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 2

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 2 2

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 2 2

4. find values by solving the model
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 2 2

5. “fixed variables”; find in data
Initial values:
“fixed variables”; find in data
io = initial inventory level
wo = initial workforce level 2 2

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