# MGOC10H3 Lecture Notes - Nonlinear Programming, Integer Programming, Production Planning

24 views3 pages

MGTC74 Analysis for Decision Making

Lecture 01

Chapter 2 – LP Model Formulation & Solution

Basic components of linear programming (LP) model:

1) Define decision variables—variables that describes the decisions to be made

2) State objective function—in LP model decision maker will want to maximize (e.g., profit,

output, revenue) or minimize (cost, risk) some function of decision variables

3) Specify constraints

4) Sign restrictions or variables—in general we can have x≥0, x≤0, x unrestricted in sign

•if x1 ,x2 must be integer, then we have an integer programming problem

•if either objective function or any of the constraints is nonlinear e.g., 3x12 + 2x2 then we have

nonlinear programming problem

Example – Production Planning

1) x1 = # of soldiers to make each week

x2 = # of trains to make each week

2) objective is to maximize profits

Profit = (27x1 + 21x2) – (10x1 + 9x2+14x1 + 10x2) = 3x1 + 2x2

3) constraint 1 no more than 100 hrs finishing time used

finish time soldier + finish time trains ≤ 100hr 2x1 + 1x2 ≤100

constraint 2 no more than 80hrs carpentry time used

1x1 + 1x2 ≤80

constraint 3 at most 40 soldiers can be sold

x1 < 40

4) cannot produce negative # of soldiers/trains so x1,x2 > 0

Final LP model

Max z = 3x1 + 2x2

2x1 + 1x2 ≤100 (finishing)

1x1 + 1x2 ≤ 0 (carpentry)

x1 < 40 (soldier demand)

x1, x2 > 0

1

## Document Summary

Chapter 2 lp model formulation & solution. Example production planning: x1 = # of soldiers to make each week x2 = # of trains to make each week, objective is to maximize profits. 1x1 + 1x2 80 constraint 3 at most 40 soldiers can be sold x1 < 40: cannot produce negative # of soldiers/trains so x1,x2 > 0. 1x1 + 1x2 0 x1 < 40 x1, x2 > 0 (finishing) (carpentry) (soldier demand) For every gallon a produced at least 3 gallons of b must be produced. A, b 0 (production regular) (custom order) (processing) (production required) Z = 50000c + 100000f z = 50c + 100f. C, f > 0 (at least 28 million w) (at least 24 million m) Max z = 0. 06b + 0. 1s + 0. 02m. B 0. 3 or b 0. 3 (b + s + m)