Operational Research Method

Topics: Optimization, Microsoft, Maxima and minima Pages: 5 (1341 words) Published: August 15, 2013
Table of Conten
1. INTRODUCTION1
2. Formulate the Problem1
2.1 CHOOSE DECISION VARIABLES1
2.2 FORMULATE THE OBJECTIVE FUNCTION1
2.3 FORMULATE CONSTRAINTS2
3. SOFTWARE2
3.1 MICROSOFT OFFICE EXCEL2
3.1.1 EXCEL DATA INPUT AND SOLVE THE PROBLEM2
3.1.2 ANSWER ANALYSIS3
3.1.3 SENSITIVITY ANALYSIS4

3.2 XPRESS-IVE ANALYSIS6
4. CONCLUSION6
APPENDIX

Operational Research Methods Report

1. Introduction

Linear programming (LP) model is a significant and popular used model of operational research technique. It helps to optimize the objective value with constraints. LP model have three essential assumptions when use this model to solve problem. Firstly, proportionality and additively, which means that the objective function and the functions in constraints are all linear. In other words, it means the equation of objective and constraints are linear equation. Secondly, LP model assume that non-integer values of the decision variables are meaningful for the problem addressed, which indicate that LP model have divisibility. Finally, LP model assume that the parameters of the model are all known constants. In this report, Microsoft Office Excel and Xpress are implemented in order to solve the problem.

2. Formulate the Problem

This report focuses to solve the problem of nurse assignment for Jefferson County Regional Hospital. Formulate the problem as a linear programing model with objective function and constraints.

Table 2.1: Nurse assignment table

3.1 Choose decision variables

As table 2.1 shows, declare 12 variables, x1 x2 … x12, which represent the numbers of nurse to start work in each time period. In this case, the coefficient of each variable has to be value 1 because it represents one person rather than price or costs.

3.2 Formulate the objective function

Depends on the require of problem description, the minimize total number of nurses can be written as (‘Z’ stands for objective value):
Minimize Z = x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12

3.3 Formulate constraints

There are 12 constraints in this case because of the minimum requirement nurse number during 12 time periods. For instance, all nurse start to work at time period 10, 11, 12 and 1 are work between 0:00 to 2:00. Thus, as the table 2.1 shows, the constraints can be written as:

x10+x11+x12+x1>=30
x11+x12+x1+x2 >=20
x12+x1+x2+x3 >=40
x1+x2+x3+x4 >=50
x2+x3+x4+x5 >=60
x3+x4+x5+x6 >=80
x4+x5+x6+x7 >=80
x5+x6+x7+x8 >=70
x6+x7+x8+x9 >=70
x7+x8+x9+x10 >=60
x8+x9+x10+x11 >=50
x9+x10+x11+x12 >=50

Where: x1>=0, x2>=0, x3>=0, x4>=0, x5>=0, x6>=0, x7>=0, x8>=0, x9>=0, x10>=0, x11>=0, x12>=0

3. Software
There are two computer software were implemented to solve the problem above that is Microsoft Office Excel and Xpress-IVE
4.4 Microsoft Office Excel

Microsoft Office Excel is a spreadsheet application, developed by Microsoft for Windows and Mac OS X operating system, to help user to calculate, graphing data. Excel Solver is one of the powerful add in tool found in Microsoft Excel. It is mainly used to determine the extreme value (maximum and minimum value) and optimization of a specific problem, which is determined by users. There are three main components, which is target cells, adjustable cells and constraint cells, are involved when use Excel Solve.

4.5.1 Excel Data Input and solve the problem
Table 3.1 shows each component and data used to solve the nurse assignment problem. Row 1 shows the variables that have been determined when formulate the problem. Row 2 is the target value of each variable that indicate the number of nurse are required to start work at those time period. Cols ‘O’ (obj value and LHS value) are the targets cells. Cell ‘O4’ indicate the objective value of minimum total nurse required in a day. Cells ‘O7’ to ‘O18’ represent targets cells of number...
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