Information Technology Reference
In-Depth Information
⎞
revenue
⎛
⎞
⎠
A,Q
a
,p<Z
aqs
Z
aqs
ζ
aqp
⎝
⎠
(8)
The objective function (Equation 8) maximizes utility minus cost plus revenue.
Constraints
γ
cst
≤
1
∀
c
∈
C, s
∈
S
(9)
T
B
apq
≤
1
∀
a
∈
A, q
∈
Q
a
(10)
P
Z
apq
≤
1
∀
a
∈
A, q
∈
Q
a
(11)
P
⎛
⎞
⎛
⎞
⎝
⎠
−
⎝
⎠
γ
cst
G
at
≤
β
apq
ζ
aqs
C,T
Q
a
,p>B
aqs
Q
a
,p<Z
aqs
∀
a
∈
A, s
∈
S
(12)
Equation 9 limits each client to one package in each scenario. Equation 10 prevents the
agent from placing more than one bid for the same (auction, quantity) pair. Equation
11 prevents the agent from placing more than one ask for the same (auction, quantity)
pair. Equation 12 prevents the agent from allocating goods that it does not own (number
allocated
≤
number bought
−
number sold).
A.2
TAC SCM Production Scheduling Problem
Index Sets
i
∈
I
indexes the set of RFQs.
j
∈
J
indexes the set of SKUs.
n
∈
N
indexes the set of scenarios.
Constants
C
is the production capacity. SKU
s
i
, quantity
q
i
,price
p
i
, and penalty
ρ
i
.
c
j
is the number of cycles required to produce SKU
j
.
ω
in
issetto1ifRFQ
i
becomes
an order in scenario
n
.
Decision Variables
v
j
is an integer variable indicating the amount of SKU
j
to pro-
duce.
z
in
is a boolean variable with value 1 if we fill order
i
in scenario
n
.
Objective Function
max
z
(
p
i
+
ρ
i
)
z
in
(13)
n
i
The objective function (Equation 13) maximizes the revenue of allocating assembled
computers to orders across scenarios. Note that the true value is obtained by subtract-
ing the quantity
i
ρ
i
from the given value; but changing the objective function by a
constant does not affect the solution.
