# DSA Lecture 4 1 2 Essay

Submitted By choiyiuhin
Words: 1050
Pages: 5

Lecture 4- Outline
1. (0-1) IP problem: an example
2. LP solution using the DecisionPro software 3. IP solution using DecisionPro
4. (0-1) IP solution using DecisionPro
5. Assignment Problem solution using
DecisionPro

(0-1) IP Problem: An
Recreation facilities selection to maximize daily usage
Example
by residents.

Resource constraints: £120,000 budget; 12 acres of land. Selection constraint: either swimming pool or tennis center (not both).
Data:
Recreation
Facility
Swimming pool
Tennis Center
Athletic field
Gymnasium

Expected Usage
(people/day)

Cost (\$)

Land
Requirement
(acres)

300
90
400
150

35,000
10,000
25,000
90,000

4
2
7
3

2

The (0-1) Integer Formulation
For The Example x1 = construction of a swimming pool x2 = construction of a tennis center x3 = construction of an athletic field x4 = construction of a gymnasium
Maximize Z = 300x1 + 90x2 + 400x3 + 150x subject to:
£35,000x1 + 10,000x2 + 25,000x3 + 90,000x4  £120,000
4x1 + 2x2 + 7x3 + 3x3  12 acres x1 + x2  1 facility x1, x2, x3, x4 = 0 or 1
3

DecisionPro General
Features

• DecisionPro is a powerful application for decision-support modelling and analysis; • DecisionPro will help you make business decisions;
• DecisionPro combines basic quantitative methods in management;
• DecisionPro has analytic capabilities for business models.
4

DecisionPro’s capabilities
• General modelling and problem solving -for tackling complex problems; • Communicating with your ideas;
• Optimisation - for allocating; resources using linear programming;
• Sensitivity Analysis - for determining which parameters drive your decisions most.
5

How an LP model can be built • By using inaDecisionPro? hierarchical tree layout;
• The hierarchical layout allows you to work with meaningful node names;
• It automatically constructs a diagram that matches the logical structure of your model;
• This is a key benefit that makes it easier for you to tackle complex, unstructured problems.
6

DecisionPro's hierarchical layout • based on the divide and conquer concept;
• to solve a complex problem you simply divide it into two or more simpler components; • To solve these component problems, you apply the same process again, breaking them down into still finer elements;
• The result is a DecisionPro hierarchical tree.

7

An LP problem example to be transferred into
DecisionPro (1)
Department

Time to process on
Product A
(hrs)

Time to process on
Product B
(hrs)

Capacity
(hrs/week)

Machining

6

6

120

Assembly

8

4

120

8

An example of LP problem to be transferred into
DecisionPro (2)

Decision variables are:
XA= the number of product A made per week
XB= the number of product B made per week
Objective Function Coefficients:
Profit contribution of product A = £ 30
Profit contribution of product A = £ 35 9

An example of LP problem to be transferred into
DecisionPro (3)
Objective function: Max 30 XA + 35XB subject to constraints :
6 XA + 6 XB  120
8 XA + 4 XB  120
XA , X B  0 10

The LP problem built in
DecisionPro

11

The LP problem to be solved by
DecisionPro

12

The solution of DecisionPro for the LP problem

13

DecisionPro's tree
• not only provides a great way to solve structure business problems, it also provides a

great way to present your analysis to others; • With DecisionPro, your models are inherently outlined;
• The root node represents the solution you seek and each branch provides increasingly more detailed information about how that solution is derived;
• This feature makes it easy for someone who is unfamiliar with your model to understand its function quickly.
14

Integer Programming Solution
Using DecisionPro Software

 Primitive functions in DecisionPro such as simplex() can accept integer variables;
 Just type simplex([Objective function,
Constraints],” Decision variables”, the number of integer variables);
 Objective function and Constraints must be placed within the bracket,
 Integer variables can be