In this presentation we
illustrate the ideas developed
in the previous presentation
with two more problems
Consider the following LPP:
Maximize z = 6 x1 + x2 + 2 x3
Subject to
1
2 x1 +2 x2 + x3 2
2
3
x1 2 x2 x3 3
4
2
1
x1 +2 x2 + x3 1
2
x1 , x2 , x3 0
Le
Algebraic Solution of LPPs - Simplex
Method
To solve an LPP algebraically, we first put it
in the standard form. This means all
decision variables are nonnegative and all
constraints (other than the nonnegativity
restrictions) are equations with nonnegati
Table of Contents
CD Chapter 19 (Inventory Management with Uncertain Demand)
A Case Study for Perishable ProductsFreddie the Newsboy (Section 19.1)
An Inventory Model for Perishable Products (Sec.19.2)
A Case Study for Stable ProductsNiko Camera Corp. (Se
Table of Contents
CD Chapter 18 (Inventory Management with Known Demand)
A Case StudyThe Atlantic Coast Tire Corp. (ACT) Problem (Section 18.1)
18.218.4
Cost Components of Inventory Models (Sec.18.2)
18.518.6
The Basic Economic Order Quantity (EOQ) Model
Table of Contents
CD Chapter 16 (PERT/CPM Models for Project Management)
A Case Study: The Reliable Construction Co. Project (Section 16.1)
Using a Network to Visually Display a Project (Section 16.2)
Scheduling a Project with PERT/CPM (Section 16.3)
Deal
Table of Contents
CD Chapter 15 (Transportation and Assignment Problems)
The P&T Company Distribution Problem (Section 15.1)
Characteristics of Transportation Problems (Section 15.2)
Variants of Transportation Problems: Better Products (Section 15.3)
Vari
Table of Contents
CD Chapter 14 (Solution Concepts for Linear Programming)
Some Key Facts About Optimal Solutions (Section 14.1)
14.214.16
The Role of Corner Points in Searching for an Optimal Solution (Sec.14.2)
14.1714.21
Solution Concepts for the Simpl
Table of Contents
Chapter 13 (Computer Simulation with Crystal Ball)
A Case Study: Freddie the Newsboys Problem (Section 13.1)
Bidding for a Construction Project (Section 13.2)
Project Management: Reliable Construction Co. (Section 13.3)
Cash Flow Managem
Generating Random Observations
from a Probability Distribution
The method for generating random observations from a continuous distribution
is called the inverse transformation method.
Notation
r is the random number
F(x) is the cumulative distribution fu
Table of Contents
Chapter 12 (Computer Simulation: Basic Concepts)
The Essence of Computer Simulation (Section 12.1)
Example 1: A Coin-Flipping Game (Section 12.1)
Example 2: Heavy Duty Company (Section 12.1)
A Case Study: Herr Cutters Barber Shop (Sectio
Table of Contents
Chapter 11 (Queueing Models)
Elements of a Queueing Model (Section 11.1)
Some Examples of Queueing Systems (Section 11.2)
Measures of Performance for Queueing Systems (Section 11.3)
A Case Study: The Dupit Corp. Problem (Section 11.4)
So
Table of Contents
Chapter 10 (Forecasting)
An Overview of Forecasting Techniques (Section 10.1)
A Case Study: The Computer Club Warehouse Problem (Section 10.2)
Applying Time-Series Forecasting to the Case Study (Section 10.3)
The Time-Series Forecasting
Table of Contents
Chapter 9 (Decision Analysis)
Decision Analysis Examples
A Case Study: The Goferbroke Company Problem (Section 9.1)
Decision Criteria (Section 9.2)
Decision Trees (Section 9.3)
Sensitivity Analysis with Decision Trees (Section 9.4)
Check
Table of Contents
Chapter 7 (Using Binary Integer Programming)
A Case Study: California Manufacturing (Section 7.1)
Using BIP for Project Selection: Tazer Corp. (Section 7.2)
Using BIP for the Selection of Sites: Caliente City (Section 7.3)
Using BIP for
Minimum Spanning Trees:
The Modern Corp. Problem
Modern Corporation has decided to have a state-of-the-art fiber-optic network
installed to provide high-speed communication (data, voice, and video)
between its major centers.
Any pair of centers do not nee
Table of Contents
Chapter 6 (Network Optimization Problems)
Minimum-Cost Flow Problems (Section 6.1)
A Case Study: The BMZ Maximum Flow Problem (Section 6.2)
Maximum Flow Problems (Section 6.3)
Shortest Path Problems: Littletown Fire Department (Section 6
Table of Contents
Chapter 5 (What-If Analysis for Linear Programming)
Continuing the Wyndor Case Study (Section 5.2)
Changes in One Objective Function Coefficient (Section 5.3)
Simultaneous Changes in Objective Function Coefficients (Section 5.4)
Single C
Table of Contents
Chapter 4 (The Art of Modeling with Spreadsheets)
The Everglade Golden Years Co. Cash Flow Problem (Section 4.1)
The Process of Modeling with Spreadsheets (Section 4.2)
4.24.3
4.34.11
Guidelines for Building Good Spreadsheet Models (Sect
Table of Contents
Chapter 2 (Linear Programming: Basic Concepts)
The Wyndor Glass Company Product Mix Problem (Section 2.1)
Formulating the Wyndor Problem on a Spreadsheet (Section 2.2)
The Algebraic Model for Wyndor (Section 2.3)
The Graphical Method App
Table of Contents
Chapter 1 (Introduction)
Special Products Break-Even Analysis (Section 1.2)
Advertising Problem (UW Lecture)
1.2 1.6
1.8 1.21
An illustration of the management science approach to a problem. At the University of Washington,
this is the v
Iterativecomputationsofthe Transportationalgorithm
Iterative computations of the Transportation algorithm After determining the starting BFS by any one of the three methods discussed earlier, we use the following algorithm to determine the optimum solutio
Determination of Starting Basic Feasible Solution
Determination of the starting Solution In any transportation model we determine a starting BFS and then iteratively move towards the optimal solution which has the least shipping cost. There are three
TheTransportationModel Formulations
The Transportation Model The transportation model is a special class of LPPs that deals with transporting(=shipping) a commodity from sources (e.g. factories) to destinations (e.g. warehouses). The objective is to deter
Explanation of the entries in any simplex tableau in terms of the entries of the starting tableau
In this lecture we explain how the starting Simplex tableau (in matrix form) gets transformed after `some' iterations. We also give the meaning of the entrie
MATRIX FORMULATION OF THE LPps
In this lecture we shall look at the matrix formulation of the LPPs. We see that the Basic feasible solutions are got by solving the matrix equation BX = b where B is a m m nonsingular submatrix of the contraint matrix of th