POTENTIAL SOURCES OF WASTE IN CONSTRUCTION PRODUCTION AND THE POTENTIAL OF BIM IN WASTE MINIMIZATION By MATHANBALAJI SABHAPATHI POTENTIAL SOURCES OF WASTE IN CONSTRUCTION: INTRODUCTION: Construction industry is the important source of waste production in the world almost in all the countries. The construction process currently generates significant quantities of waste: about a fifth of all waste and up to 40% of all solid waste is attributable to the construction sector. As much as 10% to 30%
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Fall 2014 Problem Set 1 Joon Hee Choi Handed In: 09/14/2014 Review Questions 1. 2. 3. • ∂f ∂x = 6x − y − 11‚ ∂f ∂y • ∂f ∂x = 6x − y − 11 = 0‚ = 2y − x ∂f ∂y = 2y − x = 0 ⇒ x = 2‚ y = 1 ⇒ (x‚ y) = (2‚ 1) • (a) n = 2 w1 x1 and x = . Then‚ w2 x2 wT x + b = w1 x1 + w2 x2 + b = 0 ⇒ −x1b + Let w = w1 x2 − wb =1 2 (b) n = 3 w1 x1 Let w = w2 and x = x2 . Then‚ w3 x3 T w x + b = w1 x1 + w2 x2 + w3 x3 + b = 0 ⇒ −x1b + −x2b + −x3b = 1 w1 w2 w3 x1 w1 x2 w2
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5. INTRODUCTION TO LINEAR PROGRAMMING (LP) Learning Objectives 1. Obtain an overview of the kinds of problems linear programming has been used to solve. 2. Learn how to develop linear programming models for simple problems. 3. Be able to identify the special features of a model that make it a linear programming model. 4. Learn how to solve two variable linear programming models by the graphical solution procedure. 5. Understand the importance of extreme points in
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5/12/08 12:01 PM Page 115 9 C H A P T E R Linear Programming: The Simplex Method TEACHING SUGGESTIONS Teaching Suggestion 9.1: Meaning of Slack Variables. Slack variables have an important physical interpretation and represent a valuable commodity‚ such as unused labor‚ machine time‚ money‚ space‚ and so forth. Teaching Suggestion 9.2: Initial Solutions to LP Problems. Explain that all initial solutions begin with X1 ϭ 0‚ X2 ϭ 0 (that is‚ the real variables set to zero)‚ and
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Chapter 4 Problem 4-1: Work through the simplex method (in algebraic form) step by step to solve the following problem. Maximize Z = x1 + 2x2 + 2x3‚ subject to 5x1 + 2x2 + 3x3 ≤ 15 x1 + 4x2 + 2x3 ≤ 12 2x1 + x3 ≤ 8 and x1 ≥ 0‚ x2 ≥ 0‚ x3 ≥ 0. Solution for Problem 4-1: We introduce x4‚ x5‚ and x6 as slack variables for the respective functional constraints. The augmented form of the problem then is Maximize Z = x1 + 2 x2 + 2 x3‚ subject to 5 x1 + 2 x2
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TR 3923 Programming Design in Solving Biology Problems Semester 1‚ 2011/2012 Elankovan Sundararajan School of Information Technology Faculty of Information Science and Technology TR 3923 Elankovan Sundararajan 1 Lecture 3 System of Linear Equations TR 3923 Elankovan Sundararajan 2 Introduction • Solving sets of linear equations is the most frequently used numerical procedure when real-world situations are modeled. modeled Linear equations are the basis for mathematical models
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Appendix 1.1 Chapter A1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Chapter A2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Consumer Theory 2.1 Preferences and Utility . . . . . . 2.2 The Consumer’s Problem . . . . . 2.3 Indirect Utility and Expenditure . 2.4 Properties of Consumer Demand 2.5 Equilibrium and Welfare . . . . . 3 Producer Theory 3.1 Production . . . . . 3.2 Cost . . . . . . . . . 3.3 Duality in production 3.4 The competitive firm 2 2 6
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interpretation of production rates. At other times‚ however‚ fractional solutions are not realistic‚ and we must consider the optimization problem: n Maximize j=1 cjxj‚ subject to: n j=1 ai j x j = bi xj ≥ 0 x j integer (i = 1‚ 2‚ . . . ‚ m)‚ ( j = 1‚ 2‚ . . . ‚ n)‚ (for some or all j = 1‚ 2‚ . . . ‚ n). This problem is called the (linear) integer-programming problem. It is said to be a mixed integer program when some‚ but not all‚ variables are restricted to be integer‚ and is
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Introduction “Constraint programming represents one of the closest approaches computer science has yet made to the holy grail of programming : the user states the problem‚ the computer solves it.” Eugene C. Freuder‚ Constraints‚ April 1997 CS 820 3 7.1 Introduction Constraint satisfaction problems (CSPs) Standard search problem: state is a “black box”—any old data structure that supports goal test‚ eval‚ successor CSP: state is defined by variables Vi with values from domain Di goal
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2.1 The 0-1 Knapsack Problem (KP) The Knapsack Problem is a combinatorial optimization problem‚ which search out a best solution from among many other feasible solutions. It is concerned with a fixed size knapsack that has positive integer capacity (or volume) V. There are n numbers of distinct items that may potentially be placed in the knapsack. Item i has a positive integer capacity(volume) Vi and integer benefit Bi. In addition‚ there are Qi quantity of item i available‚ where quantity Qi is
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