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 constraints.
The demand in month t must be met
by the production in month t plus the net reduction
in inventory.
Maximum inventory: This is simply an upper bound constraint
on the inventory levels.
Initial and final conditions:
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
Objective Function
