def eld_another(U,p_min,p_max,d,brk):
"""eld -- economic load dispatching in electricity generation
Parameters:
- U: set of generators (units)
- p_min[u]: minimum operating power for unit u
- p_max[u]: maximum operating power for unit u
- d: demand
- brk[u][k]: (x,y) coordinates of breakpoint k, k=0,...,K for unit u
Returns a model, ready to be solved.
"""
model = Model("Economic load dispatching")
# set objective based on piecewise linear approximation
p,F,z = {},{},{}
for u in U:
abrk = [X for (X,Y) in brk[u]]
bbrk = [Y for (X,Y) in brk[u]]
p[u],F[u],z[u] = convex_comb_sos(model,abrk,bbrk)
p[u].lb = p_min[u]
p[u].ub = p_max[u]
# demand satisfaction
model.addCons(quicksum(p[u] for u in U) == d, "demand")
# objective
model.setObjective(quicksum(F[u] for u in U), "minimize")
model.data = p
return model
def ssa(n, h, K, f, T):
"""ssa -- multi-stage (serial) safety stock allocation model
Parameters:
- n: number of stages
- h[i]: inventory cost on stage i
- K: number of linear segments
- f: (non-linear) cost function
- T[i]: production lead time on stage i
Returns the model with the piecewise linear relation on added variables x, f, and z.
"""
model = Model("safety stock allocation")
# calculate endpoints for linear segments
a, b = {}, {}
for i in range(1, n + 1):
a[i] = [k for k in range(K)]
b[i] = [f(i, k) for k in range(K)]
# x: net replenishment time for stage i
# y: corresponding cost
# s: piecewise linear segment of variable x
x, y, s = {}, {}, {}
L = {} # service time of stage i
for i in range(1, n + 1):
x[i], y[i], s[i] = convex_comb_sos(model, a[i], b[i])
if i == 1:
L[i] = model.addVar(ub=0, vtype="C", name="L[%s]" % i)
else:
L[i] = model.addVar(vtype="C", name="L[%s]" % i)
L[n + 1] = model.addVar(ub=0, vtype="C", name="L[%s]" % (n + 1))
model.update()
for i in range(1, n + 1):
# net replenishment time for each stage i
model.addConstr(x[i] + L[i] == T[i] + L[i + 1])
model.setObjective(quicksum(h[i] * y[i] for i in range(1, n + 1)),
GRB.MINIMIZE)
model.update()
model.__data = x, s, L
return model
def ssa(n,h,K,f,T):
"""ssa -- multi-stage (serial) safety stock allocation model
Parameters:
- n: number of stages
- h[i]: inventory cost on stage i
- K: number of linear segments
- f: (non-linear) cost function
- T[i]: production lead time on stage i
Returns the model with the piecewise linear relation on added variables x, f, and z.
"""
model = Model("safety stock allocation")
# calculate endpoints for linear segments
a,b = {},{}
for i in range(1,n+1):
a[i] = [k for k in range(K)]
b[i] = [f(i,k) for k in range(K)]
# x: net replenishment time for stage i
# y: corresponding cost
# s: piecewise linear segment of variable x
x,y,s = {},{},{}
L = {} # service time of stage i
for i in range(1,n+1):
x[i],y[i],s[i] = convex_comb_sos(model,a[i],b[i])
if i == 1:
L[i] = model.addVar(ub=0, vtype="C", name="L[%s]"%i)
else:
L[i] = model.addVar(vtype="C", name="L[%s]"%i)
L[n+1] = model.addVar(ub=0, vtype="C", name="L[%s]"%(n+1))
for i in range(1,n+1):
# net replenishment time for each stage i
model.addCons(x[i] + L[i] == T[i] + L[i+1])
model.setObjective(quicksum(h[i]*y[i] for i in range(1,n+1)), "minimize")
model.data = x,s,L
return model