Parameters: found in or computed from the data

1
Aggregate Production Planning by Linear
Programming Terminology

• Parameters found in or computed from the data
• Decision variables unknowns to be determined
• Objective function the bottom line
• Constraints Satisfy demands and state
  relationships among variables
• Single Product model here can be generalized

2
Parameters find these in the data!

• dt amount of product demanded in period t
• pt productivity per worker in period t
• Lt unit labor cost per worker in period t
• ht unit hiring cost per worker in period t
• ft unit firing cost per worker in period t

3
Parameters find these in the data!

• ct inventory holding cost per unit per period
  in period t
• at backorder cost per item per period in period
  t

4
Decision Variables find values by solving the
model

• wt number of workers employed in period t
• ut number of workers hired between periods t-1
  and t
• vt number of workers fired between periods t-1
  and t
• it amount of product in inventory at the end of
  period t
• bt amount backordered at the end of period t

5
Initial values fixed variables find in data

• io initial inventory level
• wo initial workforce level

6
The LP Model
Minimize ?t (Ltwt htut ftvt ctit
atbt) s.t. ut - vt wt wt-1 for each period t
workforce change ptwt it-1 - it bt bt-1
dt for each period t demand balance wt, ut, vt,
it, bt ? 0 for each time period t nonnegativity
7
LP Example based Ch 13 problems
8
LP Example based on Ch 13 problems
9
The LP Model
Minimize ?t (128wt 500ut 1000vt 10it
100bt) s.t. u1 v1 w1 w0 workforce change,
period 1, 26.67wt io i1 b1 bo dt
demand balance, period 1 wt, ut, vt, it, bt ? 0
for each time period t nonnegativity