This book is a general presentation of complex systems, examined from the point of view of management. There is no standard formula to govern such systems, nor to effectively understand and respond to them.
The interdisciplinary theory of self-organization is teeming with examples of living systems that can reorganize at a higher level of complexity when confronted with an external challenge of a certain magnitude. Modern businesses, considered as complex systems, ideally know how to flexibly and resiliently adapt to their environment, and also how to prepare for change via self-organization. Understanding sources of potential crisis is essential for leaders, though not all crises are necessarily bad news, as creative firms know how to respond to challenges through innovation: new products and markets, organizational learning for collective intelligence, and more.
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Yes, you can access Optimizations and Programming by Abdelkhalak El Hami,Bouchaib Radi in PDF and/or ePUB format, as well as other popular books in Technology & Engineering & Mechanical Engineering. We have over one million books available in our catalogue for you to explore.
Linear programming can be defined as a mathematical technique for solving management problems. For example, suppose that a manager faced with various options wishes to determine the optimal way to use the resources of a company to achieve a specific objective, such as maximizing the utility or minimizing the cost. The company’s problems can usually be modeled as a linear program (LP) consisting of a certain number of resources [HIL 90]. For instance, the labor, raw materials and capital are all resources available in limited quantities that must be distributed optimally over various manufacturing processes. The approach to solving this type of problem is divided into two key steps:
– model the problem with linear equations or inequalities that allow us to properly identify and structure the constraints satisfied by the variables of the model. The contribution of each variable to the company’s overarching objective must also be defined as a function that will be optimized;
– find the mathematical optimum using specific linear programming techniques. We will study three methods for solving the various types of linear programming problems. The first is based on graphical solving and is therefore limited to two or three variables. The second method is more algebraic; it motivates the third method presented in this chapter, which is known as the simplex method (or algorithm).
1.2. Definitions
DEFINITION 1.1.– An LP is in canonical form if it is expressed as follows:
[1.1]
An LP is in standard form if it is expressed as follows:
Every linear problem can be expressed in canonical form: min cTx = – max cTx.
THEOREM 1.1.– Every LP in standard form can be expressed in canonical form and vice versa.
