public ConstraintSolverSolution SolveB(int maxSolutions = 100)
{
ConstraintSystem S = ConstraintSystem.CreateSolver();
//Define how many agents may work per shift
CspDomain cspShiftsForceDomain = S.CreateIntegerInterval(first: 0, last: MaxAgents);
//Decision variables, one per shift, that will hold the result of how may agents must work per shift to fullfil requirements
CspTerm[] cspShiftsForce = S.CreateVariableVector(domain: cspShiftsForceDomain, key: "force", length: Shifts.Count);
//index shifts, their variable CspTerm by the shift's relative no (0=first, 1=second, etc)
ShiftsX = new Dictionary <Models.Shift, CspTerm>();
int i = 0;
Shifts.ForEach(x => { ShiftsX.Add(x, cspShiftsForce[i]); i++; });
//Constraint - Agents on every half hour must be >= requirement for that half hour
List <CspTerm> cspHalfHourExcess = new List <CspTerm>();
foreach (var halfHourRq in HalfHourRequirements)
{
//find shifts including that halftime, and calculate their sum of force
List <CspTerm> cspActive = new List <CspTerm>();
foreach (var entry in ShiftsX)
{
if (entry.Key.IncludesHalfHour(halfHourRq.Start))
{
cspActive.Add(entry.Value);
}
}
//add constraint for sum of force of active shifts on that halfhour
//if we need agents but no shifts exists for a halfhour, do not add a constraint
if (cspActive.Count > 0)
{
var s = S.Sum(cspActive.ToArray()) - S.Constant(halfHourRq.RequiredForce);
S.AddConstraints(
S.LessEqual(constant: 0, inputs: s)
);
cspHalfHourExcess.Add(s);
}
}
//var goal = S.Sum(shiftsX.Values.ToArray());
//bool ok = S.TryAddMinimizationGoals(goal);
var goalMinExcess = S.Sum(cspHalfHourExcess.ToArray());
bool ok = S.TryAddMinimizationGoals(goalMinExcess);
ConstraintSolverSolution solution = S.Solve();
Console.WriteLine();
GetSolutionsAll(solution: solution, maxSolutions: maxSolutions);
if (ShiftsForce == null || ShiftsForce.Count == 0)
{
Console.WriteLine("No solution found");
}
if (ShiftsForce != null)
{
foreach (var shiftForceEntry in ShiftsForce)
{
ShowSolution(no: shiftForceEntry.Key, shiftsForce: shiftForceEntry.Value, showAgents: true, showSlots: false);
}
}
return(solution);
}
public SimplexSolver PrepareSimplexSolver(int maxAgents, out Dictionary <Models.Shift, int> shiftsExt, out int vidGoal)
{
var SX = new SimplexSolver();
var maxRq = HalfHourRequirements.Max(x => x.RequiredForce);
var sumRq = HalfHourRequirements.Sum(x => x.RequiredForce);
shiftsExt = null;
////goal: total no of agents
//int ridgoal;
//SX.AddRow(key: "goal", vid: out ridgoal);
//SX.SetBounds(ridgoal, lower: 0, upper: maxAgents); //total agents must range from 0 to max agents available
//SX.AddGoal(vid: ridgoal, pri: 1, fMinimize: true); //minimize total number of agents for that day
//goal: total no of agents, minimize overtime
int ridgoal;
SX.AddRow(key: "goal", vid: out ridgoal);
SX.SetBounds(ridgoal, lower: 0, upper: Rational.PositiveInfinity); // upper: maxAgents); //total agents must range from 0 to max agents available
SX.AddGoal(vid: ridgoal, pri: 2, fMinimize: true); //minimize total number of agents for that day
//goal2: Minimize excess force
int ridexcess;
SX.AddRow(key: "excess", vid: out ridexcess);
SX.SetBounds(ridexcess, lower: 0, upper: sumRq); //allow excess from 0 to sum of all requirements
SX.AddGoal(vid: ridexcess, pri: 1, fMinimize: true); //try to minimize excess time
var shiftsX = new Dictionary <Models.Shift, int>();
int i = 0;
Shifts.ForEach(x => {
int vid;
SX.AddVariable(key: string.Format("{0}. {1} {2:hh}:{2:mm} - {3:hh}:{3:mm}", i + 1, x.Name, x.Start, x.End), vid: out vid);
//the no of agents on each shift may not exceed to max requirements
SX.SetBounds(vid: vid, lower: 0, upper: maxRq);
shiftsX.Add(x, vid);
//SX.SetCoefficient(vidRow: ridgoal, vidVar: vid, num: 1); //normal weight: all shifts are the same
SX.SetCoefficient(vidRow: ridgoal, vidVar: vid, num: x.Duration.Hours <= 8 ? 1 : 10); //weights per shift: overtime = *10 more expensive than normal shifts
i++;
});
//Constraint - Agents from every active shift on every half hour must be >= requirement for that half hour
HalfHourRequirements.ForEach(hh =>
{
List <int> vidShiftsActive = new List <int>();
foreach (var entry in shiftsX)
{
if (entry.Key.IncludesHalfHour(hh.Start))
{
vidShiftsActive.Add(entry.Value);
}
}
//add constraint for sum of force of active shifts on that halfhour
//if we need agents but no shifts exists for a halfhour, do not add a constraint
if (vidShiftsActive.Count > 0)
{
int ridHalf;
SX.AddRow(key: string.Format("{0:hh}:{0:mm} [{1}]", hh.Start, hh.RequiredForce), vid: out ridHalf);
//specify whichs shifts contributes to half hour's total force
vidShiftsActive.ForEach(vidShift =>
{
SX.SetCoefficient(vidRow: ridHalf, vidVar: vidShift, num: 1);
SX.SetCoefficient(vidRow: ridexcess, vidVar: vidShift, num: 1);
});
//each 30' span, must have at least as many required agents
SX.SetBounds(vid: ridHalf, lower: hh.RequiredForce, upper: Rational.PositiveInfinity);
}
});
shiftsExt = shiftsX;
vidGoal = ridgoal;
return(SX);
}
public ConstraintSystem PrepareCspSolver()
{
ConstraintSystem S = ConstraintSystem.CreateSolver();
//Define how many agents may work per shift
var maxRq = HalfHourRequirements.Max(x => x.RequiredForce);
CspDomain cspShiftsForceDomain = S.CreateIntegerInterval(first: 0, last: maxRq);
//var cspShiftsForceDomain = S.CreateIntegerSet(new int[] { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40 });
//Decision variables, one per shift, that will hold the result of how may agents must work per shift to fullfil requirements
CspTerm[] cspShiftsForce = S.CreateVariableVector(domain: cspShiftsForceDomain, key: "force", length: Shifts.Count);
//index shifts, their variable CspTerm by the shift's relative no (0=first, 1=second, etc)
ShiftsX = new Dictionary <Models.Shift, CspTerm>();
int i = 0;
Shifts.ForEach(x => { ShiftsX.Add(x, cspShiftsForce[i]); i++; });
//Constraint - Agents from every active shift on every half hour must be >= requirement for that half hour
List <CspTerm> cspHalfHourExcess = new List <CspTerm>();
foreach (var halfHourRq in HalfHourRequirements)
{
//find shifts including that halftime, and calculate their sum of force
List <CspTerm> cspActive = new List <CspTerm>();
foreach (var entry in ShiftsX)
{
if (entry.Key.IncludesHalfHour(halfHourRq.Start))
{
cspActive.Add(entry.Value);
}
}
//add constraint for sum of force of active shifts on that halfhour
//if we need agents but no shifts exists for a halfhour, do not add a constraint
if (cspActive.Count > 0)
{
//var s = S.Sum(cspActive.ToArray()) - S.Constant(halfHourRq.RequiredForce);
S.AddConstraints(
S.LessEqual(constant: halfHourRq.RequiredForce, inputs: S.Sum(cspActive.ToArray()))
);
//cspHalfHourExcess.Add(s);
}
}
//if (false && cspHalfHourExcess.Count > 0)
// S.AddConstraints(
// S.LessEqual(constant: 0, inputs: S.Sum(cspHalfHourExcess.ToArray()))
// );
bool xx = true;
if (xx)
{
var goal = S.Sum(ShiftsX.Values.ToArray());
bool ok = S.TryAddMinimizationGoals(goal);
}
else
{
//S.RemoveAllMinimizationGoals();
var goalMinExcess = S.Sum(cspHalfHourExcess.ToArray());
bool ok = S.TryAddMinimizationGoals(goalMinExcess);
}
return(S);
}
public Solution alternative_solve(out Dictionary <Models.Shift, Decision> shiftsN, out Dictionary <Models.Shift, Decision> shiftsO)
{
SolverContext SC = SolverContext.GetContext();
Model model = SC.CreateModel();
var maxRq = HalfHourRequirements.Max(x => x.RequiredForce);
shiftsN = shiftsO = null;
//split shifts into two Dictionaries (each dict holds each Shift as key and the Decision variable as Value)
var normal_shifts = new Dictionary <Models.Shift, Decision>(); //for normal shifts
int i = 0;
Shifts.ForEach(x => {
Decision des = new Decision(Domain.IntegerRange(0, maxRq), string.Format("{0}_{1}", x.Name, i));
normal_shifts.Add(x, des);
model.AddDecision(des);
i++;
});
var overtime_shifts = new Dictionary <Models.Shift, Decision>(); //for overtime shifts
i = 0;
OvertimeShifts.ForEach(x => {
Decision des = new Decision(Domain.IntegerRange(0, maxRq), string.Format("{0}_{1}", x.Name, i));
overtime_shifts.Add(x, des);
model.AddDecision(des);
i++;
});
List <Decision> excess = new List <Decision>(); //used to calculate sum of excess values
HalfHourRequirements.ForEach(hh =>
{
var ShiftsActive = new List <Decision>();
foreach (var entry in normal_shifts)
{
if (entry.Key.IncludesHalfHour(hh.Start))
{
ShiftsActive.Add(entry.Value);
excess.Add(entry.Value);
}
}
foreach (var entry in overtime_shifts)
{
if (entry.Key.IncludesHalfHour(hh.Start))
{
ShiftsActive.Add(entry.Value);
excess.Add(entry.Value);
}
}
//add constraint for sum of force of active shifts on that halfhour
//if we need agents but no shifts exists for a halfhour, do not add a constraint
if (ShiftsActive.Count > 0)
{
var sum_constr = new SumTermBuilder(ShiftsActive.Count);
ShiftsActive.ForEach(s => sum_constr.Add(s));
var constr = sum_constr.ToTerm() >= hh.RequiredForce;
model.AddConstraint(string.Format("_{0:hh}{0:mm}", hh.Start), constr);
//constr = sum_constr.ToTerm() <= hh.RequiredForce * 2.0;
//model.AddConstraint(string.Format("limitconst_for_{0:hh}{0:mm}", hh.Start), constr);
}
});
//Constrain maximum number of agents working 8hour shifts
var max_agents_constraint = new SumTermBuilder(Shifts.Count);
foreach (var entry in normal_shifts)
{
max_agents_constraint.Add(entry.Value);
}
var ma_constr = max_agents_constraint.ToTerm() <= MaxAgents;
model.AddConstraint("Max_agents_constraint", ma_constr);
//1st goal: Minimize overtime shifts (if work manageable by normal shifts, no overtime shifts will be used)
var overtime_obj = new SumTermBuilder(OvertimeShifts.Count);
foreach (var entry in overtime_shifts)
{
overtime_obj.Add(entry.Value);
}
model.AddGoal("Minimize_overtime", GoalKind.Minimize, overtime_obj.ToTerm());
//2st goal: Minimize normal shifts
var normal_obj = new SumTermBuilder(Shifts.Count);
foreach (var entry in normal_shifts)
{
normal_obj.Add(entry.Value);
}
model.AddGoal("Minimize_normal", GoalKind.Minimize, normal_obj.ToTerm());
//3rd goal: Try to minimize excess
var sumReqs = HalfHourRequirements.Sum(x => x.RequiredForce);
model.AddGoal("Minimize_excess", GoalKind.Minimize, Model.Sum(excess.ToArray()) - sumReqs);
SimplexDirective simplex = new SimplexDirective();
Solution solution = SC.Solve(simplex);
shiftsN = normal_shifts;
shiftsO = overtime_shifts;
return(solution);
}