What is the Triple Constraint?
The triple constraint of project management is the balance of the project’s scope, time and cost. Triple constraint is used to determine whether or not a project’s objectives are being met. During the planning phase of a project, a project manager will define the scope, time, and cost of a project. As the planning phase continues, the project manager discovers that there may be some changes or adjustments needed in the project’s scope, time and/or cost. When one aspect needs change or adjustment, then it directly affects one of the other factors of the triple constraint. For example, if the cost increases, it is logical to assume that the scope and time will increase as well. Or, if the cost decreases, one can assume that the scope and time will decrease. This rings true for scope and time as well. A project manager must be thorough and detailed in planning the scope, time and cost of a project in order to maintain the constraint or be prepared to fluctuate with it. Adjustments can be made during the project for various reasons to include changes made by the client as well. It is the project manager’s responsibility to be aware of the changes and how they will affect all aspects of the triple constraint and be prepared to modify each aspect accordingly.
Scope
The scope of the project is what is actually included in the project as well as what is to be excluded. A project’s size, how complex it is and its importance all affect how much effort goes into scope planning. Defining the scope of a project is important in determining the success of the project. A detailed scope overview and statement is the basis for project decisions. It helps those involved understand exactly what the outcome of the project will look like and what is to be expected. Let’s say we have a client who wants to launch an inspirational Tshirt company. This client wants to produce,...
...THEORY OF CONSTRAINTS
The Theory of Constraints (TOC) is a management philosophy where three financial
measures of profit, return on investment (ROI) and cash flow are presented. All three of
these measurements are necessary. First, we need an absolute measurement of profit, the
amount by which revenues exceed expenses. Second, we need the relative measurement of
ROI that compares the amount of money made relative to the amount invested. Finally, we
must have enough cash coming in to meet expenses, which is a measure of survival. In order
to reach the goal, these three measures should all be positive and increasing.
Profit Inventory: the money invested in purchasing things it plans to sell
Operating Expense: the money the system spends to turn Inventory into Throughput
Throughput (T) is the volume of sales in dollars less the totally variable costs of production,
such as the cost of raw materials, subcontracting, and purchasing costs, such as
transportation and duties. Investment (formerly Inventory) (I) includes the money invested in
equipment, buildings and machine oil. Operating Expense (OE) includes the cost of indirect
and direct labor.
The financial measures are calculated as follows:
Net profit = T  OE
Return on Investment = Net Profit/I
Cash flow = Net profit – (Change in I in terms of actual cash outflows and inflows)
The goal is achieved by maximizing “T”, while simultaneously minimizing “I” and “OE.” The first...
...
Keyless Entry Fob: Theory of Constraints
OPS/GM 571
Memorandum to: Director of Manufacturing
From: Operations Management, ext. 5555
Subject: Control Chip Constraints
Date: September 17, 2013
This memo is to inform you of an emerging constraint in the keyless entry fob project. The operations department was informed by the Chinese supplier of control chips that a strike has halted all transportation out of China. Expected end date to the union strike is unknown, which will create a shortage for the customers across all channels. In the following, operations management will propose a solution using Goldratt’s Theory of Constraints. Additionally, the operations team will also highlight possible impact to the inventory, scheduling, control, and budget.
Goldratt’s Theory of Constraints
Goldratt’s Theory of Constraints propose five steps of continuous improvement, identification of the constraint, deciding how to exploit the constraint, total application or resources to resolve the constraint, continuing to identify and resolve new constraints (Chase, Jacobs, & Aquilano, 2005).
In identifying the constraint, the operations team has evaluated that the apparent problem of the supplier situation is not the actual constraint but the actual constraint is synchronous...
...JIT versus the Theory of Constraints 
AMB303 International Logistics

Theory of Constraints 
Name : Hui LuStudent Number: N8035636Date: 02/09/2012Word Count:1007 
Contents
1.0 Definition……………………………..…………………….3
2.0 Discussion…………………………………………...……..3
2.1Core concept…………………………………..….3
2.2Five Steps of TOC………………………………..4
2.3 Evaluation………………………………………..4
2.3.1 Advantages…………………………...4
2.3.2 Disadvantages……………………...…4
2.4. Example……………………..…………………..5
3.0 Conclusion 6
4.0 Reference 7
1.0 Introduction
TOC is a management philosophy introduced by Dr. Eliyahu M. Goldratt in his 1984 book The Goal, which is geared to help organizations continually achieve their goal. Based upon the contention that any manageable system is limited in achieving more of its goal by a small number of constraints (that there is always at least one). The TOC process seeks to identify the constraint and restructure the rest of the organization around it, through the use of the Five Focusing Steps.
2.0 Discussion
2.1Core concept
The basic premise of TOC as applied to business is that improving any process is best done not by trying to maximize efficiency in every part of the process, but by focusing on the slowest part of the process, called the constraint. For instance, during the early days of the American Civil War, several units calling themselves legions were formed, consisting of...
...Product Mix Example
The Outdoor Furniture Corporation manufactures two products: benches and picnic tables for use in yards and parks. The firm has two main resources: its carpenters (labor) and a supply of redwood for use in the furniture. During the next production period, 1200 hours of manpower are available under a union agreement. The firm also has a stock of 5000 pounds of quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 pounds of redwood; each picnic table takes 7 labor hours and 35 pounds of redwood. Completed benches yield a profit of $9 each, and tables a profit of $20 each. We formulated the following linear program to solve this problem: Decision Variables:
Objective Function:
Constraints:
We will now solve this LP using the Excel Solver.
1.1
Getting Started
To begin using Excel, doubleclick on the Excel icon. Once Excel has loaded, enter the input data and construct relationships among data elements in a readable, easy to understand way. When building this foundation for your model, think ahead about the optimization model you will be developing. Make sure there is a cell in your spreadsheet for each of the following: • the quantity you wish to maximize or minimize • every decision variable • every quantity that you might want to constrain If you don’t have any particular initial values you want to enter for your decision variables, you can start by just entering a value of 0 in each...
...linear programming can handle.
Linear programming lets you optimize an
objective function subject to some constraints.
The objective function and constraints are all
linear.
Two feed grains are available, X and Y.
A bag of X has 2 units of A, 1 unit of B, and 1 unit of C.
A bag of Y has 1 unit of A, 1 unit of B, and 3 units of C.
A bag of X costs $2. A bag of Y costs $4.
Minimize the cost of meeting the nutrient requirements.
To solve, express the problem in equation form:
Cost = 2X + 4Y
objective function to be minimized
Constraints:
2X + 1Y $ 14 nutrient A requirement
1X + 1Y $ 12 nutrient B requirement
1X + 3Y $ 18 nutrient C requirement
8
8
Read vertically to see how much of each nutrient is in each grain.
X $ 0, Y $ 0
nonnegativity
Learning objective 2: Know the elements of a linear programming problem  what you need to
calculate a solution.
The elements are
(1) an objective function that shows the cost or profit depending on what choices you make,
(2) constraint inequalities that show the limits of what you can do, and
(3) nonnegativity restrictions, because you cannot turn outputs back into inputs.
LINEAR PROGRAMMING II
2
Graph method of solution
Graph the constraints as equalities, like before. The constraints are now $ rather than #, so the feasible
area is everything to the right and above all of the constraint...
...Pythagorean Triples
Ashley Walker
MAT126
Bridget Simmons
November 28, 2011
A Pythagorean triple is a triple of positive integers a, b, and c such that a right triangle exists with legs a, b, and hypotenuse c (Bluman, 2005). A Pythagorean triple is a triple of positive integers (a, b, c) where a2 + b2 = c2. A triple is simply a right triangle whose sides are positive integers. An easy way to generate Pythagorean triples is to multiply any known Pythagorean triple by an integer (any integer) (Vargas, 2008).
In project #4, pg. 522, (Mathematics in Our World) introduced some new information to add to my mathematics knowledge of numbers. The numbers 3, 4, and 5 are called Pythagorean triples since 32 + 42 = 52. The numbers 5, 12, and 13 are also Pythagorean triples since 52 + 122 = 132. Can you find any other Pythagorean triples? Actually, there is a set of formulas that will generate an infinite number of Pythagorean triples and write a brief report on the subject (Bluman, 2005).
When asked to find any other Pythagorean triples, I found 5, choosing 2 integers, m and n, with m less than n (Manuel, 2010). Three formulas I choose to form the Pythagorean triple, which can be calculated from:
n2 – m2
2mn
n2 + m2 (Manuel, 2010).
Project 4, pg.522
1) m=3, n=4
n2–...
...Pythagorean Triples
Tammie Strohl
MAT 126
David Gualco
November 9, 2009
Pythagorean Triples
Pythagorean Theorem states that the sum of the areas of the two squares formed along the two small sides of a right angled triangle equals the area of the square formed along the longest.
￼
If a, b, and c are positive integers, they are together called Pythagorean Triples.
The smallest such Pythagorean Triple is 3, 4 and 5. It can be seen that 32 + 42 = 52 (9+16=25).
Here are some examples:
￼￼￼
Endless
The set of Pythagorean Triples is endless.
It is easy to prove this with the help of the first Pythagorean triple, (3, 4, and 5):
Let n be any integer greater than 1: 3n, 4n and 5n would also be a set of Pythagorean triple. This is true because:
(3n)2 + (4n)2 = (5n)2
￼￼￼
￼
So, you can make infinite triples just using the (3,4,5) triple.
Euclid's Proof that there are Infinitely Many Pythagorean Triples
However, Euclid used a different reasoning to prove the set of Pythagorean triples is unending.
The proof was based on the fact that the difference of the squares of any two consecutive numbers is always an odd number.
For example, 22  12 = 41 = 3, 152  142 = 225196 = 29.
And also every odd number can be expressed as a difference of the squares of two consecutive numbers. Have a look at this table...
...What is the Theory of Constraints?
The Theory of Constraints is an organizational change method that is focused
on profit improvement. The essential concept of TOC is that every organization must have at least one constraint. A constraint is any factor that limits the organization from getting more of whatever it strives for, which is usually profit. The Goal focuses on constraints as bottleneck processes in a jobshop manufacturing organization. However, many nonmanufacturing constraints exist, such as market demand, or a sales department's ability to translate market demand into orders.
The Theory of Constraints defines a set of tools that change agents can use to manage constraints, thereby increasing profits. Most businesses can be viewed as a linked set of processes that transform inputs into saleable outputs. TOC conceptually models this system as a chain, and advocates the familiar adage that a "chain is only as strong as its weakest link." Goldratt defines a fivestep process that a change agent can use to strengthen the weakest link, or links. In The Goal, Goldratt proves that most organizations have very few true constraints. Since the focus only needs to be on the constraints, implementing TOC can result in substantial improvement without tying up a great deal of resources, with results after three months of effort....