sils -- LP lotsizing for the single item lot sizing problem
    Parameters:
        - T: number of periods
        - P: set of products
        - f[t]: set-up costs (on period t)
        - c[t]: variable costs
        - d[t]: demand values
        - h[t]: holding costs
    Returns a model, ready to be solved.

def sils(T,f,c,d,h):
    """sils -- LP lotsizing for the single item lot sizing problem
    Parameters:
        - T: number of periods
        - P: set of products
        - f[t]: set-up costs (on period t)
        - c[t]: variable costs
        - d[t]: demand values
        - h[t]: holding costs
    Returns a model, ready to be solved.
    """
    model = Model("single item lotsizing")
    Ts = range(1,T+1)
    M = sum(d[t] for t in Ts)
    y,x,I = {},{},{}
    for t in Ts:
        y[t] = model.addVar(vtype="I", ub=1, name="y(%s)"%t)
        x[t] = model.addVar(vtype="C", ub=M, name="x(%s)"%t)
        I[t] = model.addVar(vtype="C", name="I(%s)"%t)
    I[0] = 0

    for t in Ts:
        model.addCons(x[t] <= M*y[t], "ConstrUB(%s)"%t)
        model.addCons(I[t-1] + x[t] == I[t] + d[t], "FlowCons(%s)"%t)

    model.setObjective(\
        quicksum(f[t]*y[t] + c[t]*x[t] + h[t]*I[t] for t in Ts),\
        "minimize")

    model.data = y,x,I
    return model