Linear Programming Using Excel
Subject: Linear Programming using Excel Application: Microsoft Excel 2007 Task: Solving a Linear Program Using Excel Tutorial Date: 25th February, 2010 by Nathan Smith

Install the Solver Add-In

1. In the Microsoft Office button, go to excel options to click Add-ins 2. In the Add-Ins box, select Solver Add-In and click Go...

Linear Programming Using Excel - 1

Install the Solver Add-In (continue)

3. In the Add-Ins available box, check the Analysis ToolPak and then OK

Linear Programming Using Excel - 2

Setting Up the Problem on the Spreadsheet

Example Min Z = 6X + 7Y s.t 2X + 6Y â‰¥ 10 5X + 3Y â‰¥ 10 X,Y â‰¥ 0

Linear Programming Using Excel - 3

(continued)

1. Enter the coefficients of the objective function Z i.e., (6, 7) in cells E5 and F5. 2. Enter the coefficients of the Constraint-1 i.e., (2,6) and RHS value 10 in cells E9, F9 and H9 respectively 3. Enter the coefficients of the Constraint-2 i.e., (5,3) and RHS value 10 in cells E10, F10 and H10 respectively

Linear Programming Using Excel - 4

(continued)

1. For the Objective function value, enter the formula for computing Z = SUMPRODUCT(E5:F5,E6:F6). This formula uses the coefficient values and also the solution values for variables X and Y, which are supposed to be solved. 2. Similarly enter the formula for LHS of the Constraints 1 & 2 i.e., SUMPRODUCT(E9:F9,$E$6:$F$6) & SUMPRODUCT(E10:F10,$E$6:$F$6) respectively

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Now Excel Solver will be used, in the Data tab click Solver. The solver box appears as follows.

(continued)

1. Set the Target Cell for the Objective Function Z value i.e., $E$7 2. Check the Equal to Min i.e., Minimum Option. 3. For Changing Cell, select the solution values of the variables X & 7 i.e., $E$6:$F$6 Linear Programming Using Excel - 6

4. For subject to the constraints, LHS >=RHS i.e., click on the Add option and select $E$13:$E$14 >= $E$13:$E$14 5. Also all the...

...EMP 504 Quantitative methods in Management
Name: Yi-Chun Kuo
Student id: 106357165
HW #7: LinearProgrammingApplications
Due Date: 11pm on Nov 6, 2008
Davis Instrument has two manufacturing plants located in Atlanta, Georgia. Product demand varies considerably from month to month, causing Davis extreme difficulty in workforce scheduling. Recently Davis started hiring temporary workers supplied by Workers Unlimited, a company that specializes in providing temporary employees for firms in the grater Atlanta area. Workforce Unlimited offered to provide temporary employees under three contract opinions that differ in terms of the length of employment and the cost. The three options are summarized:
|options |length of employment |cost |
|1 |one month | $ 2,000 |
|2 |two months | $ 4,800 |
|3 |three months | $ 7,500 |
The longer contract periods are more expensive because Workforce Unlimited experiences greater difficulty finding temporary workers who are willing to commit to longer work assignments.
Over the next 6 months, Davis projects the following needs for additional employees.
|Months |Jan |Feb |Mar |Apr |May |Jun |
|Employees...

...LinearProgrammingApplication
Transportation Problem
The Navy has 9,000 pounds of material in Albany, Georgia that it wishes to ship to three installations: San Diego, Norfolk, and Pensacola. They require 4,000, 2,500, and 2,500 pounds, respectively. Government regulations require equal distribution of shipping among the three carriers.
The shipping costs per pound for truck, railroad, and airplane transit are shown below. Formulate and solve a linear program to determine the shipping arrangements (mode, destination, and quantity) that will minimize the total shipping cost.
Destination
Mode San Diego Norfolk Pensacola
Truck $12 $ 6 $ 5
Railroad 20 11 9
Airplane 30 26 28
1. Define the Decision Variables
We want to determine the pounds of material, xij , to be shipped by mode i to destination j. The following table summarizes the decision variables:
San Diego Norfolk Pensacola
Truck x11 x12 x13
Railroad x21 x22 x23
Airplane x31 x32 x33
2. Define the Objective Function...

...The development of linearprogramming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linearprogramming uses a mathematical model to describe the problem of concern. Linearprogramming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives.
LinearProgramming as seen by various reports by many companies has saved them thousands to even millions of dollars. Since this is true why isn’t everyone usingLinearProgramming? Maybe the reason is because there has never been an in-depth experiment focusing on certain companies that do or do not use linearprogramming. My main argument is that linearprogramming is one of the most optimal ways of resource allocation and making the most money for any company today.
I used (in conjunction with another field supporter – My Dad) the survey method to ask 28 companies that were in Delaware, New Jersey, and Pennsylvania whether they were linearprogramming users. In addition, I wanted to examine...

...RESEARCH PAPER ON
LINEARPROGRAMMING
Vikas Vasam
ID: 100-11-5919
Faculty: Prof. Dr Goran Trajkovski
CMP 561: Algorithm Analysis
VIRGINIA INTERNATIONAL UNIVERSITY
Introduction:
One of the section of mathematical programming is linearprogramming.
Methods and linearprogramming models are widely used in the optimization of processes in all sectors of the economy: the development of the production program of the company, its distribution on the performers, when placing orders between the performers and the time intervals, to determine the best range of products, in problems of perspective, current and operational planning and management, traffic planning, defining a plan of trade and distribution, in the problems of development and distribution of productive forces, bases and depots of material handling systems, resources, etc. especially widely used methods and linearprogramming model for solving problems are savings (choice of resource-saving technologies, preparation of mixes, nesting materials), production, transportation and other tasks.
Beginning of linearprogramming was initiated in 1939 by the Soviet mathematician and economist Kantorovich in his paper "Mathematical methods of organizing and planning production." The appearance of...

...TOPIC – LINEARPROGRAMMINGLinearProgramming is a mathematical procedure for determining optimal allocation of scarce resources.
Requirements of LinearProgramming
• all problems seek to maximize or minimize some quantity
• The presence of restrictions or constraints
• There must be alternative courses of action
• The objective and constraints inlinearprogramming must be expressed in terms of linear equations or
inequalities
Objective Function it maps and translates the input domain (the feasible region) into output range, with
the two-end values called the maximum and minimum values
Restriction Constraints it limits the degree to which we can pursue our objective
Decision Variables represents choices available to the decision maker in terms of amount of either inputs or outputs
Parameters these are the fixed values in which the model is solved
Basic Assumption of LinearProgramming
1. Certainty- figures or number in the objective and constraints are known with certainty and do not vary
1. Proportionality - for example 1:2 is equivalent to 5:10
1. Additivity - the total of all the activities equals the sum of the individual...

... LINEARPROGRAMMING
DATE;
5 JUNE, 14
UNIVERSITY OF CENTRAL PUNJAB
INTRODUCTION TO LINEARPROGRAMMINGLinearprogramming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linearprogramming is a special case of mathematical programming.
It is a mathematical technique used in computer modeling to find the best possible solution in allocating limited resources (energy, materials, machines, money etc) to achieve maximum profit or minimum cost.
LinearProgramming is a method of expressing and optimizing a business problem with a mathematical model. It is one of the most powerful and widespread business optimization tools.
Linearprogramming can be used in very large variety of business problems. They include:
transportation distribution problems
production scheduling in oil & gas, manufacturing, chemical, etc industries
financial and tax planning
human resource planning
facility planning
fleet scheduling.
LINEARPROGRAMMING; an optimization technique capable of solving an amazingly...

...LINEARPROGRAMMING
INTRODUCTION:
The term ‛programming′ means planning and it refers to a particular plan of action amongst several alternatives for maximizing profit or minimizing cost etc. Programming problems deal with determining optimal allocation of limited resources to meet the given objectives, such as cost, maximum profit, highest margin or least time, when resources have alternative uses.
The term ‛linear’ means that all inequations or equations used and the function to be maximized or minimized are linear. That is why linearprogramming deals with that class of problems for which all relations among the variables involved are linear.
Formally, linearprogramming deals with the optimization (maximization or minimization) of a linear function of a number of variables subject to a ¹equations in variables involved.
The general form of a linearprogramming problem is
Optimize (Maximize or Minimize) Z = c1x1 + c2x2 + ……..+ cnxn
Subject to
a11 x1 + a12x2 + ….. + a1n xn (≤ , = , ≥) b1
a21 x1+ a22x2+ ….. + a2nxn (≤ , = , ≥ ) b2
. . . .
am1 x1+ am2 x2 +...

...Term Paper
On
LinearProgrammingApplications
Submitted to : Md. Abul Kashem
Associate Professor
Department of Management Information System
Dhaka University
Submitted by : Md. Forhad hossain
ID NO: 61221-14-029
Semester: 1st , Batch : 14th
Department of management information system
Dhaka University
Date of Submission: 02/05/2012
INDEX
1. Hospital scheduling ………………………………………page-3
2. Marketing Research…………………………………… page-7
3. Blending Problem……………………………………….page-11
4. Production Scheduling………………………………….page 13
5. Product Mix………………………………………….....page 15
6. Agriculture………………………………………………page 18
7.Auditing………………………………………………….page 24
8. Assignment problem…………………………………..page 26
9. Labour Planning……………………………………….page28
10. Media selection problem……………………………..page 31
Hospital scheduling
Modern general hospital is concerned with the staffing of its emergency department. A recent analysis indicated that a typical day may be divided into four periods. In each period, a different level measured “cases ” is experienced.
|Time period |Average number of cases |
|7 A.M.- 1 P.M |120...