Lecture 20110128

Lecture 20110128 - IMSE2008 Operational Research Techniques...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
IMSE2008 Operational Research Techniques Lecture 01/28 LP Formulation eometry of Linear Programs Geometry of Linear Programs Miao Song Dept of Industrial & Manufacturing Systems Engineering
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
eview of Lecture 01/21 Review of Lecture 01/21 What is Linear Programming? ormulation of LP Formulation of LP Decision variables Objective function Constraints A production problem scheduling problem (to be continued) A scheduling problem (to be continued) 1/28/2011 2
Background image of page 2
cheduling Postal Workers Scheduling Postal Workers Each postal worker works for 5 consecutive days, followed by 2 days off, repeated weekly. Day Mon Tue Wed Thu Fri Sat Sun Demand 17 13 15 19 14 16 11 Minimize the number of postal workers (for the time being, we will permit fractional workers on each day.) 1/28/2011 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
P for the Scheduling Problem LP for the Scheduling Problem 2 34 56 7 min xx x x x x x  12 14 7 s.t. 17 x x x 7 2 36 7 13 15 x x x x x x 7 19 x x x 5 3 45 6 14 16 x x x x  23 7 11 x 1/28/2011 4 0 for 1 to 7 j x j
Background image of page 4
ome Modifications of the Model Some Modifications of the Model Suppose that we need to ensure that at least 30% of the workers have Sunday off. 1/28/2011 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
genda Agenda Formulation of Linear Programming Piecewise Linear Objective Functions j Piecewise Linear Constraints Geometry of Linear Programming 1/28/2011 6
Background image of page 6
Motivating Example A Motivating Example Suppose that the desirable number of workers on day j is d j , but it is not required. et e the “excess” number of workers day Let s j be the excess number of workers day j . s j > 0 if there are more workers on day j than d ; otherwise s 0 . j j What is the minimum cost schedule, where the “cost” of having too many workers on day j is f j ( s j ) , which is a non-linear function? What are the new decision variables? What is the resulting nonlinear model? 1/28/2011 7
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
n Nonlinear Functions On Nonlinear Functions Occasionally a nonlinear program can be transformed into a linear program Rare, but useful when it occurs In general, non-linear programming solvers can work well on a minimization problem when the objective function is onvex convex 1/28/2011 8
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 12/09/2011 for the course IMSE 0301 taught by Professor Song during the Spring '11 term at HKU.

Page1 / 35

Lecture 20110128 - IMSE2008 Operational Research Techniques...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online