Multi Suppliers Purchasing System

Standard Information

• Vairables:
  • CSold[k] new input introduced from C[k]*Sold[k]
    • C[k] an input at time k (Sell Price)
    • Sold[k] an input att time k (Amount Sold)
  • xa[k] an input at time k (Purchasing from Supplier A)
  • xb[k] an input at time k (Purchasing from Supplier B)
  • xc[k] an input at time k (Purchasing from Supplier C)
  • xd[k] an input at time k (Purchasing from Supplier D)
  • y[k] the output at time k (Profit)
• Difference Equation (make-up parameter):
  y[k] = y[k-1] + C[k]*Sold[k] - 500*xa[k-5] - 600*xb[k-3] - 400*xc[k-7] - 550*xd[k-4]
• Modified Difference Equation (eliminate nonlinearlity):
  y[k] = y[k-1] + CSold[k] - 500*xa[k-5] - 600*xb[k-3] - 400*xc[k-7] - 550*xd[k-4]

First Homework

• MATLAB file: hw1.m
• example input: graph
• simulated output: graph
• Ouput with Noise
  • Noise Amplitude: 10% of the maximum value of the output
  • Noise Characteristic: uniform random noise
  • simulated output + noise: graph
• ARX Method Result
  • Ideal input:
    y[k] = y[k-1] + CSold[k] - 500*xa[k-5] - 600*xb[k-3] - 400*xc[k-7] - 550*xd[k-4]
  • Ideal input + Noise:
    y[k] = 0.7850*y[k-1] + 0.3307*CSold[k] + 1107*xa[k-5] + 3425*xb[k-3] + 969.4*xc[k-7] + 2558*xd[k-4]
• RARX Method Result
  • Ideal input:
    y[k] = y[k-1] + CSold[k] - 500*xa[k-5] - 600*xb[k-3] - 400*xc[k-7] - 550*xd[k-4]
  • Ideal input + Noise:
    y[k] = 0.6200*y[k-1] + 8.8454*CSold[k] + 8197*xa[k-5] + 7381*xb[k-3] - 9119*xc[k-7] - 5871*xd[k-4]
• Comparision of the Quality of Parameters (2 Feb. 1996)
  • MATLAB file: hw1_e.m
  • Simulated output, graph, from ideal input with
    • the original parameter (yellow)
    • the parameter from ARX method when there is noise (red)
    • the parameter from RARX method when there is noise (green)