2.20
Input parameters. Let
C = set of can types = {S, L}
R = set of resources = {Plastic, Machine, Painting}
T = set of time periods = {1, 2, 3, 4}
dit = demand for type i cans in month t
for i ∈ C and t ∈ T
Ii0 = initial number of type i cans
for i ∈ C
ci = cost of producing 1 type i can
for i ∈ C
si = storage cost for 1 type i can
for i ∈ C
ai = inventory space required for 1 type i can
for i ∈ C
rki = amount of resource k required to make 1 type i can
bk = amount of resource k available in each period
for k ∈ R and i ∈ C
for k ∈ R
A = inventory space available in each period
Note that cS = 10, cL = 15, sS = 1, sL = 2, IS0 = 50, IL0 = 75, aS = 3, aL = 6, bMachine = 650,
bPainting = 350, bPlastic = 30000, and A = 10000. The demands dit for i ∈ C and t ∈ T and resources
required rki for k ∈ R and i ∈ C are as given in the problem description.
Decision variables.
Pit = number of type i cans produced in month t
for i ∈ C and t ∈ T
Iit = number of type i cans stored at the end of month t for i ∈ C and t ∈ T
Objective function and constraints.
XX
min
ci Pit + si Iit
(total cost)
i∈C t∈T
s.t.
Ii(t−1) + Pit = Iit + dit
X
ai Iit ≤ A
for i ∈ C and t ∈ T
(inventory balance)
for t ∈ T
(inventory space)
for t ∈ T, k ∈ R
(resource constraints)
for i ∈ C and t ∈ T
(nonnegativity)
i∈C
X
rki Pit ≤ bk
i∈C
Pit ≥ 0, Iit ≥ 0
1