Page 152 - Data Science Algorithms in a Week

136 Alfonso T. Sarmiento and Edgar Gutierrez

18,000 Units
23,000 Units
6,000 Units
37 People

16,000 Units
21,000 Units
2,000 Units
20 People
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Time (week)
Preforms WIP Level Units
Presses WIP Level Units
Finished Goods Inventory Units
Labor People

Figure 4. Behavior of variables of interest for the current policy.

For a customer order rate of 5,000 units/week the system starts out of equilibrium.
The behavior of the four variables of interest is depicted in Figure 4. Variables Preforms
WIP Level, Presses WIP Level and Labor have several oscillatory fluctuations. Variable
Finished Goods Inventory is starting to settle down, although it has not reach equilibrium
yet.
A new policy to minimize these oscillations will be determined by solving the
optimization problem presented in the next section.

Optimization Problem

This optimization problem considers the simultaneous stabilization of the following
state variables: Preforms WIP Level, Presses WIP Level, Finished Goods Inventory and
Labor according to the equations described in section 3.1.2.
Let x1 = Preforms WIP Level, x2 = Presses WIP Level, x3 = Finished Goods
Inventory, x4 = Labor
Let ai = the new equilibrium point associated to the i state variable (i = 1,..,4)
th
The following weights were assigned: w1 = 0.4, w2 = 0.4, w3 = 0.1, w4 = 0.1 to
represent the concern of management in the inventory and considering that variables x1
and x2 exhibit higher oscillations. The time horizon (T) considered was 30 weeks.
2  30  4  30 
Minimize ( J ) p   4.0  x s ) t (  a s dt    1.0  x s ) t (  a s dt 
p    
s 1 0  s 3 0 
Subject to