El Paso Manufacturing Co
Total Page：16
File Type：pdf, Size：1020Kb
El Paso Manufacturing Co. (EPMC)
Let: z number of assemblies to make
x1 number of frames to manufacture x2 number of shafts to manufacture
Objective: Maximize z
LP: Max z [number of assemblies] s.t. z x1 [frame required for each assembly] z x2 [shaft required for each assembly]
0.8x1 0.5x2 48000 [forging machine hours]
0.1x1 7200 [drilling machine hours]
0.3x1 14400 [milling machine hours]
0.5x1 0.3x2 24000 [grinding machine hours]
0.2x2 12000 [lathe machine hours] z, x1, x2 0 [nonnegativity] bubba - EPMC PROBLEM DATA IN EQUATION STYLE Maximize 1 Z Subject to FRAME REQD 1 Z - 1 X1 <= 0 SHAFT REQD 1 Z - 1 X2 <= 0 FORGING 0.8 Z + 0.5 X1 <= 48000 DRILLING 0.1 Z <= 7200 MILLING 0.3 Z <= 14400 GRINDING 0.5 Z + 0.3 X1 <= 24000 LATHE 0.2 Z <= 12000 0 <= Z 0 <= X1 0 <= X2 bubba - EPMC OPTIMAL SOLUTION - DETAILED REPORT Variable Value Cost Red. cost Status
1 Z 30000.0000 1.0000 0.0000 Basic 2 X1 30000.0000 0.0000 0.0000 Basic 3 X2 30000.0000 0.0000 0.0000 Basic
Slack Variables 4 FRAME REQD 0.0000 0.0000 -0.3750 Lower bound 5 SHAFT REQD 0.0000 0.0000 0.0000 Lower bound 6 FORGING 9000.0000 0.0000 0.0000 Basic 7 DRILLING 4200.0000 0.0000 0.0000 Basic 8 MILLING 5400.0000 0.0000 0.0000 Basic 9 GRINDING 0.0000 0.0000 -1.2500 Lower bound 10 LATHE 6000.0000 0.0000 0.0000 Basic
Objective Function Value = 30000 bubba - EPMC OPTIMAL SOLUTION - DETAILED REPORT Constraint Type RHS Slack Shadow price
1 FRAME REQD <= 0.0000 0.0000 0.3750 2 SHAFT REQD <= 0.0000 0.0000 0.0000 3 FORGING <= 48000.0000 9000.0000 0.0000 4 DRILLING <= 7200.0000 4200.0000 0.0000 5 MILLING <= 14400.0000 5400.0000 0.0000 6 GRINDING <= 24000.0000 0.0000 1.2500 7 LATHE <= 12000.0000 6000.0000 0.0000
Objective Function Value = 30000
Grinding Machine constraint is tight (slack = 0; shadow price = 1.25). EPMC should first consider increasing the number of grinding machines. Alternative Formulation
Let: x number of frames to manufacture 1 x2 number of shafts to manufacture
Objective: Maximize x1 (or x2 )
LP:
Max x1 [number of assemblies ( number of frames)] s.t. x1 x2 [1 frame & 1 shaft required for each assembly]
0.8x1 0.5x2 48000 [forging machine hours]
0.1x1 7200 [drilling machine hours]
0.3x1 14400 [milling machine hours]
0.5x1 0.3x2 24000 [grinding machine hours]
0.2x2 12000 [lathe machine hours] x1, x2 0 [nonnegativity] bubba - EPMC PROBLEM DATA IN EQUATION STYLE Maximize 1 X1 Subject to FR EQ SHFT 1 X1 - 1 X2 = 0 FORGING 0.8 X1 + 0.5 X2 <= 48000 DRILLING 0.1 X1 <= 7200 MILLING 0.3 X1 <= 14400 GRINDING 0.5 X1 + 0.3 X2 <= 24000 LATHE 0.2 X2 <= 12000 0 <= X1 0 <= X2 bubba - EPMC OPTIMAL SOLUTION - DETAILED REPORT Variable Value Cost Red. cost Status
1 X1 30000.0000 1.0000 0.0000 Basic 2 X2 30000.0000 0.0000 0.0000 Basic
Slack Variables 4 FORGING 9000.0000 0.0000 0.0000 Basic 5 DRILLING 4200.0000 0.0000 0.0000 Basic 6 MILLING 5400.0000 0.0000 0.0000 Basic 7 GRINDING 0.0000 0.0000 -1.2500 Lower bound 8 LATHE 6000.0000 0.0000 0.0000 Basic
Objective Function Value = 30000 bubba - EPMC OPTIMAL SOLUTION - DETAILED REPORT Constraint Type RHS Slack Shadow price
1 FR EQ SHFT = 0.0000 0.0000 0.3750 2 FORGING <= 48000.0000 9000.0000 0.0000 3 DRILLING <= 7200.0000 4200.0000 0.0000 4 MILLING <= 14400.0000 5400.0000 0.0000 5 GRINDING <= 24000.0000 0.0000 1.2500 6 LATHE <= 12000.0000 6000.0000 0.0000
Objective Function Value = 30000
Grinding Machine constraint is tight (slack = 0; shadow price = 1.25). EPMC should first consider increasing the number of grinding machines.