private PeriodInformation GetPredecessor(PeriodInformation currentPeriod)
{
if (currentPeriod.Period <= 1)
{
throw new InvalidOperationException($"There is no period before T={currentPeriod.Period}.");
}
// make query fail/throw if data is not correct.
return(this.PeriodInformation.Single(p => p.Period == currentPeriod.Period - 1));
}
/// <summary>
/// Initializes a new instance of the
/// <see cref="CapacitatedLotsizingModel"/> class and initializes all fields
/// </summary>
/// <param name="timesteps">
/// The time steps of the problem
/// </param>
public CapacitatedLotsizingModel(IEnumerable <PeriodInformation> timesteps)
{
this.PeriodInformation = timesteps.ToList();
this.Model = new Model();
// Binary indicator variables
this.y = new VariableCollection <PeriodInformation>(
this.Model,
this.PeriodInformation,
"y",
timestep => $"machines_active_in_period_{timestep.Period}",
timestep => 0,
timestep => 1,
VariableType.Binary);
// Continuous production variables
this.x = new VariableCollection <PeriodInformation>(
this.Model,
this.PeriodInformation,
"x",
timestep => $"produced_amount_period_{timestep.Period}",
timestep => 0,
timestep => timestep.Capacity,
VariableType.Continuous);
// Continuous inventory variables
this.s = new VariableCollection <PeriodInformation>(
this.Model,
this.PeriodInformation,
"s",
timestep => $"storage_end_of_period_{timestep.Period}",
timestep => 0,
// The maximum storage content is limited by the cumulative production.
// Since we need to fulfill demands from 'some' previous production,
// the maximum available stock amount can be reduced by the occuring demands.
timestep => this.ComputeStorageVariableUpperBound(timestep),
VariableType.Continuous);
// Create constraints
// flow balance: 'input == output'
// input: previous storage + production
// output: outgoing storage + demand
foreach (var periodInformation in this.PeriodInformation)
{
var flowBalanceExpression = this.x[periodInformation] - this.s[periodInformation] - periodInformation.Demand;
// 'previous storage' only exists after the initial period
if (periodInformation.Period > 1)
{
var previousPeriodInformation = this.GetPredecessor(periodInformation);
flowBalanceExpression += this.s[previousPeriodInformation];
}
this.Model.AddConstraint(
flowBalanceExpression == 0,
$"flow_balance_{periodInformation.Period}");
}
// Final inventory needs to be 0
var last = PeriodInformation.Last();
this.Model.AddConstraint(
this.s[last] == 0,
$"final_storage");
// Production volume 'x' of a time step can not be larger than the capacity
foreach (var periodInfo in this.PeriodInformation)
{
this.Model.AddConstraint(
this.x[periodInfo] <= periodInfo.Capacity * this.y[periodInfo],
$"production_capacity_{periodInfo}");
}
// Add the objective:
// Sum of the setup, production and inventory costs for all time steps
// \sum_{time step in Time steps} \{ x_{time step} * SetupCost_{time step} +
// y_{time step} * ProductionCost_{time step} +
// s_{time step} * InventoryCost_{time step} \}
this.Model.AddObjective(
new Objective(Expression.Sum(this.PeriodInformation.Select
(timestep => (y[timestep] * timestep.SetupCost +
x[timestep] * timestep.ProductionCost +
s[timestep] * timestep.InventoryCost))),
"totalCost",
ObjectiveSense.Minimize)
);
}
private double ComputeStorageVariableUpperBound(PeriodInformation currentPeriod)
{
// we cannot store more than 'theoretical production limit' - 'required amount' (=demand)
return(this.PeriodInformation.Where(pi => pi.Period <= currentPeriod.Period)
.Sum(pi => pi.Capacity - pi.Demand));
}
