scenarios, t in timeperiods, q5 in queues, r5 in resources) {   


S[s][t][q5] <= R[t][r5];

}

//Number of Staffing Hours Available for Each Human Resources (8 hours each)

//==========================================================================

forall (r1 in resources) {

sum (t in timeperiods) R[t][r1] <= 8;

}

forall (r2 in resources) {

sum (t in timeperiods) R[t][r2] <= 8;

}

forall (r3 in resources) {

sum (t in timeperiods) R[t][r3] <= 8;

}

//Availability of atleast One Resource of each Type in each Period

//================================================================

forall (t in timeperiods, r1 in resources) {

R[t][r1] >= 1;

}

forall (t in timeperiods, r2 in resources) {

R[t][r2] >= 1;

}

forall (t in timeperiods, r3 in resources) {

R[t][r3] >= 1;

}

forall (t in timeperiods, r4 in resources) {

R[t][r4] >= 1;

}

forall (t in timeperiods, r5 in resources) {

R[t][r5] >= 1;

}

}

The Data for testing the Model:

t = 3;

q = 5;

arrivalrate = [

[[14,10,95,34,23],

[90,80,60,34,23],


[50,30,20,34,23]],

[[14,13,11,34,23],

[50,30,20,34,23],


[12,31,27,34,23]],

[[14,10,95,34,23],

[90,80,60,34,23],


[50,30,20,34,23]],

];

servicecapacity = [

[[14,10,95,34,23],

[90,80,60,34,23],


[50,30,20,34,23]],

[[14,13,11,34,23],

[50,30,20,34,23],


[12,31,27,34,23]],

[[14,10,95,34,23],

[90,80,60,34,23],


[50,30,20,34,23]],

];

Answer 1

You model is not feasible and that is why you do not get any solution. If you name 2 constraints in order to get some relaxation / conflict

cta:W[s][t1][q1] == arrivalrate[s][1][q];

ctb:W[s][t1][q2] == 0;

Then you get a conflict between cta and ctb

If you comment

//forall (s in scenarios, t1 in timeperiods, q1, q2, q3, q4, q5, q in queues) {
//
//cta:W[s][t1][q1] == arrivalrate[s][1][q];
//
////ctb:W[s][t1][q2] == 0;
//
////ctc:W[s][t1][q3] == 0;
//
////ctd:W[s][t1][q4] == 0;
//
////cte:W[s][t1][q5] == 0;
////
////ctf:S[s][t1][q1] == 0;
////
////ctg:S[s][t1][q2] == 0;
////
////cth:S[s][t1][q3] == 0;
////
////S[s][t1][q4] == 0;
////
////S[s][t1][q5] == 0;
//
//}

//Update on the Number of Patients in each Queue at every Period

//==============================================================

//forall (s in scenarios, t2, t3 in timeperiods, q1 in queues) {
//
//ct2:W[s][t][q1] == W[s][t-1][q1] + arrivalrate[s][t][1] - S[s][t-1][q1];
//
//}

then you will get a feasible solution and adding constraint one by one you can see what is wrong with your constraints