Class Notes (837,839)
MGOC10H3 (34)
Vinh Quan (14)
Lecture

# Lecture - Sept 25.doc

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Department
Management (MGO)
Course
MGOC10H3
Professor
Vinh Quan
Semester
Fall

Description
MGTC74 Analysis for Decision Making Lecture 03 Chapter 2 – Solving LP Models with LINDO Solver Suite • Can use LINGO - www.lindo.com, can download student/demo version of software. • Can also solve Linear Programs with Excel – see textbook Appendix 2.3. Some LINGO syntax • There is an “=” after the MAX or MIN in objective. Min = 6*V11+ 2*V12; • LINGO statements end with semicolon • Start program with “MODEL:” end of program with “END” • Arithmetic Operators: Power “^”, Multiply “*”, Division “/”, Addition “+”, Subtraction “-“. Order of operations applies • Limit of 32 characters in variable name, must begin with A-Z. • To enter ≤ type “<=”, to enter ≥ type “>=”. • Comments may be placed anywhere, comments are denoted by “!” and end with “;” • Only constant values, not variables, are permitted on the right hand side of a constraint equation. Conversely, only variables and their coefficients are permitted on the left-hand side of constraints. • @FREE(x1) - allows variable x1 to be unrestricted in sign. @BIN(x1) – specifies that x1 is 0 or 1 (binary) @GIN(x1) - specifies that x1 is integer Example - Giapetto’s Woodcarving LP model LINGO code x1= # soldiers produced each week x = # trains produced each week 2 MODEL: Max z = 3x 1 2x 2 ! MGTC74 LINGO example; ST 2x +11 x ≤2100 [OBJ] MAX = 3*X1 + 2*X2; 1x1+ 1x 2 80 [FINISH] 2*X1 + X2 <= 100; x1≤ 40 [CARPENTRY] X1 + X2 <= 80; x1≥ 0 and x2≥ 0 [DEMAND] X1 <= 40; END What is the optimal number of soldiers and trains to produce? Profits? LINGO Output: Global optimal solution found. Objective value: 180.0000 Total solver iterations: 2 Variable Value Reduced Cost X1 20.00000 0.000000 X2 60.00000 0.000000 Row Slack or Surplus Dual Price OBJ 180.0000 1.000000 FINISH 0.000000 1.000000 CARPENTRY 0.000000 1.000000 DEMAND 20.00000 0.000000 1 # of soldiers produced = X1 = 20, # of trains produced = X2 = 60, Profits=objective value =\$180 Chapter 3 - SensitivityAnalysis using LINGO Example – 2 product 3 machine problem A company produces two products using three machines. The profits from each product, the time each product takes to produce and the amount of time available for each machine is given in the table below. The objective is to max revenue. Machine Product 1 Product 2 Hours Available 1 1 0 4 2 0 2 12 3 3 2 18 Revenue \$3 \$5 LP model LINGO code Let Xi = # of product i to produce MODEL: Max Z = 3X 1 5X 2 [OBJ] MAX = 3*X1 + 5*X2; ST X ≤ 1 [MACH1] X1 <= 4; 2X 2 12 [MACH2] 2*X2 <= 12; 3X 1 2X ≤218 [MACH3] 3*X1 + 2*X2 <= 18; END X 1 X2≥ 0 LINGO output Global optimal solution found at step:2 Objective value: 36.00000 Variable Value Reduced Cost X1 2.000000 0.0000000 X2 6.000000 0.0000000 Row Slack or Surplus Dual Price OBJ 36.00000 1.000000 MACH1 2.000000 0.0000000 MACH2 0.0000000 1.500000 MACH3 0.0000000 1.000000 (a) What is the optimal solution (revenue? number of product 1 and 2 made?) What does the slack or surplus mean? • For machine 1, slack or surplus = 2 means there are 2 unused hours • For machine
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