VARIABLE DEFINITIONS
The dimensions of all variables are units of
product. The index t ranges from 1 to 6.
 P(t) :
production level in month t
 I(t):
inventory level at the end of month t
PARAMETERS
The problem statement identifies the following
parameters:
 D(t)
: demand in month t
 I(0)
: initial inventory level
 I(6)
: final inventory level
CONSTRAINTS
Conservation of flow: A basic requirement in
production planning problems is that product or material must be
conserved. In our case, this leads to the following production constraint
I(t1)
+ P(t) — I(t)
= D(t), t = 1,...,6
that states that the demand in month t
must be met by the production in month t plus the net change
in inventory.
Maximum inventory: This is simply an upper bound
constraint on the inventory levels.
I(t)
< 250, t = 1,...,6
Initial and final conditions:
I(0)
= 200, I(6)
= 100
Although I(0)
and I(6)
have constant values because of these constraints, we leave them
as variables in the model. Aggregate planning models, as well as
many others, are meant to be solved over and over again as time
advances and as parameters change. It is easier to treat the initial
and final values as constraints rather than replace the two variables
by their equivalent values.
NONNEGATIVITY
I(t)
> 0, P(t)
> 0 for all t
OBJECTIVE FUNCTION
Minimize Z = 100P1
+ 105P2
+ 110P3
+ 115P4
+ 110P5
+ 110P6
+ 4I1
+ 4I2
+ 4I3
+ 4I4
+ 4I5
+ 4I6
